# Abstract groups downloaded from the LMFDB on 23 August 2026.
# Search link: https://www.lmfdb.org/Groups/Abstract/
# Query "{'order': {'$gte': 65, '$lte': 127}}" returned 682 groups, sorted by order.

# Each entry in the following data list has the form:
#    [Label, Name, Order, Exponent, $\card{\mathrm{conj}(G)}$, Center, Type - length]
# For more details, see the definitions at the bottom of the file.



"65.1"	"C_{65}"	65	65	65	"65.1"	"Cyclic"
"66.1"	"S_3\\times C_{11}"	66	66	33	"11.1"	"Solvable - 2"
"66.2"	"C_3\\times D_{11}"	66	66	21	"3.1"	"Solvable - 2"
"66.3"	"D_{33}"	66	66	18	"1.1"	"Solvable - 2"
"66.4"	"C_{66}"	66	66	66	"66.4"	"Cyclic"
"67.1"	"C_{67}"	67	67	67	"67.1"	"Cyclic"
"68.1"	"C_{17}:C_4"	68	68	20	"2.1"	"Solvable - 2"
"68.2"	"C_{68}"	68	68	68	"68.2"	"Cyclic"
"68.3"	"C_{17}:C_4"	68	68	8	"1.1"	"Solvable - 2"
"68.4"	"D_{34}"	68	34	20	"2.1"	"Solvable - 2"
"68.5"	"C_2\\times C_{34}"	68	34	68	"68.5"	"Abelian - 2"
"69.1"	"C_{69}"	69	69	69	"69.1"	"Cyclic"
"70.1"	"C_7\\times D_5"	70	70	28	"7.1"	"Solvable - 2"
"70.2"	"C_5\\times D_7"	70	70	25	"5.1"	"Solvable - 2"
"70.3"	"D_{35}"	70	70	19	"1.1"	"Solvable - 2"
"70.4"	"C_{70}"	70	70	70	"70.4"	"Cyclic"
"71.1"	"C_{71}"	71	71	71	"71.1"	"Cyclic"
"72.1"	"C_9:C_8"	72	72	24	"4.1"	"Solvable - 2"
"72.2"	"C_{72}"	72	72	72	"72.2"	"Cyclic"
"72.3"	"Q_8:C_9"	72	36	21	"6.2"	"Solvable - 3"
"72.4"	"C_9:Q_8"	72	36	21	"2.1"	"Solvable - 2"
"72.5"	"C_4\\times D_9"	72	36	24	"4.1"	"Solvable - 2"
"72.6"	"D_{36}"	72	36	21	"2.1"	"Solvable - 2"
"72.7"	"C_{18}:C_4"	72	36	24	"4.2"	"Solvable - 2"
"72.8"	"C_9:D_4"	72	36	21	"2.1"	"Solvable - 2"
"72.9"	"C_2\\times C_{36}"	72	36	72	"72.9"	"Abelian - 2"
"72.10"	"D_4\\times C_9"	72	36	45	"18.2"	"Nilpotent - 2"
"72.11"	"Q_8\\times C_9"	72	36	45	"18.2"	"Nilpotent - 2"
"72.12"	"C_3:C_{24}"	72	24	36	"12.2"	"Solvable - 2"
"72.13"	"C_3^2:C_8"	72	24	24	"4.1"	"Solvable - 2"
"72.14"	"C_3\\times C_{24}"	72	24	72	"72.14"	"Abelian - 2"
"72.15"	"C_2^2:D_9"	72	36	9	"1.1"	"Solvable - 3"
"72.16"	"C_2^2:C_{18}"	72	18	24	"6.2"	"Solvable - 2"
"72.17"	"C_2\\times D_{18}"	72	18	24	"4.2"	"Solvable - 2"
"72.18"	"C_2^2\\times C_{18}"	72	18	72	"72.18"	"Abelian - 3"
"72.19"	"C_3^2:C_8"	72	24	12	"2.1"	"Solvable - 2"
"72.20"	"C_6.D_6"	72	12	18	"2.1"	"Solvable - 2"
"72.21"	"C_6.D_6"	72	12	18	"2.1"	"Solvable - 2"
"72.22"	"D_6:S_3"	72	12	15	"2.1"	"Solvable - 2"
"72.23"	"C_3:D_{12}"	72	12	15	"2.1"	"Solvable - 2"
"72.24"	"C_3^2:Q_8"	72	12	15	"2.1"	"Solvable - 2"
"72.25"	"C_3\\times \\SL(2,3)"	72	12	21	"6.2"	"Solvable - 3"
"72.26"	"C_3^2:Q_8"	72	12	27	"6.2"	"Solvable - 2"
"72.27"	"S_3\\times C_{12}"	72	12	36	"12.2"	"Solvable - 2"
"72.28"	"C_3\\times D_{12}"	72	12	27	"6.2"	"Solvable - 2"
"72.29"	"C_6:C_{12}"	72	12	36	"12.5"	"Solvable - 2"
"72.30"	"C_6\\wr C_2"	72	12	27	"6.2"	"Solvable - 2"
"72.31"	"C_3^2:Q_8"	72	12	21	"2.1"	"Solvable - 2"
"72.32"	"C_{12}:S_3"	72	12	24	"4.1"	"Solvable - 2"
"72.33"	"C_3:D_{12}"	72	12	21	"2.1"	"Solvable - 2"
"72.34"	"C_6.D_6"	72	12	24	"4.2"	"Solvable - 2"
"72.35"	"C_6^2:C_2"	72	12	21	"2.1"	"Solvable - 2"
"72.36"	"C_6\\times C_{12}"	72	12	72	"72.36"	"Abelian - 2"
"72.37"	"D_4\\times C_3^2"	72	12	45	"18.5"	"Nilpotent - 2"
"72.38"	"Q_8\\times C_3^2"	72	12	45	"18.5"	"Nilpotent - 2"
"72.39"	"F_9"	72	24	9	"1.1"	"Solvable - 2"
"72.40"	"\\SOPlus(4,2)"	72	12	9	"1.1"	"Solvable - 3"
"72.41"	"\\PSU(3,2)"	72	12	6	"1.1"	"Solvable - 3"
"72.42"	"C_3\\times S_4"	72	12	15	"3.1"	"Solvable - 3"
"72.43"	"C_3:S_4"	72	12	9	"1.1"	"Solvable - 3"
"72.44"	"S_3\\times A_4"	72	6	12	"1.1"	"Solvable - 2"
"72.45"	"C_2\\times C_3^2:C_4"	72	12	12	"2.1"	"Solvable - 2"
"72.46"	"S_3\\times D_6"	72	6	18	"2.1"	"Solvable - 2"
"72.47"	"C_6\\times A_4"	72	6	24	"6.2"	"Solvable - 2"
"72.48"	"C_6\\times D_6"	72	6	36	"12.5"	"Solvable - 2"
"72.49"	"C_6:D_6"	72	6	24	"4.2"	"Solvable - 2"
"72.50"	"C_2\\times C_6^2"	72	6	72	"72.50"	"Abelian - 3"
"73.1"	"C_{73}"	73	73	73	"73.1"	"Cyclic"
"74.1"	"D_{37}"	74	74	20	"1.1"	"Solvable - 2"
"74.2"	"C_{74}"	74	74	74	"74.2"	"Cyclic"
"75.1"	"C_{75}"	75	75	75	"75.1"	"Cyclic"
"75.2"	"C_5^2:C_3"	75	15	11	"1.1"	"Solvable - 2"
"75.3"	"C_5\\times C_{15}"	75	15	75	"75.3"	"Abelian - 2"
"76.1"	"C_{19}:C_4"	76	76	22	"2.1"	"Solvable - 2"
"76.2"	"C_{76}"	76	76	76	"76.2"	"Cyclic"
"76.3"	"D_{38}"	76	38	22	"2.1"	"Solvable - 2"
"76.4"	"C_2\\times C_{38}"	76	38	76	"76.4"	"Abelian - 2"
"77.1"	"C_{77}"	77	77	77	"77.1"	"Cyclic"
"78.1"	"C_{13}:C_6"	78	78	8	"1.1"	"Solvable - 2"
"78.2"	"C_{13}:C_6"	78	78	14	"2.1"	"Solvable - 2"
"78.3"	"S_3\\times C_{13}"	78	78	39	"13.1"	"Solvable - 2"
"78.4"	"C_3\\times D_{13}"	78	78	24	"3.1"	"Solvable - 2"
"78.5"	"D_{39}"	78	78	21	"1.1"	"Solvable - 2"
"78.6"	"C_{78}"	78	78	78	"78.6"	"Cyclic"
"79.1"	"C_{79}"	79	79	79	"79.1"	"Cyclic"
"80.1"	"C_5:C_{16}"	80	80	32	"8.1"	"Solvable - 2"
"80.2"	"C_{80}"	80	80	80	"80.2"	"Cyclic"
"80.3"	"C_5:C_{16}"	80	80	20	"4.1"	"Solvable - 2"
"80.4"	"C_8\\times D_5"	80	40	32	"8.1"	"Solvable - 2"
"80.5"	"C_{40}:C_2"	80	40	26	"4.1"	"Solvable - 2"
"80.6"	"C_{40}:C_2"	80	40	23	"2.1"	"Solvable - 2"
"80.7"	"D_{40}"	80	40	23	"2.1"	"Solvable - 2"
"80.8"	"C_5:Q_{16}"	80	40	23	"2.1"	"Solvable - 2"
"80.9"	"C_{10}:C_8"	80	40	32	"8.2"	"Solvable - 2"
"80.10"	"C_5:\\OD_{16}"	80	40	26	"4.1"	"Solvable - 2"
"80.11"	"C_{20}:C_4"	80	20	32	"8.2"	"Solvable - 2"
"80.12"	"C_{10}.D_4"	80	20	26	"4.2"	"Solvable - 2"
"80.13"	"C_{20}:C_4"	80	20	26	"4.2"	"Solvable - 2"
"80.14"	"D_{10}:C_4"	80	20	26	"4.2"	"Solvable - 2"
"80.15"	"C_5:D_8"	80	40	17	"2.1"	"Solvable - 2"
"80.16"	"C_5:\\SD_{16}"	80	40	17	"2.1"	"Solvable - 2"
"80.17"	"Q_8:D_5"	80	40	17	"2.1"	"Solvable - 2"
"80.18"	"C_5:Q_{16}"	80	40	17	"2.1"	"Solvable - 2"
"80.19"	"C_{10}.D_4"	80	20	26	"4.2"	"Solvable - 2"
"80.20"	"C_4\\times C_{20}"	80	20	80	"80.20"	"Abelian - 2"
"80.21"	"C_2^2:C_{20}"	80	20	50	"20.5"	"Nilpotent - 2"
"80.22"	"C_4:C_{20}"	80	20	50	"20.5"	"Nilpotent - 2"
"80.23"	"C_2\\times C_{40}"	80	40	80	"80.23"	"Abelian - 2"
"80.24"	"C_5\\times \\OD_{16}"	80	40	50	"20.2"	"Nilpotent - 2"
"80.25"	"C_5\\times D_8"	80	40	35	"10.2"	"Nilpotent - 3"
"80.26"	"C_5\\times \\SD_{16}"	80	40	35	"10.2"	"Nilpotent - 3"
"80.27"	"C_5\\times Q_{16}"	80	40	35	"10.2"	"Nilpotent - 3"
"80.28"	"D_5:C_8"	80	40	20	"4.1"	"Solvable - 2"
"80.29"	"C_5:\\OD_{16}"	80	40	14	"2.1"	"Solvable - 2"
"80.30"	"C_4\\times F_5"	80	20	20	"4.1"	"Solvable - 2"
"80.31"	"C_{20}:C_4"	80	20	14	"2.1"	"Solvable - 2"
"80.32"	"C_{10}:C_8"	80	40	20	"4.2"	"Solvable - 2"
"80.33"	"C_5:\\OD_{16}"	80	40	14	"2.1"	"Solvable - 2"
"80.34"	"D_{10}:C_4"	80	20	14	"2.1"	"Solvable - 2"
"80.35"	"C_{10}:Q_8"	80	20	26	"4.2"	"Solvable - 2"
"80.36"	"C_4\\times D_{10}"	80	20	32	"8.2"	"Solvable - 2"
"80.37"	"C_2\\times D_{20}"	80	20	26	"4.2"	"Solvable - 2"
"80.38"	"D_{20}:C_2"	80	20	26	"4.1"	"Solvable - 2"
"80.39"	"D_4\\times D_5"	80	20	20	"2.1"	"Solvable - 2"
"80.40"	"D_4:D_5"	80	20	20	"2.1"	"Solvable - 2"
"80.41"	"Q_8\\times D_5"	80	20	20	"2.1"	"Solvable - 2"
"80.42"	"D_{20}:C_2"	80	20	20	"2.1"	"Solvable - 2"
"80.43"	"C_2^2.D_{10}"	80	20	32	"8.5"	"Solvable - 2"
"80.44"	"C_{10}:D_4"	80	20	26	"4.2"	"Solvable - 2"
"80.45"	"C_2^2\\times C_{20}"	80	20	80	"80.45"	"Abelian - 3"
"80.46"	"D_4\\times C_{10}"	80	20	50	"20.5"	"Nilpotent - 2"
"80.47"	"Q_8\\times C_{10}"	80	20	50	"20.5"	"Nilpotent - 2"
"80.48"	"D_4:C_{10}"	80	20	50	"20.2"	"Nilpotent - 2"
"80.49"	"C_2^4:C_5"	80	10	8	"1.1"	"Solvable - 2"
"80.50"	"C_2^2\\times F_5"	80	20	20	"4.2"	"Solvable - 2"
"80.51"	"C_2^2\\times D_{10}"	80	10	32	"8.5"	"Solvable - 2"
"80.52"	"C_2^3\\times C_{10}"	80	10	80	"80.52"	"Abelian - 4"
"81.1"	"C_{81}"	81	81	81	"81.1"	"Cyclic"
"81.2"	"C_9^2"	81	9	81	"81.2"	"Abelian - 2"
"81.3"	"C_3^2:C_9"	81	9	33	"9.2"	"Nilpotent - 2"
"81.4"	"C_9:C_9"	81	9	33	"9.2"	"Nilpotent - 2"
"81.5"	"C_3\\times C_{27}"	81	27	81	"81.5"	"Abelian - 2"
"81.6"	"C_{27}:C_3"	81	27	33	"9.1"	"Nilpotent - 2"
"81.7"	"C_3\\wr C_3"	81	9	17	"3.1"	"Nilpotent - 3"
"81.8"	"C_3.\\He_3"	81	9	17	"3.1"	"Nilpotent - 3"
"81.9"	"\\He_3:C_3"	81	9	17	"3.1"	"Nilpotent - 3"
"81.10"	"C_3.\\He_3"	81	9	17	"3.1"	"Nilpotent - 3"
"81.11"	"C_3^2\\times C_9"	81	9	81	"81.11"	"Abelian - 3"
"81.12"	"C_3\\times \\He_3"	81	3	33	"9.2"	"Nilpotent - 2"
"81.13"	"C_9:C_3^2"	81	9	33	"9.2"	"Nilpotent - 2"
"81.14"	"C_9.C_3^2"	81	9	33	"9.1"	"Nilpotent - 2"
"81.15"	"C_3^4"	81	3	81	"81.15"	"Abelian - 4"
"82.1"	"D_{41}"	82	82	22	"1.1"	"Solvable - 2"
"82.2"	"C_{82}"	82	82	82	"82.2"	"Cyclic"
"83.1"	"C_{83}"	83	83	83	"83.1"	"Cyclic"
"84.1"	"C_7:C_{12}"	84	84	14	"2.1"	"Solvable - 2"
"84.2"	"C_7:C_{12}"	84	84	20	"4.1"	"Solvable - 2"
"84.3"	"C_3:C_{28}"	84	84	42	"14.2"	"Solvable - 2"
"84.4"	"C_7:C_{12}"	84	84	30	"6.2"	"Solvable - 2"
"84.5"	"C_{21}:C_4"	84	84	24	"2.1"	"Solvable - 2"
"84.6"	"C_{84}"	84	84	84	"84.6"	"Cyclic"
"84.7"	"C_2\\times F_7"	84	42	14	"2.1"	"Solvable - 2"
"84.8"	"S_3\\times D_7"	84	42	15	"1.1"	"Solvable - 2"
"84.9"	"C_{14}:C_6"	84	42	20	"4.2"	"Solvable - 2"
"84.10"	"C_7\\times A_4"	84	42	28	"7.1"	"Solvable - 2"
"84.11"	"C_7:A_4"	84	42	12	"1.1"	"Solvable - 2"
"84.12"	"C_3\\times D_{14}"	84	42	30	"6.2"	"Solvable - 2"
"84.13"	"S_3\\times C_{14}"	84	42	42	"14.2"	"Solvable - 2"
"84.14"	"D_{42}"	84	42	24	"2.1"	"Solvable - 2"
"84.15"	"C_2\\times C_{42}"	84	42	84	"84.15"	"Abelian - 2"
"85.1"	"C_{85}"	85	85	85	"85.1"	"Cyclic"
"86.1"	"D_{43}"	86	86	23	"1.1"	"Solvable - 2"
"86.2"	"C_{86}"	86	86	86	"86.2"	"Cyclic"
"87.1"	"C_{87}"	87	87	87	"87.1"	"Cyclic"
"88.1"	"C_{11}:C_8"	88	88	28	"4.1"	"Solvable - 2"
"88.2"	"C_{88}"	88	88	88	"88.2"	"Cyclic"
"88.3"	"C_{11}:Q_8"	88	44	25	"2.1"	"Solvable - 2"
"88.4"	"C_4\\times D_{11}"	88	44	28	"4.1"	"Solvable - 2"
"88.5"	"D_{44}"	88	44	25	"2.1"	"Solvable - 2"
"88.6"	"C_{22}:C_4"	88	44	28	"4.2"	"Solvable - 2"
"88.7"	"C_{11}:D_4"	88	44	25	"2.1"	"Solvable - 2"
"88.8"	"C_2\\times C_{44}"	88	44	88	"88.8"	"Abelian - 2"
"88.9"	"D_4\\times C_{11}"	88	44	55	"22.2"	"Nilpotent - 2"
"88.10"	"Q_8\\times C_{11}"	88	44	55	"22.2"	"Nilpotent - 2"
"88.11"	"C_2\\times D_{22}"	88	22	28	"4.2"	"Solvable - 2"
"88.12"	"C_2^2\\times C_{22}"	88	22	88	"88.12"	"Abelian - 3"
"89.1"	"C_{89}"	89	89	89	"89.1"	"Cyclic"
"90.1"	"C_5\\times D_9"	90	90	30	"5.1"	"Solvable - 2"
"90.2"	"C_9\\times D_5"	90	90	36	"9.1"	"Solvable - 2"
"90.3"	"D_{45}"	90	90	24	"1.1"	"Solvable - 2"
"90.4"	"C_{90}"	90	90	90	"90.4"	"Cyclic"
"90.5"	"C_3^2\\times D_5"	90	30	36	"9.2"	"Solvable - 2"
"90.6"	"S_3\\times C_{15}"	90	30	45	"15.1"	"Solvable - 2"
"90.7"	"C_3\\times D_{15}"	90	30	27	"3.1"	"Solvable - 2"
"90.8"	"C_{15}:S_3"	90	30	30	"5.1"	"Solvable - 2"
"90.9"	"C_3:D_{15}"	90	30	24	"1.1"	"Solvable - 2"
"90.10"	"C_3\\times C_{30}"	90	30	90	"90.10"	"Abelian - 2"
"91.1"	"C_{91}"	91	91	91	"91.1"	"Cyclic"
"92.1"	"C_{23}:C_4"	92	92	26	"2.1"	"Solvable - 2"
"92.2"	"C_{92}"	92	92	92	"92.2"	"Cyclic"
"92.3"	"D_{46}"	92	46	26	"2.1"	"Solvable - 2"
"92.4"	"C_2\\times C_{46}"	92	46	92	"92.4"	"Abelian - 2"
"93.1"	"C_{31}:C_3"	93	93	13	"1.1"	"Solvable - 2"
"93.2"	"C_{93}"	93	93	93	"93.2"	"Cyclic"
"94.1"	"D_{47}"	94	94	25	"1.1"	"Solvable - 2"
"94.2"	"C_{94}"	94	94	94	"94.2"	"Cyclic"
"95.1"	"C_{95}"	95	95	95	"95.1"	"Cyclic"
"96.1"	"C_3:C_{32}"	96	96	48	"16.1"	"Solvable - 2"
"96.2"	"C_{96}"	96	96	96	"96.2"	"Cyclic"
"96.3"	"C_2^3.A_4"	96	12	12	"2.1"	"Solvable - 3"
"96.4"	"S_3\\times C_{16}"	96	48	48	"16.1"	"Solvable - 2"
"96.5"	"C_{48}:C_2"	96	48	36	"8.1"	"Solvable - 2"
"96.6"	"D_{48}"	96	48	27	"2.1"	"Solvable - 2"
"96.7"	"C_{48}:C_2"	96	48	27	"2.1"	"Solvable - 2"
"96.8"	"C_3:Q_{32}"	96	48	27	"2.1"	"Solvable - 2"
"96.9"	"C_{12}:C_8"	96	24	48	"16.2"	"Solvable - 2"
"96.10"	"C_6.C_4^2"	96	24	36	"8.2"	"Solvable - 2"
"96.11"	"C_{12}:C_8"	96	24	36	"8.2"	"Solvable - 2"
"96.12"	"D_{12}:C_4"	96	24	30	"4.1"	"Solvable - 2"
"96.13"	"C_2^2.D_{12}"	96	12	21	"2.1"	"Solvable - 2"
"96.14"	"C_6.D_8"	96	24	24	"4.2"	"Solvable - 2"
"96.15"	"C_{12}.Q_8"	96	24	24	"4.2"	"Solvable - 2"
"96.16"	"D_{12}:C_4"	96	24	24	"4.2"	"Solvable - 2"
"96.17"	"C_4.D_{12}"	96	24	24	"4.2"	"Solvable - 2"
"96.18"	"C_6:C_{16}"	96	48	48	"16.5"	"Solvable - 2"
"96.19"	"C_3:\\OD_{32}"	96	48	36	"8.1"	"Solvable - 2"
"96.20"	"C_{24}:C_4"	96	24	48	"16.5"	"Solvable - 2"
"96.21"	"C_{12}.D_4"	96	24	36	"8.2"	"Solvable - 2"
"96.22"	"C_{24}:C_4"	96	24	36	"8.2"	"Solvable - 2"
"96.23"	"C_6.Q_{16}"	96	24	30	"4.2"	"Solvable - 2"
"96.24"	"C_{24}:C_4"	96	24	30	"4.2"	"Solvable - 2"
"96.25"	"C_{24}:C_4"	96	24	30	"4.2"	"Solvable - 2"
"96.26"	"C_{24}.C_4"	96	24	30	"4.1"	"Solvable - 2"
"96.27"	"D_6:C_8"	96	24	36	"8.2"	"Solvable - 2"
"96.28"	"D_{12}:C_4"	96	24	30	"4.2"	"Solvable - 2"
"96.29"	"C_{12}.D_4"	96	24	24	"4.1"	"Solvable - 2"
"96.30"	"C_4.D_{12}"	96	24	21	"2.1"	"Solvable - 2"
"96.31"	"C_4.D_{12}"	96	24	21	"2.1"	"Solvable - 2"
"96.32"	"D_{12}:C_4"	96	24	24	"4.1"	"Solvable - 2"
"96.33"	"C_3:D_{16}"	96	48	18	"2.1"	"Solvable - 2"
"96.34"	"C_3:\\SD_{32}"	96	48	18	"2.1"	"Solvable - 2"
"96.35"	"Q_{16}:S_3"	96	48	18	"2.1"	"Solvable - 2"
"96.36"	"C_3:Q_{32}"	96	48	18	"2.1"	"Solvable - 2"
"96.37"	"C_{12}.D_4"	96	24	36	"8.2"	"Solvable - 2"
"96.38"	"C_6.C_4^2"	96	12	36	"8.5"	"Solvable - 2"
"96.39"	"C_6.D_8"	96	24	24	"4.2"	"Solvable - 2"
"96.40"	"C_{12}.D_4"	96	24	21	"2.1"	"Solvable - 2"
"96.41"	"C_2^3.D_6"	96	12	21	"2.1"	"Solvable - 2"
"96.42"	"C_6.Q_{16}"	96	24	24	"4.2"	"Solvable - 2"
"96.43"	"C_{12}.D_4"	96	24	21	"2.1"	"Solvable - 2"
"96.44"	"C_{12}.D_4"	96	24	24	"4.1"	"Solvable - 2"
"96.45"	"C_6.C_4^2"	96	12	60	"24.15"	"Nilpotent - 2"
"96.46"	"C_4\\times C_{24}"	96	24	96	"96.46"	"Abelian - 2"
"96.47"	"C_8:C_{12}"	96	24	60	"24.9"	"Nilpotent - 2"
"96.48"	"C_2^2:C_{24}"	96	24	60	"24.9"	"Nilpotent - 2"
"96.49"	"C_2^3:C_{12}"	96	12	33	"6.2"	"Nilpotent - 3"
"96.50"	"\\OD_{16}:C_6"	96	24	33	"6.2"	"Nilpotent - 3"
"96.51"	"C_{12}.D_4"	96	24	33	"6.2"	"Nilpotent - 3"
"96.52"	"D_4:C_{12}"	96	24	42	"12.5"	"Nilpotent - 3"
"96.53"	"Q_8:C_{12}"	96	24	42	"12.5"	"Nilpotent - 3"
"96.54"	"D_4:C_{12}"	96	24	42	"12.2"	"Nilpotent - 3"
"96.55"	"C_4:C_{24}"	96	24	60	"24.9"	"Nilpotent - 2"
"96.56"	"C_8:C_{12}"	96	24	42	"12.5"	"Nilpotent - 3"
"96.57"	"C_8:C_{12}"	96	24	42	"12.5"	"Nilpotent - 3"
"96.58"	"C_8.C_{12}"	96	24	42	"12.2"	"Nilpotent - 3"
"96.59"	"C_2\\times C_{48}"	96	48	96	"96.59"	"Abelian - 2"
"96.60"	"C_3\\times \\OD_{32}"	96	48	60	"24.2"	"Nilpotent - 2"
"96.61"	"C_3\\times D_{16}"	96	48	33	"6.2"	"Nilpotent - 4"
"96.62"	"C_3\\times \\SD_{32}"	96	48	33	"6.2"	"Nilpotent - 4"
"96.63"	"C_3\\times Q_{32}"	96	48	33	"6.2"	"Nilpotent - 4"
"96.64"	"C_4^2:S_3"	96	24	10	"1.1"	"Solvable - 3"
"96.65"	"A_4:C_8"	96	24	20	"4.1"	"Solvable - 3"
"96.66"	"\\SL(2,3):C_4"	96	24	16	"4.2"	"Solvable - 4"
"96.67"	"\\Unitary(2,3)"	96	24	16	"4.1"	"Solvable - 4"
"96.68"	"C_4^2:C_6"	96	12	16	"2.1"	"Solvable - 2"
"96.69"	"C_4\\times \\SL(2,3)"	96	12	28	"8.2"	"Solvable - 3"
"96.70"	"C_2^3:A_4"	96	12	10	"1.1"	"Solvable - 2"
"96.71"	"C_4^2:C_6"	96	12	10	"1.1"	"Solvable - 2"
"96.72"	"C_4^2:C_6"	96	12	10	"1.1"	"Solvable - 2"
"96.73"	"C_8\\times A_4"	96	24	32	"8.1"	"Solvable - 2"
"96.74"	"C_8.A_4"	96	24	28	"8.1"	"Solvable - 3"
"96.75"	"C_{12}:Q_8"	96	12	36	"8.2"	"Solvable - 2"
"96.76"	"C_{12}:Q_8"	96	12	30	"4.2"	"Solvable - 2"
"96.77"	"C_{12}.Q_8"	96	12	30	"4.2"	"Solvable - 2"
"96.78"	"S_3\\times C_4^2"	96	12	48	"16.2"	"Solvable - 2"
"96.79"	"C_4^2:S_3"	96	12	36	"8.2"	"Solvable - 2"
"96.80"	"C_4\\times D_{12}"	96	12	36	"8.2"	"Solvable - 2"
"96.81"	"C_4:D_{12}"	96	12	30	"4.2"	"Solvable - 2"
"96.82"	"C_4^2:S_3"	96	12	30	"4.2"	"Solvable - 2"
"96.83"	"C_4^2:S_3"	96	12	30	"4.2"	"Solvable - 2"
"96.84"	"C_2^3.D_6"	96	12	30	"4.2"	"Solvable - 2"
"96.85"	"C_2^3.D_6"	96	12	24	"4.2"	"Solvable - 2"
"96.86"	"C_2^3.D_6"	96	12	24	"4.2"	"Solvable - 2"
"96.87"	"D_6.D_4"	96	12	30	"4.2"	"Solvable - 2"
"96.88"	"C_2^3.D_6"	96	12	30	"4.2"	"Solvable - 2"
"96.89"	"C_2^2:D_{12}"	96	12	24	"4.2"	"Solvable - 2"
"96.90"	"D_6.D_4"	96	12	24	"4.2"	"Solvable - 2"
"96.91"	"D_6:D_4"	96	12	24	"4.2"	"Solvable - 2"
"96.92"	"C_2^3.D_6"	96	12	24	"4.2"	"Solvable - 2"
"96.93"	"C_2^2.D_{12}"	96	12	24	"4.2"	"Solvable - 2"
"96.94"	"C_3:(C_4\\times Q_8)"	96	12	30	"4.2"	"Solvable - 2"
"96.95"	"C_{12}:Q_8"	96	12	24	"4.2"	"Solvable - 2"
"96.96"	"(C_2\\times C_4).D_6"	96	12	24	"4.2"	"Solvable - 2"
"96.97"	"C_{12}.Q_8"	96	12	24	"4.2"	"Solvable - 2"
"96.98"	"D_6.D_4"	96	12	30	"4.2"	"Solvable - 2"
"96.99"	"(C_4\\times S_3):C_4"	96	12	30	"4.2"	"Solvable - 2"
"96.100"	"D_{12}:C_4"	96	12	30	"4.2"	"Solvable - 2"
"96.101"	"D_6.D_4"	96	12	24	"4.2"	"Solvable - 2"
"96.102"	"C_4:D_{12}"	96	12	24	"4.2"	"Solvable - 2"
"96.103"	"D_6:Q_8"	96	12	24	"4.2"	"Solvable - 2"
"96.104"	"D_6:Q_8"	96	12	24	"4.2"	"Solvable - 2"
"96.105"	"(C_2\\times C_4).D_6"	96	12	24	"4.2"	"Solvable - 2"
"96.106"	"C_8\\times D_6"	96	24	48	"16.5"	"Solvable - 2"
"96.107"	"C_8:D_6"	96	24	36	"8.2"	"Solvable - 2"
"96.108"	"C_8.D_6"	96	24	36	"8.1"	"Solvable - 2"
"96.109"	"C_8:D_6"	96	24	30	"4.2"	"Solvable - 2"
"96.110"	"C_2\\times D_{24}"	96	24	30	"4.2"	"Solvable - 2"
"96.111"	"D_{24}:C_2"	96	24	30	"4.1"	"Solvable - 2"
"96.112"	"C_6:Q_{16}"	96	24	30	"4.2"	"Solvable - 2"
"96.113"	"S_3\\times \\OD_{16}"	96	24	30	"4.1"	"Solvable - 2"
"96.114"	"C_8.D_6"	96	24	30	"4.1"	"Solvable - 2"
"96.115"	"C_8:D_6"	96	24	21	"2.1"	"Solvable - 2"
"96.116"	"C_4.D_{12}"	96	24	21	"2.1"	"Solvable - 2"
"96.117"	"S_3\\times D_8"	96	24	21	"2.1"	"Solvable - 2"
"96.118"	"C_8:D_6"	96	24	18	"2.1"	"Solvable - 2"
"96.119"	"D_8:S_3"	96	24	21	"2.1"	"Solvable - 2"
"96.120"	"S_3\\times \\SD_{16}"	96	24	21	"2.1"	"Solvable - 2"
"96.121"	"C_8:D_6"	96	24	18	"2.1"	"Solvable - 2"
"96.122"	"C_8.D_6"	96	24	18	"2.1"	"Solvable - 2"
"96.123"	"C_8.D_6"	96	24	21	"2.1"	"Solvable - 2"
"96.124"	"S_3\\times Q_{16}"	96	24	21	"2.1"	"Solvable - 2"
"96.125"	"Q_{16}:S_3"	96	24	18	"2.1"	"Solvable - 2"
"96.126"	"D_{24}:C_2"	96	24	21	"2.1"	"Solvable - 2"
"96.127"	"C_{12}.C_2^3"	96	24	48	"16.10"	"Solvable - 2"
"96.128"	"C_6:\\OD_{16}"	96	24	36	"8.2"	"Solvable - 2"
"96.129"	"C_6:C_4^2"	96	12	48	"16.10"	"Solvable - 2"
"96.130"	"C_2^3.D_6"	96	12	36	"8.5"	"Solvable - 2"
"96.131"	"C_{12}.D_4"	96	12	30	"4.2"	"Solvable - 2"
"96.132"	"C_2^2.D_{12}"	96	12	36	"8.5"	"Solvable - 2"
"96.133"	"C_2^3.D_6"	96	12	36	"8.2"	"Solvable - 2"
"96.134"	"C_2^2.D_{12}"	96	12	36	"8.5"	"Solvable - 2"
"96.135"	"C_{12}:D_4"	96	12	36	"8.2"	"Solvable - 2"
"96.136"	"C_2^3.D_6"	96	12	30	"4.2"	"Solvable - 2"
"96.137"	"C_{12}:D_4"	96	12	30	"4.2"	"Solvable - 2"
"96.138"	"C_6:D_8"	96	24	24	"4.2"	"Solvable - 2"
"96.139"	"D_{12}:C_2^2"	96	24	21	"2.1"	"Solvable - 2"
"96.140"	"C_6:\\SD_{16}"	96	24	24	"4.2"	"Solvable - 2"
"96.141"	"C_2^3.D_6"	96	12	30	"4.2"	"Solvable - 2"
"96.142"	"C_2^3.D_6"	96	12	24	"4.2"	"Solvable - 2"
"96.143"	"C_{12}.D_4"	96	12	24	"4.2"	"Solvable - 2"
"96.144"	"D_6:D_4"	96	12	24	"4.2"	"Solvable - 2"
"96.145"	"C_{12}:D_4"	96	12	24	"4.2"	"Solvable - 2"
"96.146"	"C_2^3.D_6"	96	12	24	"4.2"	"Solvable - 2"
"96.147"	"C_{12}:D_4"	96	12	24	"4.2"	"Solvable - 2"
"96.148"	"Q_8:D_6"	96	24	24	"4.2"	"Solvable - 2"
"96.149"	"C_{12}.D_4"	96	24	21	"2.1"	"Solvable - 2"
"96.150"	"C_6:Q_{16}"	96	24	24	"4.2"	"Solvable - 2"
"96.151"	"C_{12}.D_4"	96	12	24	"4.2"	"Solvable - 2"
"96.152"	"C_3:C_4\\times Q_8"	96	12	30	"4.2"	"Solvable - 2"
"96.153"	"D_6:Q_8"	96	12	24	"4.2"	"Solvable - 2"
"96.154"	"C_{12}.D_4"	96	12	24	"4.2"	"Solvable - 2"
"96.155"	"C_{12}.C_2^3"	96	24	30	"4.1"	"Solvable - 2"
"96.156"	"D_4:D_6"	96	24	21	"2.1"	"Solvable - 2"
"96.157"	"C_{12}.D_4"	96	24	24	"4.1"	"Solvable - 2"
"96.158"	"C_{12}.D_4"	96	24	21	"2.1"	"Solvable - 2"
"96.159"	"C_2^3.D_6"	96	12	36	"8.5"	"Solvable - 2"
"96.160"	"C_2^4:S_3"	96	12	30	"4.2"	"Solvable - 2"
"96.161"	"C_2\\times C_4\\times C_{12}"	96	12	96	"96.161"	"Abelian - 3"
"96.162"	"C_2^3:C_{12}"	96	12	60	"24.15"	"Nilpotent - 2"
"96.163"	"C_2\\times C_4:C_{12}"	96	12	60	"24.15"	"Nilpotent - 2"
"96.164"	"C_4^2:C_6"	96	12	60	"24.9"	"Nilpotent - 2"
"96.165"	"D_4\\times C_{12}"	96	12	60	"24.9"	"Nilpotent - 2"
"96.166"	"Q_8\\times C_{12}"	96	12	60	"24.9"	"Nilpotent - 2"
"96.167"	"C_2^4:C_6"	96	12	42	"12.5"	"Nilpotent - 2"
"96.168"	"C_{12}:D_4"	96	12	42	"12.5"	"Nilpotent - 2"
"96.169"	"C_{12}.D_4"	96	12	42	"12.5"	"Nilpotent - 2"
"96.170"	"(C_2^2\\times C_{12}):C_2"	96	12	42	"12.5"	"Nilpotent - 2"
"96.171"	"C_4^2:C_6"	96	12	42	"12.5"	"Nilpotent - 2"
"96.172"	"C_{12}.Q_8"	96	12	42	"12.5"	"Nilpotent - 2"
"96.173"	"C_4^2:C_6"	96	12	42	"12.5"	"Nilpotent - 2"
"96.174"	"C_{12}:D_4"	96	12	42	"12.5"	"Nilpotent - 2"
"96.175"	"C_{12}:Q_8"	96	12	42	"12.5"	"Nilpotent - 2"
"96.176"	"C_2^2\\times C_{24}"	96	24	96	"96.176"	"Abelian - 3"
"96.177"	"C_6\\times \\OD_{16}"	96	24	60	"24.9"	"Nilpotent - 2"
"96.178"	"\\OD_{16}:C_6"	96	24	60	"24.2"	"Nilpotent - 2"
"96.179"	"C_6\\times D_8"	96	24	42	"12.5"	"Nilpotent - 3"
"96.180"	"C_6\\times \\SD_{16}"	96	24	42	"12.5"	"Nilpotent - 3"
"96.181"	"C_6\\times Q_{16}"	96	24	42	"12.5"	"Nilpotent - 3"
"96.182"	"D_8:C_6"	96	24	42	"12.2"	"Nilpotent - 3"
"96.183"	"D_8:C_6"	96	24	33	"6.2"	"Nilpotent - 3"
"96.184"	"Q_{16}:C_6"	96	24	33	"6.2"	"Nilpotent - 3"
"96.185"	"A_4:Q_8"	96	12	14	"2.1"	"Solvable - 3"
"96.186"	"C_4\\times S_4"	96	12	20	"4.1"	"Solvable - 3"
"96.187"	"C_4:S_4"	96	12	14	"2.1"	"Solvable - 3"
"96.188"	"C_2^2.S_4"	96	24	16	"4.2"	"Solvable - 4"
"96.189"	"C_2\\times \\GL(2,3)"	96	24	16	"4.2"	"Solvable - 4"
"96.190"	"\\GL(2,3):C_2"	96	24	13	"2.1"	"Solvable - 4"
"96.191"	"C_4.S_4"	96	24	13	"2.1"	"Solvable - 4"
"96.192"	"\\GL(2,3):C_2"	96	24	16	"4.1"	"Solvable - 4"
"96.193"	"\\GL(2,3):C_2"	96	24	13	"2.1"	"Solvable - 4"
"96.194"	"C_2^2.S_4"	96	12	20	"4.2"	"Solvable - 3"
"96.195"	"\\GL(2,\\mathbb{Z}/4)"	96	12	14	"2.1"	"Solvable - 3"
"96.196"	"C_2^3:C_{12}"	96	12	32	"8.2"	"Solvable - 2"
"96.197"	"D_4\\times A_4"	96	12	20	"2.1"	"Solvable - 2"
"96.198"	"C_2^2\\times \\SL(2,3)"	96	12	28	"8.5"	"Solvable - 3"
"96.199"	"Q_8\\times A_4"	96	12	20	"2.1"	"Solvable - 2"
"96.200"	"\\SL(2,3):C_2^2"	96	12	28	"8.2"	"Solvable - 3"
"96.201"	"\\SL(2,3):C_2^2"	96	12	19	"2.1"	"Solvable - 3"
"96.202"	"D_4.A_4"	96	12	19	"2.1"	"Solvable - 3"
"96.203"	"Q_8:A_4"	96	12	12	"2.1"	"Solvable - 3"
"96.204"	"Q_8:A_4"	96	12	11	"2.1"	"Solvable - 3"
"96.205"	"C_6.C_2^4"	96	12	36	"8.5"	"Solvable - 2"
"96.206"	"C_{12}:C_2^3"	96	12	48	"16.10"	"Solvable - 2"
"96.207"	"C_2^2\\times D_{12}"	96	12	36	"8.5"	"Solvable - 2"
"96.208"	"D_{12}:C_2^2"	96	12	36	"8.2"	"Solvable - 2"
"96.209"	"D_4\\times D_6"	96	12	30	"4.2"	"Solvable - 2"
"96.210"	"D_4:D_6"	96	12	30	"4.2"	"Solvable - 2"
"96.211"	"D_4:D_6"	96	12	27	"2.1"	"Solvable - 2"
"96.212"	"Q_8\\times D_6"	96	12	30	"4.2"	"Solvable - 2"
"96.213"	"Q_8:D_6"	96	12	30	"4.2"	"Solvable - 2"
"96.214"	"Q_8.D_6"	96	12	27	"2.1"	"Solvable - 2"
"96.215"	"D_4:D_6"	96	12	30	"4.1"	"Solvable - 2"
"96.216"	"D_4:D_6"	96	12	27	"2.1"	"Solvable - 2"
"96.217"	"D_4.D_6"	96	12	27	"2.1"	"Solvable - 2"
"96.218"	"C_6.C_2^4"	96	12	48	"16.14"	"Solvable - 2"
"96.219"	"C_2^3:D_6"	96	12	36	"8.5"	"Solvable - 2"
"96.220"	"C_2^3\\times C_{12}"	96	12	96	"96.220"	"Abelian - 4"
"96.221"	"C_{12}:C_2^3"	96	12	60	"24.15"	"Nilpotent - 2"
"96.222"	"C_6.C_2^4"	96	12	60	"24.15"	"Nilpotent - 2"
"96.223"	"C_6.C_2^4"	96	12	60	"24.9"	"Nilpotent - 2"
"96.224"	"C_6.C_2^4"	96	12	51	"6.2"	"Nilpotent - 2"
"96.225"	"C_6.C_2^4"	96	12	51	"6.2"	"Nilpotent - 2"
"96.226"	"C_2^2\\times S_4"	96	12	20	"4.2"	"Solvable - 3"
"96.227"	"C_2^2:S_4"	96	12	10	"1.1"	"Solvable - 3"
"96.228"	"C_2^3\\times A_4"	96	6	32	"8.5"	"Solvable - 2"
"96.229"	"C_2^3:A_4"	96	6	16	"2.1"	"Solvable - 2"
"96.230"	"C_2^3\\times D_6"	96	6	48	"16.14"	"Solvable - 2"
"96.231"	"C_2^4\\times C_6"	96	6	96	"96.231"	"Abelian - 5"
"97.1"	"C_{97}"	97	97	97	"97.1"	"Cyclic"
"98.1"	"D_{49}"	98	98	26	"1.1"	"Solvable - 2"
"98.2"	"C_{98}"	98	98	98	"98.2"	"Cyclic"
"98.3"	"C_7\\times D_7"	98	14	35	"7.1"	"Solvable - 2"
"98.4"	"C_7:D_7"	98	14	26	"1.1"	"Solvable - 2"
"98.5"	"C_7\\times C_{14}"	98	14	98	"98.5"	"Abelian - 2"
"99.1"	"C_{99}"	99	99	99	"99.1"	"Cyclic"
"99.2"	"C_3\\times C_{33}"	99	33	99	"99.2"	"Abelian - 2"
"100.1"	"C_{25}:C_4"	100	100	28	"2.1"	"Solvable - 2"
"100.2"	"C_{100}"	100	100	100	"100.2"	"Cyclic"
"100.3"	"C_{25}:C_4"	100	100	10	"1.1"	"Solvable - 2"
"100.4"	"D_{50}"	100	50	28	"2.1"	"Solvable - 2"
"100.5"	"C_2\\times C_{50}"	100	50	100	"100.5"	"Abelian - 2"
"100.6"	"C_5:C_{20}"	100	20	40	"10.2"	"Solvable - 2"
"100.7"	"C_5^2:C_4"	100	20	28	"2.1"	"Solvable - 2"
"100.8"	"C_5\\times C_{20}"	100	20	100	"100.8"	"Abelian - 2"
"100.9"	"C_5\\times F_5"	100	20	25	"5.1"	"Solvable - 2"
"100.10"	"C_5:F_5"	100	20	13	"1.1"	"Solvable - 2"
"100.11"	"C_5:F_5"	100	20	10	"1.1"	"Solvable - 2"
"100.12"	"C_5:F_5"	100	20	10	"1.1"	"Solvable - 2"
"100.13"	"D_5^2"	100	10	16	"1.1"	"Solvable - 2"
"100.14"	"C_5\\times D_{10}"	100	10	40	"10.2"	"Solvable - 2"
"100.15"	"C_5:D_{10}"	100	10	28	"2.1"	"Solvable - 2"
"100.16"	"C_{10}^2"	100	10	100	"100.16"	"Abelian - 2"
"101.1"	"C_{101}"	101	101	101	"101.1"	"Cyclic"
"102.1"	"S_3\\times C_{17}"	102	102	51	"17.1"	"Solvable - 2"
"102.2"	"C_3\\times D_{17}"	102	102	30	"3.1"	"Solvable - 2"
"102.3"	"D_{51}"	102	102	27	"1.1"	"Solvable - 2"
"102.4"	"C_{102}"	102	102	102	"102.4"	"Cyclic"
"103.1"	"C_{103}"	103	103	103	"103.1"	"Cyclic"
"104.1"	"C_{13}:C_8"	104	104	32	"4.1"	"Solvable - 2"
"104.2"	"C_{104}"	104	104	104	"104.2"	"Cyclic"
"104.3"	"C_{13}:C_8"	104	104	14	"2.1"	"Solvable - 2"
"104.4"	"C_{13}:Q_8"	104	52	29	"2.1"	"Solvable - 2"
"104.5"	"C_4\\times D_{13}"	104	52	32	"4.1"	"Solvable - 2"
"104.6"	"D_{52}"	104	52	29	"2.1"	"Solvable - 2"
"104.7"	"C_{26}:C_4"	104	52	32	"4.2"	"Solvable - 2"
"104.8"	"C_{13}:D_4"	104	52	29	"2.1"	"Solvable - 2"
"104.9"	"C_2\\times C_{52}"	104	52	104	"104.9"	"Abelian - 2"
"104.10"	"D_4\\times C_{13}"	104	52	65	"26.2"	"Nilpotent - 2"
"104.11"	"Q_8\\times C_{13}"	104	52	65	"26.2"	"Nilpotent - 2"
"104.12"	"C_{26}:C_4"	104	52	14	"2.1"	"Solvable - 2"
"104.13"	"C_2\\times D_{26}"	104	26	32	"4.2"	"Solvable - 2"
"104.14"	"C_2^2\\times C_{26}"	104	26	104	"104.14"	"Abelian - 3"
"105.1"	"C_7:C_{15}"	105	105	25	"5.1"	"Solvable - 2"
"105.2"	"C_{105}"	105	105	105	"105.2"	"Cyclic"
"106.1"	"D_{53}"	106	106	28	"1.1"	"Solvable - 2"
"106.2"	"C_{106}"	106	106	106	"106.2"	"Cyclic"
"107.1"	"C_{107}"	107	107	107	"107.1"	"Cyclic"
"108.1"	"C_{27}:C_4"	108	108	30	"2.1"	"Solvable - 2"
"108.2"	"C_{108}"	108	108	108	"108.2"	"Cyclic"
"108.3"	"C_2^2:C_{27}"	108	54	36	"9.1"	"Solvable - 2"
"108.4"	"D_{54}"	108	54	30	"2.1"	"Solvable - 2"
"108.5"	"C_2\\times C_{54}"	108	54	108	"108.5"	"Abelian - 2"
"108.6"	"C_9:C_{12}"	108	36	36	"6.2"	"Solvable - 2"
"108.7"	"C_3:C_{36}"	108	36	54	"18.2"	"Solvable - 2"
"108.8"	"C_3^2:C_{12}"	108	12	20	"2.1"	"Solvable - 2"
"108.9"	"C_9:C_{12}"	108	36	20	"2.1"	"Solvable - 2"
"108.10"	"C_6.D_9"	108	36	30	"2.1"	"Solvable - 2"
"108.11"	"\\He_3:C_4"	108	12	20	"6.2"	"Solvable - 3"
"108.12"	"C_3\\times C_{36}"	108	36	108	"108.12"	"Abelian - 2"
"108.13"	"C_4\\times \\He_3"	108	12	44	"12.2"	"Nilpotent - 2"
"108.14"	"C_9:C_{12}"	108	36	44	"12.2"	"Nilpotent - 2"
"108.15"	"\\He_3:C_4"	108	12	14	"3.1"	"Solvable - 3"
"108.16"	"S_3\\times D_9"	108	18	18	"1.1"	"Solvable - 2"
"108.17"	"C_3^2:D_6"	108	6	11	"1.1"	"Solvable - 3"
"108.18"	"C_9\\times A_4"	108	18	36	"9.1"	"Solvable - 2"
"108.19"	"C_9:A_4"	108	18	20	"3.1"	"Solvable - 2"
"108.20"	"C_3^2.A_4"	108	18	36	"9.2"	"Solvable - 2"
"108.21"	"C_3^2.A_4"	108	18	20	"3.1"	"Solvable - 2"
"108.22"	"C_3^2:A_4"	108	6	20	"3.1"	"Solvable - 2"
"108.23"	"C_3\\times D_{18}"	108	18	36	"6.2"	"Solvable - 2"
"108.24"	"S_3\\times C_{18}"	108	18	54	"18.2"	"Solvable - 2"
"108.25"	"C_3^2:D_6"	108	6	20	"2.1"	"Solvable - 2"
"108.26"	"C_{18}:C_6"	108	18	20	"2.1"	"Solvable - 2"
"108.27"	"C_3:D_{18}"	108	18	30	"2.1"	"Solvable - 2"
"108.28"	"C_3^2:D_6"	108	6	20	"6.2"	"Solvable - 3"
"108.29"	"C_6\\times C_{18}"	108	18	108	"108.29"	"Abelian - 2"
"108.30"	"C_2^2\\times \\He_3"	108	6	44	"12.5"	"Nilpotent - 2"
"108.31"	"C_{18}:C_6"	108	18	44	"12.5"	"Nilpotent - 2"
"108.32"	"C_3^2:C_{12}"	108	12	54	"18.5"	"Solvable - 2"
"108.33"	"C_3^2:C_{12}"	108	12	36	"6.2"	"Solvable - 2"
"108.34"	"C_3^3:C_4"	108	12	30	"2.1"	"Solvable - 2"
"108.35"	"C_3^2\\times C_{12}"	108	12	108	"108.35"	"Abelian - 3"
"108.36"	"C_3^2:C_{12}"	108	12	18	"3.1"	"Solvable - 2"
"108.37"	"C_3^3:C_4"	108	12	12	"1.1"	"Solvable - 2"
"108.38"	"C_3\\times S_3^2"	108	6	27	"3.1"	"Solvable - 2"
"108.39"	"C_3:S_3^2"	108	6	18	"1.1"	"Solvable - 2"
"108.40"	"C_3:S_3^2"	108	6	15	"1.1"	"Solvable - 2"
"108.41"	"C_3^2\\times A_4"	108	6	36	"9.2"	"Solvable - 2"
"108.42"	"C_3^2\\times D_6"	108	6	54	"18.5"	"Solvable - 2"
"108.43"	"C_3^2:D_6"	108	6	36	"6.2"	"Solvable - 2"
"108.44"	"C_3^2:D_6"	108	6	30	"2.1"	"Solvable - 2"
"108.45"	"C_3\\times C_6^2"	108	6	108	"108.45"	"Abelian - 3"
"109.1"	"C_{109}"	109	109	109	"109.1"	"Cyclic"
"110.1"	"F_{11}"	110	110	11	"1.1"	"Solvable - 2"
"110.2"	"C_{11}:C_{10}"	110	110	14	"2.1"	"Solvable - 2"
"110.3"	"D_5\\times C_{11}"	110	110	44	"11.1"	"Solvable - 2"
"110.4"	"C_5\\times D_{11}"	110	110	35	"5.1"	"Solvable - 2"
"110.5"	"D_{55}"	110	110	29	"1.1"	"Solvable - 2"
"110.6"	"C_{110}"	110	110	110	"110.6"	"Cyclic"
"111.1"	"C_{37}:C_3"	111	111	15	"1.1"	"Solvable - 2"
"111.2"	"C_{111}"	111	111	111	"111.2"	"Cyclic"
"112.1"	"C_7:C_{16}"	112	112	40	"8.1"	"Solvable - 2"
"112.2"	"C_{112}"	112	112	112	"112.2"	"Cyclic"
"112.3"	"C_8\\times D_7"	112	56	40	"8.1"	"Solvable - 2"
"112.4"	"C_{56}:C_2"	112	56	34	"4.1"	"Solvable - 2"
"112.5"	"C_{56}:C_2"	112	56	31	"2.1"	"Solvable - 2"
"112.6"	"D_{56}"	112	56	31	"2.1"	"Solvable - 2"
"112.7"	"C_7:Q_{16}"	112	56	31	"2.1"	"Solvable - 2"
"112.8"	"C_{14}:C_8"	112	56	40	"8.2"	"Solvable - 2"
"112.9"	"C_7:\\OD_{16}"	112	56	34	"4.1"	"Solvable - 2"
"112.10"	"C_{28}:C_4"	112	28	40	"8.2"	"Solvable - 2"
"112.11"	"C_{14}.D_4"	112	28	34	"4.2"	"Solvable - 2"
"112.12"	"C_{28}:C_4"	112	28	34	"4.2"	"Solvable - 2"
"112.13"	"D_{14}:C_4"	112	28	34	"4.2"	"Solvable - 2"
"112.14"	"C_7:D_8"	112	56	22	"2.1"	"Solvable - 2"
"112.15"	"C_7:\\SD_{16}"	112	56	22	"2.1"	"Solvable - 2"
"112.16"	"Q_8:D_7"	112	56	22	"2.1"	"Solvable - 2"
"112.17"	"C_7:Q_{16}"	112	56	22	"2.1"	"Solvable - 2"
"112.18"	"C_{14}.D_4"	112	28	34	"4.2"	"Solvable - 2"
"112.19"	"C_4\\times C_{28}"	112	28	112	"112.19"	"Abelian - 2"
"112.20"	"C_2^2:C_{28}"	112	28	70	"28.4"	"Nilpotent - 2"
"112.21"	"C_4:C_{28}"	112	28	70	"28.4"	"Nilpotent - 2"
"112.22"	"C_2\\times C_{56}"	112	56	112	"112.22"	"Abelian - 2"
"112.23"	"C_7\\times \\OD_{16}"	112	56	70	"28.2"	"Nilpotent - 2"
"112.24"	"C_7\\times D_8"	112	56	49	"14.2"	"Nilpotent - 3"
"112.25"	"C_7\\times \\SD_{16}"	112	56	49	"14.2"	"Nilpotent - 3"
"112.26"	"C_7\\times Q_{16}"	112	56	49	"14.2"	"Nilpotent - 3"
"112.27"	"C_{14}:Q_8"	112	28	34	"4.2"	"Solvable - 2"
"112.28"	"C_4\\times D_{14}"	112	28	40	"8.2"	"Solvable - 2"
"112.29"	"C_2\\times D_{28}"	112	28	34	"4.2"	"Solvable - 2"
"112.30"	"D_{28}:C_2"	112	28	34	"4.1"	"Solvable - 2"
"112.31"	"D_4\\times D_7"	112	28	25	"2.1"	"Solvable - 2"
"112.32"	"D_4:D_7"	112	28	25	"2.1"	"Solvable - 2"
"112.33"	"Q_8\\times D_7"	112	28	25	"2.1"	"Solvable - 2"
"112.34"	"D_{28}:C_2"	112	28	25	"2.1"	"Solvable - 2"
"112.35"	"C_2^2.D_{14}"	112	28	40	"8.5"	"Solvable - 2"
"112.36"	"C_{14}:D_4"	112	28	34	"4.2"	"Solvable - 2"
"112.37"	"C_2^2\\times C_{28}"	112	28	112	"112.37"	"Abelian - 3"
"112.38"	"D_4\\times C_{14}"	112	28	70	"28.4"	"Nilpotent - 2"
"112.39"	"Q_8\\times C_{14}"	112	28	70	"28.4"	"Nilpotent - 2"
"112.40"	"D_4:C_{14}"	112	28	70	"28.2"	"Nilpotent - 2"
"112.41"	"C_2\\times F_8"	112	14	16	"2.1"	"Solvable - 2"
"112.42"	"C_2^2\\times D_{14}"	112	14	40	"8.5"	"Solvable - 2"
"112.43"	"C_2^3\\times C_{14}"	112	14	112	"112.43"	"Abelian - 4"
"113.1"	"C_{113}"	113	113	113	"113.1"	"Cyclic"
"114.1"	"C_{19}:C_6"	114	114	9	"1.1"	"Solvable - 2"
"114.2"	"C_{19}:C_6"	114	114	18	"2.1"	"Solvable - 2"
"114.3"	"S_3\\times C_{19}"	114	114	57	"19.1"	"Solvable - 2"
"114.4"	"C_3\\times D_{19}"	114	114	33	"3.1"	"Solvable - 2"
"114.5"	"D_{57}"	114	114	30	"1.1"	"Solvable - 2"
"114.6"	"C_{114}"	114	114	114	"114.6"	"Cyclic"
"115.1"	"C_{115}"	115	115	115	"115.1"	"Cyclic"
"116.1"	"C_{29}:C_4"	116	116	32	"2.1"	"Solvable - 2"
"116.2"	"C_{116}"	116	116	116	"116.2"	"Cyclic"
"116.3"	"C_{29}:C_4"	116	116	11	"1.1"	"Solvable - 2"
"116.4"	"D_{58}"	116	58	32	"2.1"	"Solvable - 2"
"116.5"	"C_2\\times C_{58}"	116	58	116	"116.5"	"Abelian - 2"
"117.1"	"C_{13}:C_9"	117	117	21	"3.1"	"Solvable - 2"
"117.2"	"C_{117}"	117	117	117	"117.2"	"Cyclic"
"117.3"	"C_{39}:C_3"	117	39	21	"3.1"	"Solvable - 2"
"117.4"	"C_3\\times C_{39}"	117	39	117	"117.4"	"Abelian - 2"
"118.1"	"D_{59}"	118	118	31	"1.1"	"Solvable - 2"
"118.2"	"C_{118}"	118	118	118	"118.2"	"Cyclic"
"119.1"	"C_{119}"	119	119	119	"119.1"	"Cyclic"
"120.1"	"C_3:C_{40}"	120	120	60	"20.2"	"Solvable - 2"
"120.2"	"C_5:C_{24}"	120	120	48	"12.2"	"Solvable - 2"
"120.3"	"C_{15}:C_8"	120	120	36	"4.1"	"Solvable - 2"
"120.4"	"C_{120}"	120	120	120	"120.4"	"Cyclic"
"120.5"	"\\SL(2,5)"	120	60	9	"2.1"	"Non-Solvable - 2"
"120.6"	"C_5:C_{24}"	120	120	30	"6.2"	"Solvable - 2"
"120.7"	"C_{15}:C_8"	120	120	18	"2.1"	"Solvable - 2"
"120.8"	"C_6.D_{10}"	120	60	24	"2.1"	"Solvable - 2"
"120.9"	"C_6.D_{10}"	120	60	24	"2.1"	"Solvable - 2"
"120.10"	"D_{15}:C_4"	120	60	24	"2.1"	"Solvable - 2"
"120.11"	"C_{15}:D_4"	120	60	21	"2.1"	"Solvable - 2"
"120.12"	"C_3:D_{20}"	120	60	21	"2.1"	"Solvable - 2"
"120.13"	"C_5:D_{12}"	120	60	21	"2.1"	"Solvable - 2"
"120.14"	"C_{15}:Q_8"	120	60	21	"2.1"	"Solvable - 2"
"120.15"	"C_5\\times \\SL(2,3)"	120	60	35	"10.2"	"Solvable - 3"
"120.16"	"C_{15}:Q_8"	120	60	39	"6.2"	"Solvable - 2"
"120.17"	"D_5\\times C_{12}"	120	60	48	"12.2"	"Solvable - 2"
"120.18"	"C_3\\times D_{20}"	120	60	39	"6.2"	"Solvable - 2"
"120.19"	"C_{10}:C_{12}"	120	60	48	"12.5"	"Solvable - 2"
"120.20"	"C_{15}:D_4"	120	60	39	"6.2"	"Solvable - 2"
"120.21"	"C_{15}:Q_8"	120	60	45	"10.2"	"Solvable - 2"
"120.22"	"S_3\\times C_{20}"	120	60	60	"20.2"	"Solvable - 2"
"120.23"	"C_5\\times D_{12}"	120	60	45	"10.2"	"Solvable - 2"
"120.24"	"C_6:C_{20}"	120	60	60	"20.5"	"Solvable - 2"
"120.25"	"C_{15}:D_4"	120	60	45	"10.2"	"Solvable - 2"
"120.26"	"C_{15}:Q_8"	120	60	33	"2.1"	"Solvable - 2"
"120.27"	"C_4\\times D_{15}"	120	60	36	"4.1"	"Solvable - 2"
"120.28"	"D_{60}"	120	60	33	"2.1"	"Solvable - 2"
"120.29"	"C_{30}:C_4"	120	60	36	"4.2"	"Solvable - 2"
"120.30"	"C_{15}:D_4"	120	60	33	"2.1"	"Solvable - 2"
"120.31"	"C_2\\times C_{60}"	120	60	120	"120.31"	"Abelian - 2"
"120.32"	"D_4\\times C_{15}"	120	60	75	"30.4"	"Nilpotent - 2"
"120.33"	"Q_8\\times C_{15}"	120	60	75	"30.4"	"Nilpotent - 2"
"120.34"	"S_5"	120	60	7	"1.1"	"Non-Solvable - 2"
"120.35"	"C_2\\times A_5"	120	30	10	"2.1"	"Non-Solvable - 2"
"120.36"	"S_3\\times F_5"	120	60	15	"1.1"	"Solvable - 2"
"120.37"	"C_5\\times S_4"	120	60	25	"5.1"	"Solvable - 3"
"120.38"	"C_5:S_4"	120	60	13	"1.1"	"Solvable - 3"
"120.39"	"D_5\\times A_4"	120	30	16	"1.1"	"Solvable - 2"
"120.40"	"C_6\\times F_5"	120	60	30	"6.2"	"Solvable - 2"
"120.41"	"C_{30}:C_4"	120	60	18	"2.1"	"Solvable - 2"
"120.42"	"S_3\\times D_{10}"	120	30	24	"2.1"	"Solvable - 2"
"120.43"	"C_{10}\\times A_4"	120	30	40	"10.2"	"Solvable - 2"
"120.44"	"C_6\\times D_{10}"	120	30	48	"12.5"	"Solvable - 2"
"120.45"	"C_{10}\\times D_6"	120	30	60	"20.5"	"Solvable - 2"
"120.46"	"C_2\\times D_{30}"	120	30	36	"4.2"	"Solvable - 2"
"120.47"	"C_2^2\\times C_{30}"	120	30	120	"120.47"	"Abelian - 3"
"121.1"	"C_{121}"	121	121	121	"121.1"	"Cyclic"
"121.2"	"C_{11}^2"	121	11	121	"121.2"	"Abelian - 2"
"122.1"	"D_{61}"	122	122	32	"1.1"	"Solvable - 2"
"122.2"	"C_{122}"	122	122	122	"122.2"	"Cyclic"
"123.1"	"C_{123}"	123	123	123	"123.1"	"Cyclic"
"124.1"	"C_{31}:C_4"	124	124	34	"2.1"	"Solvable - 2"
"124.2"	"C_{124}"	124	124	124	"124.2"	"Cyclic"
"124.3"	"D_{62}"	124	62	34	"2.1"	"Solvable - 2"
"124.4"	"C_2\\times C_{62}"	124	62	124	"124.4"	"Abelian - 2"
"125.1"	"C_{125}"	125	125	125	"125.1"	"Cyclic"
"125.2"	"C_5\\times C_{25}"	125	25	125	"125.2"	"Abelian - 2"
"125.3"	"\\He_5"	125	5	29	"5.1"	"Nilpotent - 2"
"125.4"	"C_{25}:C_5"	125	25	29	"5.1"	"Nilpotent - 2"
"125.5"	"C_5^3"	125	5	125	"125.5"	"Abelian - 3"
"126.1"	"C_7:C_{18}"	126	126	21	"3.1"	"Solvable - 2"
"126.2"	"C_7:C_{18}"	126	126	30	"6.2"	"Solvable - 2"
"126.3"	"C_7\\times D_9"	126	126	42	"7.1"	"Solvable - 2"
"126.4"	"C_9\\times D_7"	126	126	45	"9.1"	"Solvable - 2"
"126.5"	"D_{63}"	126	126	33	"1.1"	"Solvable - 2"
"126.6"	"C_{126}"	126	126	126	"126.6"	"Cyclic"
"126.7"	"C_3\\times F_7"	126	42	21	"3.1"	"Solvable - 2"
"126.8"	"C_{21}:C_6"	126	42	15	"1.1"	"Solvable - 2"
"126.9"	"C_{21}:C_6"	126	42	12	"1.1"	"Solvable - 2"
"126.10"	"C_{21}:C_6"	126	42	30	"6.2"	"Solvable - 2"
"126.11"	"C_3^2\\times D_7"	126	42	45	"9.2"	"Solvable - 2"
"126.12"	"S_3\\times C_{21}"	126	42	63	"21.2"	"Solvable - 2"
"126.13"	"C_3\\times D_{21}"	126	42	36	"3.1"	"Solvable - 2"
"126.14"	"C_{21}:S_3"	126	42	42	"7.1"	"Solvable - 2"
"126.15"	"C_3:D_{21}"	126	42	33	"1.1"	"Solvable - 2"
"126.16"	"C_3\\times C_{42}"	126	42	126	"126.16"	"Abelian - 2"
"127.1"	"C_{127}"	127	127	127	"127.1"	"Cyclic"


# Label --
#    The **label** for a group $G$ has the form $\mathtt{N.i}$, where $\mathtt{N}$ is the order of the group and $\mathtt{i}$ is the small group id that distinguishes groups of the same order (as determined in GAP). If a group is not in GAP Small Groups database, we replace $\mathtt{i}$ with an incrementing letter code, assigning labels to groups as they are added to our database.

#    Subgroups are labeled using the ambient group, index, and an ordering of subgroups up to automorphism and then up to conjugacy with the same  invariants.



#Name (tex_name) --
#    We describe abstract groups using standard building blocks:
#    <ul>
#     <li> $C_n$ denotes the cyclic group of order $n$.
#     <li> $S_n$ denotes the symmetric group on $n$ letters.
#     <li> $A_n$ denotes the alternating group on $n$ letters.
#     <li> $D_n$ denotes the dihedral group of order $2n$.
#     <li> $Q_n$ denotes the (generalized) quaternion group of order $n$.
#     <li> $F_q$ denotes the Frobenius group for a prime power $q$. It is the group of affine linear transformations of the finite field $\mathbb{F}_q$. In other words, $F_q$ is a semidirect product  $\mathbb{F}_q : \mathbb{F}_q^{\times}$.
#     <li> Sporadic Groups (refer to this <a href="https://en.wikipedia.org/wiki/Sporadic_group">wikipage</a>):
#    <ul>
#     <li> $M_n$ for $n=11,12, 22,23, 24$ denotes the Mathieu groups
#     <li> $\Ru$ denotes the Rudvalis group
#     <li> $\McL$ denotes the McLaughlin group
#     <li> $\He$ denotes the Held group
#     <li> $\HS$ denotes the Higman–Sims group
#     <li> $J_1$, $J_2$, $J_3$ denote the Janko groups
#     <li> $\Co_2$ and $\Co_3$ denote the Conway groups
#    </ul>
#     <li> Here is a list of finite groups of Lie type.
#     <li> $\SD_n$ denotes the semidihedral group or quasidihedral group of order $n=2^k$.
#     <li> $\OD_n$ denotes the other-dihedral group (or modular maximal-cyclic group) of order $n=2^k$. It is the non-trivial semidirect product $C_{2^{k-1}} : C_2$ which is not isomorphic to either $\SD_n$ or $D_{2^{k-1}}$.
#     <li> $\He_p$ denotes the Heisenberg group, the unique non-abelian group of order $p^3$ and exponent $p$ for an odd prime $p$.
#    </ul>

#    Groups $A$ and $B$ may be used to construct a larger group:

#    - $A\times B$ for the direct product of $A$ and $B$.
#    - $A:B$ for the semidirect product of $A$ and $B$ (with normal subgroup $A$).
#    - $A.B$ an extension with normal subgroup $A$ and quotient isomorphic to $B$.
#    - $A\wr B$ for the wreath product of $A$ and $B$.


# Order --
#    The **order** of a group is its cardinality as a set.


# Exponent --
#    The **exponent of a group** $G$ is the smallest positive integer $n$ such that $g^n=e$ for all $g\in G$.  If no such positive integer exists, then the exponent of the group is infinite.


#$\card{\mathrm{conj}(G)}$ (number_conjugacy_classes) --
#    If $G$ is a group and $x\in G$, the **conjugacy class** of $x$ is the set $\{gxg^{-1}\mid g\in G\}$.  These sets partition $G$, and the set of conjugacy classes is denoted by $\mathrm{conj}(G)$.

#    Since conjugation by fixed $g\in G$ is an automorphism of $G$, all conjugate elements have the same order in the group.


#Center (center_label) --
#    If $G$ is a group, the **center** of $G$ is the set
#    \[ Z(G) = \{g\in G\mid gh=hg \text{ for all } h\in G\}.\]
#    It is a normal subgroup of $G$.


#Type - length (type) --
#    For a finite group $G$, we write **Type - length** as follows

#    <ul>
#    <li> If $G$ is cyclic we write "Cyclic".  For abelian groups that are not cyclic we write "Abelian - $n$", where $n$ is the number of cyclic groups in the unique cyclic decomposition of $G$ as $C_{d_1} \times C_{d_2}\times \cdots \times C_{d_n}$ with $d_i\mid d_{i+1}$ and $d_i>0$.</li>

#    <li> If $G$ is nilpotent but not abelian then we write  "Nilpotent - $n$", where $n$ is the nilpotency class of $G$.</li>

#    <li> If $G$ is solvable but not nilpotent then we write  "Solvable - $n$", where $n$ is the derived length of $G$.</li>

#    <li> If $G$ is simple we write "Simple".

#     <li> For non-simple, non-solvable groups we write "Non-solvable - $n$", where $n$ is the number of Jordan factors of $G$.</li>
#    </ul>