# gps_conj_classes downloaded from the LMFDB on 24 October 2026.
# Search link: https://www.lmfdb.org/Groups/Abstract/ConjugacyClasses?group=20922789888000.a
# Query "{'group_order': 20922789888000, 'group_counter': 1}" returned 231 gps_conj_classes, sorted by group.

# Each entry in the following data list has the form:
#    [Group, Label, Order, Size, Centralizer, Powers, Representative]
# For more details, see the definitions at the bottom of the file.



"20922789888000.a"	"1A"	1	1	NULL	"1A,1A,1A,1A,1A,1A"	"()"
"20922789888000.a"	"2A"	2	120	NULL	"1A,2A,2A,2A,2A,2A"	"(7,8)"
"20922789888000.a"	"2B"	2	5460	NULL	"1A,2B,2B,2B,2B,2B"	"(2,5)(3,16)"
"20922789888000.a"	"2C"	2	120120	NULL	"1A,2C,2C,2C,2C,2C"	"(3,12)(6,13)(7,16)"
"20922789888000.a"	"2D"	2	1351350	NULL	"1A,2D,2D,2D,2D,2D"	"(2,6)(5,10)(7,9)(11,12)"
"20922789888000.a"	"2E"	2	2027025	NULL	"1A,2E,2E,2E,2E,2E"	"(1,9)(2,11)(3,10)(4,12)(5,13)(6,14)(7,15)(8,16)"
"20922789888000.a"	"2F"	2	7567560	NULL	"1A,2F,2F,2F,2F,2F"	"(1,14)(3,11)(5,10)(6,7)(9,15)"
"20922789888000.a"	"2G"	2	16216200	NULL	"1A,2G,2G,2G,2G,2G"	"(1,16)(2,3)(5,6)(7,8)(9,11)(12,13)(14,15)"
"20922789888000.a"	"2H"	2	18918900	NULL	"1A,2H,2H,2H,2H,2H"	"(2,3)(5,16)(6,13)(7,11)(8,10)(9,14)"
"20922789888000.a"	"3A"	3	1120	NULL	"3A,1A,3A,3A,3A,3A"	"(3,6,13)"
"20922789888000.a"	"3B"	3	320320	NULL	"3B,1A,3B,3B,3B,3B"	"(6,9,11)(7,13,14)"
"20922789888000.a"	"3C"	3	25625600	NULL	"3C,1A,3C,3C,3C,3C"	"(1,4,5)(3,6,7)(10,15,14)"
"20922789888000.a"	"3D"	3	448448000	NULL	"3D,1A,3D,3D,3D,3D"	"(1,9,6)(2,11,7)(4,16,10)(5,12,8)"
"20922789888000.a"	"3E"	3	717516800	NULL	"3E,1A,3E,3E,3E,3E"	"(1,11,6)(2,14,4)(3,15,8)(7,13,9)(10,12,16)"
"20922789888000.a"	"4A"	4	10920	NULL	"2B,4A,4A,4A,4A,4A"	"(3,15,5,8)"
"20922789888000.a"	"4B"	4	720720	NULL	"2B,4B,4B,4B,4B,4B"	"(2,16,5,3)(7,8)"
"20922789888000.a"	"4C"	4	16216200	NULL	"2D,4C,4C,4C,4C,4C"	"(2,13,6,7)(4,15,11,16)"
"20922789888000.a"	"4D"	4	16216200	NULL	"2B,4D,4D,4D,4D,4D"	"(2,4)(3,13)(6,9,11,15)"
"20922789888000.a"	"4E"	4	113513400	NULL	"2B,4E,4E,4E,4E,4E"	"(1,14)(2,4)(3,7)(5,6)(8,9,15,12)(10,11)(13,16)"
"20922789888000.a"	"4F"	4	151351200	NULL	"2B,4F,4F,4F,4F,4F"	"(2,9,14,4)(7,8)(10,16)(11,12)"
"20922789888000.a"	"4G"	4	454053600	NULL	"2D,4G,4G,4G,4G,4G"	"(3,16,8,6)(4,10)(7,13,9,12)"
"20922789888000.a"	"4H"	4	567567000	NULL	"2B,4H,4H,4H,4H,4H"	"(1,13)(2,4)(3,7,5,9)(6,15)(10,16)"
"20922789888000.a"	"4I"	4	681080400	NULL	"2B,4I,4I,4I,4I,4I"	"(1,14,10,11)(2,16)(3,15)(4,13)(5,12)(6,7)"
"20922789888000.a"	"4J"	4	1702701000	NULL	"2D,4J,4J,4J,4J,4J"	"(1,9,5,12)(2,16)(3,13,7,6)(4,8)(10,11)(14,15)"
"20922789888000.a"	"4K"	4	2270268000	NULL	"2H,4K,4K,4K,4K,4K"	"(1,11,8,4)(2,12,10,6)(5,16,9,7)"
"20922789888000.a"	"4L"	4	3405402000	NULL	"2E,4L,4L,4L,4L,4L"	"(1,5,9,13)(2,6,11,14)(3,7,10,15)(4,8,12,16)"
"20922789888000.a"	"4M"	4	3405402000	NULL	"2D,4M,4M,4M,4M,4M"	"(1,8)(2,12,6,11)(4,15)(5,9,10,7)"
"20922789888000.a"	"4N"	4	6810804000	NULL	"2H,4N,4N,4N,4N,4N"	"(1,12)(2,10,7,6)(3,5,4,15)(8,9,14,16)(11,13)"
"20922789888000.a"	"4O"	4	6810804000	NULL	"2D,4O,4O,4O,4O,4O"	"(2,10)(3,12)(5,13,6,8)(7,14,9,15)(11,16)"
"20922789888000.a"	"4P"	4	13621608000	NULL	"2H,4P,4P,4P,4P,4P"	"(1,3,13,4)(2,7,11,12)(5,8,10,16)(9,15)"
"20922789888000.a"	"5A"	5	104832	NULL	"5A,5A,1A,5A,5A,5A"	"(1,5,8,11,14)"
"20922789888000.a"	"5B"	5	581188608	NULL	"5B,5B,1A,5B,5B,5B"	"(1,6,9,10,15)(3,5,7,12,14)"
"20922789888000.a"	"5C"	5	27897053184	NULL	"5C,5C,1A,5C,5C,5C"	"(1,4,13,3,10)(2,9,15,12,11)(6,14,7,8,16)"
"20922789888000.a"	"6A"	6	87360	NULL	"3A,2A,6A,6A,6A,6A"	"(7,8)(9,11,10)"
"20922789888000.a"	"6B"	6	960960	NULL	"3B,2C,6B,6B,6B,6B"	"(1,14,16,9,3,15)"
"20922789888000.a"	"6C"	6	2402400	NULL	"3A,2B,6C,6C,6C,6C"	"(2,14)(3,13,6)(4,9)"
"20922789888000.a"	"6D"	6	14414400	NULL	"3B,2A,6D,6D,6D,6D"	"(2,6,4)(7,11)(8,9,13)"
"20922789888000.a"	"6E"	6	28828800	NULL	"3A,2C,6E,6E,6E,6E"	"(3,12)(6,13)(7,16)(8,10,15)"
"20922789888000.a"	"6F"	6	43243200	NULL	"3B,2D,6F,6F,6F,6F"	"(2,14,11,9,3,12)(4,13)"
"20922789888000.a"	"6G"	6	151351200	NULL	"3A,2D,6G,6G,6G,6G"	"(1,3)(2,7)(4,12)(9,13,16)(10,14)"
"20922789888000.a"	"6H"	6	151351200	NULL	"3A,2H,6H,6H,6H,6H"	"(1,3)(4,6)(5,8)(7,14)(9,10)(11,12,13)(15,16)"
"20922789888000.a"	"6I"	6	201801600	NULL	"3B,2B,6I,6I,6I,6I"	"(2,5)(3,16)(6,11,10)(9,14,13)"
"20922789888000.a"	"6J"	6	230630400	NULL	"3C,2C,6J,6J,6J,6J"	"(1,3,13,4,9,15)(7,14,10)"
"20922789888000.a"	"6K"	6	302702400	NULL	"3A,2F,6K,6K,6K,6K"	"(1,6,3)(2,7)(4,15)(5,12)(8,9)(13,16)"
"20922789888000.a"	"6L"	6	302702400	NULL	"3B,2F,6L,6L,6L,6L"	"(1,10,9)(2,3)(4,12,15)(5,11)(6,8)(7,14)(13,16)"
"20922789888000.a"	"6M"	6	538137600	NULL	"3C,2A,6M,6M,6M,6M"	"(1,2,11)(3,10,13)(4,7,8)(9,14)"
"20922789888000.a"	"6N"	6	605404800	NULL	"3B,2F,6N,6N,6N,6N"	"(1,6,10,14,7,5)(3,11)(9,15)"
"20922789888000.a"	"6O"	6	908107200	NULL	"3B,2E,6O,6O,6O,6O"	"(1,3)(2,16,13,11,8,4)(5,6)(7,9)(10,12)(14,15)"
"20922789888000.a"	"6P"	6	1009008000	NULL	"3B,2C,6P,6P,6P,6P"	"(1,2,14)(5,6,15)(7,13)(8,16)(10,11)"
"20922789888000.a"	"6Q"	6	1345344000	NULL	"3D,2B,6Q,6Q,6Q,6Q"	"(1,9)(2,14,13)(3,15,16)(4,12,8)(5,6,11)(7,10)"
"20922789888000.a"	"6R"	6	1513512000	NULL	"3B,2D,6R,6R,6R,6R"	"(1,14,9)(2,6)(3,5,8)(4,11)(7,13)(15,16)"
"20922789888000.a"	"6S"	6	2690688000	NULL	"3C,2C,6S,6S,6S,6S"	"(1,5,4)(3,7,6)(8,12)(9,16)(10,14,15)(11,13)"
"20922789888000.a"	"6T"	6	2690688000	NULL	"3C,2B,6T,6T,6T,6T"	"(1,5,13)(2,7)(3,11,10)(4,6,16)(8,14)"
"20922789888000.a"	"6U"	6	2690688000	NULL	"3D,2A,6U,6U,6U,6U"	"(1,11)(2,16,10)(3,7,15)(5,12,8)(6,9,14)"
"20922789888000.a"	"6V"	6	3027024000	NULL	"3B,2H,6V,6V,6V,6V"	"(2,3)(5,16)(6,7,9,13,11,14)(8,10)"
"20922789888000.a"	"6W"	6	4540536000	NULL	"3B,2G,6W,6W,6W,6W"	"(1,4,7,15,13,5)(3,10)(6,9)(8,16)(11,14)"
"20922789888000.a"	"6X"	6	4843238400	NULL	"3C,2D,6X,6X,6X,6X"	"(2,3,9,15,5,11)(6,10,12)(7,16)"
"20922789888000.a"	"6Y"	6	8072064000	NULL	"3D,2C,6Y,6Y,6Y,6Y"	"(2,11,3)(4,9,6)(5,14,8,12,10,13)"
"20922789888000.a"	"6Z"	6	12108096000	NULL	"3D,2H,6Z,6Z,6Z,6Z"	"(1,12,9,8,6,5)(2,16,11,10,7,4)"
"20922789888000.a"	"6AA"	6	21525504000	NULL	"3E,2C,6AA,6AA,6AA,6AA"	"(1,5,12)(3,14,13,11,8,4)(6,7,10)(9,15,16)"
"20922789888000.a"	"6AB"	6	24216192000	NULL	"3C,2F,6AB,6AB,6AB,6AB"	"(1,10,2)(3,4)(7,12)(8,13,16,11,14,9)"
"20922789888000.a"	"6AC"	6	24216192000	NULL	"3C,2H,6AC,6AC,6AC,6AC"	"(1,2,9,6,10,12)(3,4)(5,7)(8,15,11)(14,16)"
"20922789888000.a"	"6AD"	6	24216192000	NULL	"3D,2F,6AD,6AD,6AD,6AD"	"(1,6,8)(2,3,7)(4,15,13,11,10,16)(5,14)(9,12)"
"20922789888000.a"	"6AE"	6	36324288000	NULL	"3D,2E,6AE,6AE,6AE,6AE"	"(1,5,3,10,13,6)(2,14,15,12,7,9)(4,8)(11,16)"
"20922789888000.a"	"6AF"	6	48432384000	NULL	"3D,2D,6AF,6AF,6AF,6AF"	"(1,13)(2,15,14)(4,11,8,10,9,12)(6,7,16)"
"20922789888000.a"	"6AG"	6	72648576000	NULL	"3D,2G,6AG,6AG,6AG,6AG"	"(2,4,8,9,12,3)(6,15,13,11,16,10)(7,14)"
"20922789888000.a"	"6AH"	6	96864768000	NULL	"3E,2H,6AH,6AH,6AH,6AH"	"(1,9,12)(2,16,4,13,8,10)(3,11,7,5,14,6)"
"20922789888000.a"	"7A"	7	8236800	NULL	"7A,7A,7A,1A,7A,7A"	"(1,11,4,9,2,14,5)"
"20922789888000.a"	"7B"	7	106748928000	NULL	"7B,7B,7B,1A,7B,7B"	"(1,6,11,15,2,7,12)(3,8,13,16,5,9,14)"
"20922789888000.a"	"8A"	8	64864800	NULL	"4C,8A,8A,8A,8A,8A"	"(1,16,10,6,12,11,2,13)"
"20922789888000.a"	"8B"	8	1816214400	NULL	"4C,8B,8B,8B,8B,8B"	"(2,9)(3,14,6,7,5,8,16,4)"
"20922789888000.a"	"8C"	8	6810804000	NULL	"4C,8C,8C,8C,8C,8C"	"(1,14,11,15,10,16,6,7)(2,12)(3,4)(5,8)(9,13)"
"20922789888000.a"	"8D"	8	13621608000	NULL	"4C,8D,8D,8D,8D,8D"	"(1,5)(2,14,7,9,13,3,15,8)(11,12)"
"20922789888000.a"	"8E"	8	27243216000	NULL	"4C,8E,8E,8E,8E,8E"	"(1,5)(2,11,13,16,6,4,7,15)(3,9)(8,14)"
"20922789888000.a"	"8F"	8	27243216000	NULL	"4M,8F,8F,8F,8F,8F"	"(1,2,14,4,3,7,10,12)(5,15,11,6)"
"20922789888000.a"	"8G"	8	81729648000	NULL	"4M,8G,8G,8G,8G,8G"	"(1,13,7,3,11,5,15,8)(2,9)(4,12,14,10)(6,16)"
"20922789888000.a"	"8H"	8	81729648000	NULL	"4J,8H,8H,8H,8H,8H"	"(1,13,2,14,12,4,5,11)(3,7,16,8)(6,15,10,9)"
"20922789888000.a"	"8I"	8	163459296000	NULL	"4L,8I,8I,8I,8I,8I"	"(1,3,5,7,9,10,13,15)(2,4,6,8,11,12,14,16)"
"20922789888000.a"	"8J"	8	163459296000	NULL	"4M,8J,8J,8J,8J,8J"	"(1,15,8,4)(2,5,12,9,6,10,11,7)(13,14)"
"20922789888000.a"	"9A"	9	461260800	NULL	"9A,3C,9A,9A,9A,9A"	"(1,4,11,13,16,3,5,6,10)"
"20922789888000.a"	"9B"	9	32288256000	NULL	"9B,3C,9B,9B,9B,9B"	"(1,8,6,15,2,4,3,11,7)(5,16,12)"
"20922789888000.a"	"9C"	9	129153024000	NULL	"9C,3C,9C,9C,9C,9C"	"(1,7,15,4,3,14,5,6,10)(8,11,16)(9,12,13)"
"20922789888000.a"	"10A"	10	5765760	NULL	"5A,10A,2A,10A,10A,10A"	"(1,12,2,3,16)(7,8)"
"20922789888000.a"	"10B"	10	103783680	NULL	"5A,10B,2B,10B,10B,10B"	"(1,10,2,15,11)(5,12)(7,9)"
"20922789888000.a"	"10C"	10	726485760	NULL	"5A,10C,2C,10C,10C,10C"	"(3,13,16,5,6)(7,14)(9,10)(12,15)"
"20922789888000.a"	"10D"	10	1089728640	NULL	"5A,10D,2F,10D,10D,10D"	"(1,14)(2,12,8,16,4)(3,11)(5,10)(6,7)(9,15)"
"20922789888000.a"	"10E"	10	1816214400	NULL	"5A,10E,2D,10E,10E,10E"	"(2,8,16,15,4)(3,9)(5,12)(6,7)(10,14)"
"20922789888000.a"	"10F"	10	2905943040	NULL	"5B,10F,2F,10F,10F,10F"	"(2,5,4,9,13,7,12,15,8,16)"
"20922789888000.a"	"10G"	10	8717829120	NULL	"5B,10G,2C,10G,10G,10G"	"(1,9)(2,13,10,4,8)(3,14)(5,12,7,6,11)(15,16)"
"20922789888000.a"	"10H"	10	8717829120	NULL	"5B,10H,2A,10H,10H,10H"	"(2,5,6,3,10)(4,15,8,11,16)(12,13)"
"20922789888000.a"	"10I"	10	26153487360	NULL	"5B,10I,2B,10I,10I,10I"	"(1,2,5,10,13)(4,6,11,16,14)(8,15)(9,12)"
"20922789888000.a"	"10J"	10	43589145600	NULL	"5B,10J,2E,10J,10J,10J"	"(1,12,6,14,9,3,10,5,15,7)(2,11)(4,13)(8,16)"
"20922789888000.a"	"10K"	10	43589145600	NULL	"5B,10K,2H,10K,10K,10K"	"(1,16,4,9,14,3,15,6,10,7)(5,8)"
"20922789888000.a"	"10L"	10	130767436800	NULL	"5B,10L,2G,10L,10L,10L"	"(1,14)(2,5,10,8,15,16,3,12,11,9)(4,6)"
"20922789888000.a"	"10M"	10	418455797760	NULL	"5C,10M,2F,10M,10M,10M"	"(1,12,10,8,3,4,7,5,13,11)(2,15,6,14,16)"
"20922789888000.a"	"11A"	11	15850598400	NULL	"11A,11A,11A,11A,1A,11A"	"(2,16,15,13,12,10,9,7,6,4,3)"
"20922789888000.a"	"12A"	12	4804800	NULL	"6C,4A,12A,12A,12A,12A"	"(1,12,3,9)(4,6,7)"
"20922789888000.a"	"12B"	12	172972800	NULL	"6C,4B,12B,12B,12B,12B"	"(4,13,6)(5,7,12,9)(8,14)"
"20922789888000.a"	"12C"	12	403603200	NULL	"6I,4A,12C,12C,12C,12C"	"(2,12,13)(3,5,14,9)(8,10,16)"
"20922789888000.a"	"12D"	12	1210809600	NULL	"6I,4F,12D,12D,12D,12D"	"(1,16,13,6,11,12)(3,10,9,5)"
"20922789888000.a"	"12E"	12	1816214400	NULL	"6G,4C,12E,12E,12E,12E"	"(1,13,11)(3,14,9,10)(5,7,12,6)"
"20922789888000.a"	"12F"	12	1816214400	NULL	"6C,4D,12F,12F,12F,12F"	"(2,15)(3,5)(4,14,7,16)(6,11,10)"
"20922789888000.a"	"12G"	12	2690688000	NULL	"6Q,4A,12G,12G,12G,12G"	"(1,13,2,4)(3,6,5)(7,15,11)(8,10,9)(12,16,14)"
"20922789888000.a"	"12H"	12	4540536000	NULL	"6C,4H,12H,12H,12H,12H"	"(1,4,2,15)(3,9,8)(6,16)(7,11)(10,13)(12,14)"
"20922789888000.a"	"12I"	12	5381376000	NULL	"6T,4A,12I,12I,12I,12I"	"(1,15,3)(2,11,8)(4,7,6)(9,13,14,10)"
"20922789888000.a"	"12J"	12	6054048000	NULL	"6I,4B,12J,12J,12J,12J"	"(2,3,5,16)(6,10,11)(7,8)(9,13,14)"
"20922789888000.a"	"12K"	12	6054048000	NULL	"6C,4F,12K,12K,12K,12K"	"(2,4,14,9)(3,6,13)(7,8)(10,16)(11,12)"
"20922789888000.a"	"12L"	12	6054048000	NULL	"6I,4F,12L,12L,12L,12L"	"(1,6,10,13)(2,9,12)(3,4)(5,14,15)(7,8)(11,16)"
"20922789888000.a"	"12M"	12	16144128000	NULL	"6T,4B,12M,12M,12M,12M"	"(1,13,5)(2,14,7,8)(3,10,11)(4,16,6)(12,15)"
"20922789888000.a"	"12N"	12	18162144000	NULL	"6R,4C,12N,12N,12N,12N"	"(1,9,14)(2,7,6,13)(3,8,5)(4,16,11,15)"
"20922789888000.a"	"12O"	12	18162144000	NULL	"6I,4E,12O,12O,12O,12O"	"(1,12,2,6)(3,7)(4,15)(5,16,9,11,10,8)(13,14)"
"20922789888000.a"	"12P"	12	18162144000	NULL	"6G,4G,12P,12P,12P,12P"	"(1,2,5)(3,6,8,16)(4,10)(7,12,9,13)"
"20922789888000.a"	"12Q"	12	18162144000	NULL	"6R,4G,12Q,12Q,12Q,12Q"	"(1,12,3,10)(2,11,14)(4,13,16)(5,6,7,15)(8,9)"
"20922789888000.a"	"12R"	12	18162144000	NULL	"6I,4D,12R,12R,12R,12R"	"(1,13,9)(2,4,14,10)(3,15,16)(5,6)(8,11)"
"20922789888000.a"	"12S"	12	18162144000	NULL	"6H,4K,12S,12S,12S,12S"	"(1,5,15)(2,16,3,9)(4,6,13,14)(7,8,11,12)"
"20922789888000.a"	"12T"	12	18162144000	NULL	"6I,4H,12T,12T,12T,12T"	"(1,4,7,16,10,5)(6,12,14,15)(8,9)"
"20922789888000.a"	"12U"	12	27243216000	NULL	"6G,4M,12U,12U,12U,12U"	"(1,10,3,14)(2,12,7,4)(5,11)(6,15)(9,16,13)"
"20922789888000.a"	"12V"	12	48432384000	NULL	"6Q,4F,12V,12V,12V,12V"	"(1,10,9,7)(2,4,14,12,13,8)(3,16,15)(5,11,6)"
"20922789888000.a"	"12W"	12	48432384000	NULL	"6T,4F,12W,12W,12W,12W"	"(1,16,14,4)(3,7,5,13,8,12)(6,9,10)"
"20922789888000.a"	"12X"	12	54486432000	NULL	"6R,4J,12X,12X,12X,12X"	"(1,12,5,9)(2,11,15,16,10,14)(3,6,7,13)(4,8)"
"20922789888000.a"	"12Y"	12	54486432000	NULL	"6I,4I,12Y,12Y,12Y,12Y"	"(1,7,3,15,10,5)(2,16)(4,14,8,12)(6,11)"
"20922789888000.a"	"12Z"	12	54486432000	NULL	"6R,4O,12Z,12Z,12Z,12Z"	"(2,3,16,10,12,11)(5,8,6,13)(7,15,9,14)"
"20922789888000.a"	"12AA"	12	72648576000	NULL	"6Z,4K,12AA,12AA,12AA,12AA"	"(1,16,12,11,9,10,8,7,6,4,5,2)"
"20922789888000.a"	"12AB"	12	72648576000	NULL	"6Q,4E,12AB,12AB,12AB,12AB"	"(1,6,7,8)(2,4,10,13,14,9)(3,16,12,5,11,15)"
"20922789888000.a"	"12AC"	12	145297152000	NULL	"6T,4H,12AC,12AC,12AC,12AC"	"(1,2,15,13,4,6)(3,9,5,7)(8,12,11)(10,16)"
"20922789888000.a"	"12AD"	12	217945728000	NULL	"6Z,4N,12AD,12AD,12AD,12AD"	"(1,12)(2,14,4,10,16,15,7,8,3,6,9,5)(11,13)"
"20922789888000.a"	"12AE"	12	435891456000	NULL	"6Z,4P,12AE,12AE,12AE,12AE"	"(1,2,5,3,7,8,13,11,10,4,12,16)(9,15)"
"20922789888000.a"	"12AF"	12	435891456000	NULL	"6AE,4L,12AF,12AF,12AF,12AF"	"(1,7,5,9,3,2,10,14,13,15,6,12)(4,11,8,16)"
"20922789888000.a"	"12AG"	12	581188608000	NULL	"6AH,4K,12AG,12AG,12AG,12AG"	"(1,12,9)(2,3,16,11,4,7,13,5,8,14,10,6)"
"20922789888000.a"	"13A"	13	268240896000	NULL	"13A,13A,13A,13A,13A,1A"	"(1,16,14,13,12,11,9,8,7,6,4,3,2)"
"20922789888000.a"	"14A"	14	296524800	NULL	"7A,14A,14A,2A,14A,14A"	"(1,10,3,5,12,16,15)(7,11)"
"20922789888000.a"	"14B"	14	3113510400	NULL	"7A,14B,14B,2B,14B,14B"	"(1,14,12,10,8,7,16)(6,11)(9,15)"
"20922789888000.a"	"14C"	14	7783776000	NULL	"7A,14C,14C,2D,14C,14C"	"(1,16,10,15,8,5,6)(2,9)(3,14)(4,13)(11,12)"
"20922789888000.a"	"14D"	14	10378368000	NULL	"7A,14D,14D,2C,14D,14D"	"(1,2,11,14,4,5,9)(3,12)(6,13)(7,16)"
"20922789888000.a"	"14E"	14	106748928000	NULL	"7B,14E,14E,2A,14E,14E"	"(1,7,6,16,14,10,9)(2,4,8,13,15,12,11)(3,5)"
"20922789888000.a"	"14F"	14	747242496000	NULL	"7B,14F,14F,2G,14F,14F"	"(1,3,6,8,11,13,15,16,2,5,7,9,12,14)"
"20922789888000.a"	"14G"	14	747242496000	NULL	"7B,14G,14G,2E,14G,14G"	"(1,8,12,3,9,16,7,13,5,15,10,2,6,11)(4,14)"
"20922789888000.a"	"15A"	15	34594560	NULL	"15A,5A,3A,15A,15A,15A"	"(1,16,3,2,12)(9,11,10)"
"20922789888000.a"	"15B"	15	1937295360	NULL	"15B,5A,3B,15B,15B,15B"	"(1,7,10)(2,4,16,8,12)(5,14,6)"
"20922789888000.a"	"15C"	15	12915302400	NULL	"15C,5A,3C,15C,15C,15C"	"(1,13,4,8,14)(2,5,9)(3,11,15)(6,10,12)"
"20922789888000.a"	"15D"	15	23247544320	NULL	"15D,5B,3B,15D,15D,15D"	"(1,9,15,6,10)(2,8,13)(3,7,14,5,12)(4,11,16)"
"20922789888000.a"	"15E"	15	23247544320	NULL	"15E,5B,3A,15E,15E,15E"	"(1,6,3)(2,13,8,4,12)(5,7,16,9,15)"
"20922789888000.a"	"15F"	15	1394852659200	NULL	"15F,5C,3E,15F,15F,15F"	"(1,7,12,4,8,11,13,16,2,3,6,9,10,14,15)"
"20922789888000.a"	"16A"	16	1307674368000	NULL	"8I,16A,16A,16A,16A,16A"	"(1,11,3,12,5,14,7,16,9,2,10,4,13,6,15,8)"
"20922789888000.a"	"18A"	18	9686476800	NULL	"9A,6M,18A,18A,18A,18A"	"(2,12,3,9,6,16,13,15,4)(7,14)"
"20922789888000.a"	"18B"	18	48432384000	NULL	"9A,6T,18B,18B,18B,18B"	"(1,3,4,5,11,6,13,10,16)(2,7)(8,14)"
"20922789888000.a"	"18C"	18	48432384000	NULL	"9A,6S,18C,18C,18C,18C"	"(1,9,16,13,2,10,7,14,12)(3,5)(4,11)(6,8)"
"20922789888000.a"	"18D"	18	96864768000	NULL	"9B,6T,18D,18D,18D,18D"	"(1,4,8,3,6,11,15,7,2)(5,12,16)(9,14)(10,13)"
"20922789888000.a"	"18E"	18	193729536000	NULL	"9B,6M,18E,18E,18E,18E"	"(1,4,13,2,7,3,11,8,10)(6,15,12)(9,14)"
"20922789888000.a"	"18F"	18	387459072000	NULL	"9C,6S,18F,18F,18F,18F"	"(1,14,7,5,15,6,4,10,3)(8,9,11,12,16,13)"
"20922789888000.a"	"20A"	20	207567360	NULL	"10B,20A,4A,20A,20A,20A"	"(1,6,7,11,4)(3,9,14,5)"
"20922789888000.a"	"20B"	20	4358914560	NULL	"10B,20B,4B,20B,20B,20B"	"(1,15,10,11,2)(5,9,12,7)(8,14)"
"20922789888000.a"	"20C"	20	21794572800	NULL	"10E,20C,4C,20C,20C,20C"	"(2,15,8,4,16)(3,10,9,14)(5,6,12,7)"
"20922789888000.a"	"20D"	20	21794572800	NULL	"10B,20D,4F,20D,20D,20D"	"(1,6)(3,5,9,10)(4,15,7,8,14)(11,16)(12,13)"
"20922789888000.a"	"20E"	20	21794572800	NULL	"10B,20E,4D,20E,20E,20E"	"(1,8,12,13,9)(2,15)(3,5)(4,16,7,14)"
"20922789888000.a"	"20F"	20	52306974720	NULL	"10I,20F,4B,20F,20F,20F"	"(1,13,3,10,2)(4,12,15,5,9)(6,11)(7,14,16,8)"
"20922789888000.a"	"20G"	20	52306974720	NULL	"10I,20G,4A,20G,20G,20G"	"(1,7,12,6,16)(2,5,3,11,15)(4,10,8,13)"
"20922789888000.a"	"20H"	20	65383718400	NULL	"10E,20H,4G,20H,20H,20H"	"(1,4,11,16)(2,9,15,14,6)(3,10,12,13)(7,8)"
"20922789888000.a"	"20I"	20	261534873600	NULL	"10I,20I,4E,20I,20I,20I"	"(1,11,2,16,5,14,10,4,13,6)(3,7)(8,9,15,12)"
"20922789888000.a"	"20J"	20	261534873600	NULL	"10I,20J,4I,20J,20J,20J"	"(1,14,10,11)(2,15,6,5,13,16,3,7,12,4)"
"20922789888000.a"	"21A"	21	1383782400	NULL	"21A,7A,21A,3A,21A,21A"	"(1,14,9,11,5,2,4)(8,15,10)"
"20922789888000.a"	"21B"	21	18450432000	NULL	"21B,7A,21B,3C,21B,21B"	"(1,13,9)(2,5,12,6,8,16,11)(3,4,15)(7,10,14)"
"20922789888000.a"	"21C"	21	27675648000	NULL	"21C,7A,21C,3B,21C,21C"	"(1,15,6,10,5,16,8)(2,11,3)(9,12,14)"
"20922789888000.a"	"22A"	22	158505984000	NULL	"11A,22A,22A,22A,2A,22A"	"(1,10)(2,4,6,3,16,11,5,8,13,14,12)"
"20922789888000.a"	"22B"	22	237758976000	NULL	"11A,22B,22B,22B,2B,22B"	"(1,10,6,4,12,16,14,11,13,9,7)(3,5)(8,15)"
"20922789888000.a"	"24A"	24	7264857600	NULL	"12E,8A,24A,24A,24A,24A"	"(1,11,13)(3,12,14,6,9,5,10,7)"
"20922789888000.a"	"24B"	24	72648576000	NULL	"12N,8B,24B,24B,24B,24B"	"(1,11,13)(2,9)(3,7,16,14,5,4,6,8)(10,12,15)"
"20922789888000.a"	"24C"	24	72648576000	NULL	"12N,8A,24C,24C,24C,24C"	"(1,8,10)(2,16,9,6,7,4,11,3)(5,15,14)"
"20922789888000.a"	"24D"	24	72648576000	NULL	"12E,8B,24D,24D,24D,24D"	"(1,15,9,8,12,11,4,2)(3,5)(6,10,7)"
"20922789888000.a"	"24E"	24	108972864000	NULL	"12E,8D,24E,24E,24E,24E"	"(1,5)(2,9,15,14,13,8,7,3)(4,10,6)(11,12)"
"20922789888000.a"	"24F"	24	217945728000	NULL	"12N,8E,24F,24F,24F,24F"	"(1,8,9,5,14,3)(2,16,7,11,6,15,13,4)"
"20922789888000.a"	"24G"	24	217945728000	NULL	"12U,8F,24G,24G,24G,24G"	"(1,4,10,2,3,12,14,7)(5,6,11,15)(9,13,16)"
"20922789888000.a"	"24H"	24	217945728000	NULL	"12N,8C,24H,24H,24H,24H"	"(1,15,6,14,10,7,11,16)(2,3,13,12,4,9)(5,8)"
"20922789888000.a"	"26A"	26	804722688000	NULL	"13A,26A,26A,26A,26A,2A"	"(1,7,14,2,5,8,11,15,3,4,6,9,13)(10,12)"
"20922789888000.a"	"28A"	28	6227020800	NULL	"14B,28A,28A,4A,28A,28A"	"(1,11,8,5)(2,9,12,7,16,4,10)"
"20922789888000.a"	"28B"	28	62270208000	NULL	"14B,28B,28B,4B,28B,28B"	"(1,6,8,15,11,3,16)(4,13)(9,12,14,10)"
"20922789888000.a"	"28C"	28	93405312000	NULL	"14C,28C,28C,4C,28C,28C"	"(1,2,12,10)(3,14,5,4,8,7,15)(6,16,13,11)"
"20922789888000.a"	"28D"	28	93405312000	NULL	"14B,28D,28D,4D,28D,28D"	"(1,8,14,7,12,16,10)(2,4)(3,13)(6,15,11,9)"
"20922789888000.a"	"30A"	30	968647680	NULL	"15A,10A,6A,30A,30A,30A"	"(1,2,16,12,3)(7,8)(9,10,11)"
"20922789888000.a"	"30B"	30	3632428800	NULL	"15A,10E,6G,30B,30B,30B"	"(1,13,11)(2,16,4,8,15)(3,9)(5,12)(6,7)(10,14)"
"20922789888000.a"	"30C"	30	5811886080	NULL	"15B,10C,6B,30C,30C,30C"	"(1,5,7,12,11)(3,16,10,6,14,4)"
"20922789888000.a"	"30D"	30	7264857600	NULL	"15A,10B,6C,30D,30D,30D"	"(1,2,11,10,15)(4,13,6)(5,12)(7,9)"
"20922789888000.a"	"30E"	30	12915302400	NULL	"15C,10A,6M,30E,30E,30E"	"(1,11,8,5,10)(2,13,9)(3,4,16)(6,12,15)(7,14)"
"20922789888000.a"	"30F"	30	14529715200	NULL	"15A,10C,6E,30F,30F,30F"	"(1,4,11)(3,16,6,13,5)(7,14)(9,10)(12,15)"
"20922789888000.a"	"30G"	30	19372953600	NULL	"15B,10A,6D,30G,30G,30G"	"(1,14,10)(2,13,15,16,12)(4,11,7)(5,8)"
"20922789888000.a"	"30H"	30	29059430400	NULL	"15B,10B,6I,30H,30H,30H"	"(1,4,11,7,6)(2,12,13)(3,14)(5,9)(8,10,16)"
"20922789888000.a"	"30I"	30	58118860800	NULL	"15B,10E,6F,30I,30I,30I"	"(2,4,6,8,14)(3,16,11,5,15,12)(10,13)"
"20922789888000.a"	"30J"	30	69742632960	NULL	"15D,10G,6B,30J,30J,30J"	"(1,15,3,9,16,14)(2,10,8,13,4)(5,7,11,12,6)"
"20922789888000.a"	"30K"	30	69742632960	NULL	"15E,10H,6A,30K,30K,30K"	"(1,14,7)(2,6,10,5,3)(4,8,16,15,11)(12,13)"
"20922789888000.a"	"30L"	30	87178291200	NULL	"15B,10D,6N,30L,30L,30L"	"(1,5,7,14,10,6)(2,8,4,12,16)(3,11)(9,15)"
"20922789888000.a"	"30M"	30	116237721600	NULL	"15E,10F,6K,30M,30M,30M"	"(1,3,6)(2,15,13,5,8,7,4,16,12,9)"
"20922789888000.a"	"30N"	30	116237721600	NULL	"15D,10F,6L,30N,30N,30N"	"(1,9,10)(2,16,11,6,7,3,13,5,8,14)(4,15,12)"
"20922789888000.a"	"30O"	30	116237721600	NULL	"15C,10E,6X,30O,30O,30O"	"(1,8,13,14,4)(2,11,5,15,9,3)(6,12,10)(7,16)"
"20922789888000.a"	"30P"	30	116237721600	NULL	"15C,10C,6J,30P,30P,30P"	"(1,9,4,12,8)(2,16,13,3,6,15)(5,14,10)"
"20922789888000.a"	"30Q"	30	348713164800	NULL	"15D,10J,6O,30Q,30Q,30Q"	"(1,5,9,12,15,3,6,7,10,14)(2,4,8,11,13,16)"
"20922789888000.a"	"30R"	30	348713164800	NULL	"15E,10K,6H,30R,30R,30R"	"(1,6,14,16,10,3,4,7,15,9)(5,8)(11,13,12)"
"20922789888000.a"	"33A"	33	317011968000	NULL	"33A,11A,33A,33A,3A,33A"	"(2,13,11,6,12,8,16,4,14,5,3)(7,9,15)"
"20922789888000.a"	"35A"	35	24908083200	NULL	"35A,35A,7A,5A,35A,35A"	"(2,4,7,9,10,16,12)(3,6,15,14,13)"
"20922789888000.a"	"36A"	36	96864768000	NULL	"18B,12I,36A,36A,36A,36A"	"(1,5,16,4,6,8,15,14,9)(2,13,3,10)"
"20922789888000.a"	"36B"	36	193729536000	NULL	"18D,12I,36B,36B,36B,36B"	"(1,11,4,15,8,7,3,2,6)(5,16,12)(9,10,14,13)"
"20922789888000.a"	"36C"	36	290594304000	NULL	"18B,12M,36C,36C,36C,36C"	"(1,6,3,13,4,10,5,16,11)(2,8,7,14)(12,15)"
"20922789888000.a"	"39A"	39	536481792000	NULL	"39A,13A,39A,39A,39A,3A"	"(1,6,11,16,4,9,14,3,8,13,2,7,12)(5,10,15)"
"20922789888000.a"	"40A"	40	87178291200	NULL	"20C,40A,8A,40A,40A,40A"	"(2,4,15,16,8)(3,7,10,5,9,6,14,12)"
"20922789888000.a"	"40B"	40	261534873600	NULL	"20C,40B,8B,40B,40B,40B"	"(1,4,8,15,13,12,11,14)(2,5)(3,10,9,7,16)"
"20922789888000.a"	"42A"	42	20756736000	NULL	"21A,14D,42A,6E,42A,42A"	"(1,5,14,2,9,4,11)(3,12)(6,13)(7,16)(8,10,15)"
"20922789888000.a"	"42B"	42	20756736000	NULL	"21A,14A,42B,6A,42B,42B"	"(2,16,4,12,7,13,14)(3,5)(8,10,9)"
"20922789888000.a"	"42C"	42	62270208000	NULL	"21A,14B,42C,6C,42C,42C"	"(1,3)(4,7,6)(5,16,13,11,14,15,10)(9,12)"
"20922789888000.a"	"42D"	42	83026944000	NULL	"21C,14A,42D,6D,42D,42D"	"(1,16,5,10,15,12,3)(2,6,4)(7,11)(8,9,13)"
"20922789888000.a"	"42E"	42	83026944000	NULL	"21C,14D,42E,6B,42E,42E"	"(1,8,10,11,15,2)(3,4,13,7,16,6,14)"
"20922789888000.a"	"42F"	42	166053888000	NULL	"21B,14D,42F,6J,42F,42F"	"(1,3,13,4,9,15)(2,8,5,16,12,11,6)(7,14,10)"
"20922789888000.a"	"42G"	42	249080832000	NULL	"21C,14C,42G,6F,42G,42G"	"(1,5,15,16,6,8,10)(2,14,11,9,3,12)(4,13)"
"20922789888000.a"	"44A"	44	475517952000	NULL	"22B,44A,44A,44A,4A,44A"	"(1,14,10,11,6,13,4,9,12,7,16)(3,8,5,15)"
"20922789888000.a"	"45A"	45	232475443200	NULL	"45A,15C,9A,45A,45A,45A"	"(1,10,5,8,11)(2,6,4,9,15,3,13,12,16)"
"20922789888000.a"	"55A"	55	380414361600	NULL	"55A,55A,11A,55A,5A,55A"	"(1,5,8,11,14)(2,4,7,10,13,16,3,6,9,12,15)"
"20922789888000.a"	"56A"	56	373621248000	NULL	"28C,56A,56A,8A,56A,56A"	"(1,13,2,11,12,6,10,16)(3,8,14,7,5,15,4)"
"20922789888000.a"	"60A"	60	14529715200	NULL	"30D,20A,12A,60A,60A,60A"	"(1,9,7,8,14)(2,12,16,4)(10,15,11)"
"20922789888000.a"	"60B"	60	43589145600	NULL	"30B,20C,12E,60B,60B,60B"	"(1,11,13)(2,8,16,15,4)(3,14,9,10)(5,7,12,6)"
"20922789888000.a"	"60C"	60	43589145600	NULL	"30D,20E,12F,60C,60C,60C"	"(1,12,9,8,13)(2,15)(3,5)(4,14,7,16)(6,10,11)"
"20922789888000.a"	"60D"	60	58118860800	NULL	"30H,20A,12C,60D,60D,60D"	"(1,7,4,6,11)(2,13,12)(3,5,14,9)(8,16,10)"
"20922789888000.a"	"60E"	60	87178291200	NULL	"30D,20B,12B,60E,60E,60E"	"(1,10,2,15,11)(4,6,13)(5,7,12,9)(8,14)"
"20922789888000.a"	"60F"	60	174356582400	NULL	"30H,20D,12D,60F,60F,60F"	"(1,12,11,6,13,16)(3,10,9,5)(4,7,14,15,8)"
"20922789888000.a"	"63A"	63	332107776000	NULL	"63A,21B,63A,9A,63A,63A"	"(1,2,6,14,16,9,12)(3,15,11,4,13,10,8,5,7)"
"20922789888000.a"	"66A"	66	317011968000	NULL	"33A,22A,66A,66A,6A,66A"	"(1,10)(2,16,13,4,11,14,6,5,12,3,8)(7,15,9)"
"20922789888000.a"	"70A"	70	74724249600	NULL	"35A,70A,14B,10B,70A,70A"	"(1,8)(2,10,4,16,7,12,9)(3,14,6,13,15)(5,11)"
"20922789888000.a"	"70B"	70	149448499200	NULL	"35A,70B,14A,10A,70B,70B"	"(1,10,12,15,3,8,2)(4,9,14,7,11)(6,13)"
"20922789888000.a"	"84A"	84	124540416000	NULL	"42C,28A,84A,12A,84A,84A"	"(1,9,3,12)(4,6,7)(5,14,16,15,13,10,11)"
"20922789888000.a"	"84B"	84	124540416000	NULL	"42C,28B,84B,12B,84B,84B"	"(1,3,15,6,16,11,8)(2,7,5)(4,13)(9,10,14,12)"
"20922789888000.a"	"90A"	90	232475443200	NULL	"45A,30E,18A,90A,90A,90A"	"(1,8,10,11,5)(2,3,6,13,4,12,9,16,15)(7,14)"
"20922789888000.a"	"105A"	105	199264665600	NULL	"105A,35A,21A,15A,105A,105A"	"(1,4,16,8,7)(2,14,3,9,15,12,11)(6,13,10)"
"20922789888000.a"	"120A"	120	174356582400	NULL	"60B,40A,24A,120A,120A,120A"	"(1,13,11)(2,15,8,4,16)(3,5,14,7,9,12,10,6)"
"20922789888000.a"	"140A"	140	149448499200	NULL	"70A,140A,28A,20A,140A,140A"	"(1,11,8,5)(2,7,10,12,4,9,16)(3,13,14,15,6)"


# Group --
#    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 $B$.


# Label --
#    The **label** of a rational conjugacy class of a group $G$ has the format $NA$ where $N$ is the order of elements in the conjugacy class, $A$ is a sequence of capital letters.


#    The **label** of a complex conjugacy class of a group $G$ has the format $NAj$ where $NA$ is the label of the division containing it, (so $N$ is the order of elements in the conjugacy class), and $j$ is an enumeration of class within that rational conjugacy class ($j$ is omitted if there is a single class within rational conjugacy classes).


# Order --
#    All elements in a particular conjugacy class are of the same order in the group.


# Size --
#    The **size** of a conjugacy class of a finite group is the cardinality of the set of elements conjugate to each other.

#    By the Orbit-Stabilizer Theorem, the size of a conjugacy class divides the order of the group. Since conjugacy classes partition a group, the sum of the sizes of the conjugacy classes equals the size of the group.

#    A conjugacy class is of size $1$ if and only if the element is in the center of the group.




# Centralizer --
#    If $G$ is a group and $H$ is a subgroup of $G$, then the **centralizer** of $H$ in $G$ is
#    \[ C_G(H) = \{g\in G\mid gh=hg \text{ for all } h\in H\}.\]


# Powers --
#    If $G$ is a group, $g\in G$ is an element of a conjugacy class $P$, and $n$ is a positive integer, then $nP$ denotes the conjugacy class of the element $g^n$.


# Representative --
#    A representative of each conjugacy class is given in different formats depending on how the abstract group is stored in the database.

#    For *permutation groups* the representative is given as a permutation of degree given in the Construction section of this group's main page.

#    For *matrix groups* the representatives are given by matrices in the group described in the Construction section of this group's main page.

#    For solvable groups, the representatives are given as words in the generators from the presentation given in the Construction section of this group's main page.