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Order Exponent Nilpotency class Nilpotent
Center Commutator Central quotient Abelianization
Abelian Cyclic Solvable Simple
Perfect Direct product Semidirect product Wreath product
Automorphism group Automorphisms Min. transitive degree Min. permutation degree
Number of subgroups Num. of normal subs Num. of conj. classes
Order statistics Family Order factorization Commutator length
Min. degree of $\C$-irrep Min. degree of $\Q$-irrep Min. degree of $\C$-rep Min. degree of $\Q$-rep
Outer aut. group Outer automorphisms Metabelian Metacyclic
Almost simple Quasisimple A-group Z-group
Frattini subgroup Derived length Rank Schur multiplier
Supersolvable Monomial Rational
Num. of char. subgroups Num. of aut. classes Number of divisions
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Results (1-50 of 991 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
2.1 $C_2$ $2$ $2$ 2 $C_2$ $C_1$ $C_1$ $C_{2}$ Cyclic
4.2 $C_2^2$ $2^{2}$ $2$ 4 $C_2^2$ $C_1$ $C_1$ $C_{2}^{2}$ Abelian - 2
6.1 $S_3$ $2 \cdot 3$ $2 \cdot 3$ 3 $C_1$ $S_3$ $C_3$ $C_{2}$ Solvable - 2
8.3 $D_4$ $2^{3}$ $2^{2}$ 5 $C_2$ $C_2^2$ $C_2$ $C_{2}^{2}$ Nilpotent - 2
10.1 $D_5$ $2 \cdot 5$ $2 \cdot 5$ 4 $C_1$ $D_5$ $C_5$ $C_{2}$ Solvable - 2
12.4 $D_6$ $2^{2} \cdot 3$ $2 \cdot 3$ 6 $C_2$ $S_3$ $C_3$ $C_{2}^{2}$ Solvable - 2
14.1 $D_7$ $2 \cdot 7$ $2 \cdot 7$ 5 $C_1$ $D_7$ $C_7$ $C_{2}$ Solvable - 2
16.7 $D_8$ $2^{4}$ $2^{3}$ 7 $C_2$ $D_4$ $C_4$ $C_{2}^{2}$ Nilpotent - 3
18.1 $D_9$ $2 \cdot 3^{2}$ $2 \cdot 3^{2}$ 6 $C_1$ $D_9$ $C_9$ $C_{2}$ Solvable - 2
20.4 $D_{10}$ $2^{2} \cdot 5$ $2 \cdot 5$ 8 $C_2$ $D_5$ $C_5$ $C_{2}^{2}$ Solvable - 2
22.1 $D_{11}$ $2 \cdot 11$ $2 \cdot 11$ 7 $C_1$ $D_{11}$ $C_{11}$ $C_{2}$ Solvable - 2
24.6 $D_{12}$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ 9 $C_2$ $D_6$ $C_6$ $C_{2}^{2}$ Solvable - 2
26.1 $D_{13}$ $2 \cdot 13$ $2 \cdot 13$ 8 $C_1$ $D_{13}$ $C_{13}$ $C_{2}$ Solvable - 2
28.3 $D_{14}$ $2^{2} \cdot 7$ $2 \cdot 7$ 10 $C_2$ $D_7$ $C_7$ $C_{2}^{2}$ Solvable - 2
30.3 $D_{15}$ $2 \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ 9 $C_1$ $D_{15}$ $C_{15}$ $C_{2}$ Solvable - 2
32.18 $D_{16}$ $2^{5}$ $2^{4}$ 11 $C_2$ $D_8$ $C_8$ $C_{2}^{2}$ Nilpotent - 4
34.1 $D_{17}$ $2 \cdot 17$ $2 \cdot 17$ 10 $C_1$ $D_{17}$ $C_{17}$ $C_{2}$ Solvable - 2
36.4 $D_{18}$ $2^{2} \cdot 3^{2}$ $2 \cdot 3^{2}$ 12 $C_2$ $D_9$ $C_9$ $C_{2}^{2}$ Solvable - 2
38.1 $D_{19}$ $2 \cdot 19$ $2 \cdot 19$ 11 $C_1$ $D_{19}$ $C_{19}$ $C_{2}$ Solvable - 2
40.6 $D_{20}$ $2^{3} \cdot 5$ $2^{2} \cdot 5$ 13 $C_2$ $D_{10}$ $C_{10}$ $C_{2}^{2}$ Solvable - 2
42.5 $D_{21}$ $2 \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ 12 $C_1$ $D_{21}$ $C_{21}$ $C_{2}$ Solvable - 2
44.3 $D_{22}$ $2^{2} \cdot 11$ $2 \cdot 11$ 14 $C_2$ $D_{11}$ $C_{11}$ $C_{2}^{2}$ Solvable - 2
46.1 $D_{23}$ $2 \cdot 23$ $2 \cdot 23$ 13 $C_1$ $D_{23}$ $C_{23}$ $C_{2}$ Solvable - 2
48.7 $D_{24}$ $2^{4} \cdot 3$ $2^{3} \cdot 3$ 15 $C_2$ $D_{12}$ $C_{12}$ $C_{2}^{2}$ Solvable - 2
50.1 $D_{25}$ $2 \cdot 5^{2}$ $2 \cdot 5^{2}$ 14 $C_1$ $D_{25}$ $C_{25}$ $C_{2}$ Solvable - 2
52.4 $D_{26}$ $2^{2} \cdot 13$ $2 \cdot 13$ 16 $C_2$ $D_{13}$ $C_{13}$ $C_{2}^{2}$ Solvable - 2
54.1 $D_{27}$ $2 \cdot 3^{3}$ $2 \cdot 3^{3}$ 15 $C_1$ $D_{27}$ $C_{27}$ $C_{2}$ Solvable - 2
56.5 $D_{28}$ $2^{3} \cdot 7$ $2^{2} \cdot 7$ 17 $C_2$ $D_{14}$ $C_{14}$ $C_{2}^{2}$ Solvable - 2
58.1 $D_{29}$ $2 \cdot 29$ $2 \cdot 29$ 16 $C_1$ $D_{29}$ $C_{29}$ $C_{2}$ Solvable - 2
60.12 $D_{30}$ $2^{2} \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ 18 $C_2$ $D_{15}$ $C_{15}$ $C_{2}^{2}$ Solvable - 2
62.1 $D_{31}$ $2 \cdot 31$ $2 \cdot 31$ 17 $C_1$ $D_{31}$ $C_{31}$ $C_{2}$ Solvable - 2
64.52 $D_{32}$ $2^{6}$ $2^{5}$ 19 $C_2$ $D_{16}$ $C_{16}$ $C_{2}^{2}$ Nilpotent - 5
66.3 $D_{33}$ $2 \cdot 3 \cdot 11$ $2 \cdot 3 \cdot 11$ 18 $C_1$ $D_{33}$ $C_{33}$ $C_{2}$ Solvable - 2
68.4 $D_{34}$ $2^{2} \cdot 17$ $2 \cdot 17$ 20 $C_2$ $D_{17}$ $C_{17}$ $C_{2}^{2}$ Solvable - 2
70.3 $D_{35}$ $2 \cdot 5 \cdot 7$ $2 \cdot 5 \cdot 7$ 19 $C_1$ $D_{35}$ $C_{35}$ $C_{2}$ Solvable - 2
72.6 $D_{36}$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 21 $C_2$ $D_{18}$ $C_{18}$ $C_{2}^{2}$ Solvable - 2
74.1 $D_{37}$ $2 \cdot 37$ $2 \cdot 37$ 20 $C_1$ $D_{37}$ $C_{37}$ $C_{2}$ Solvable - 2
76.3 $D_{38}$ $2^{2} \cdot 19$ $2 \cdot 19$ 22 $C_2$ $D_{19}$ $C_{19}$ $C_{2}^{2}$ Solvable - 2
78.5 $D_{39}$ $2 \cdot 3 \cdot 13$ $2 \cdot 3 \cdot 13$ 21 $C_1$ $D_{39}$ $C_{39}$ $C_{2}$ Solvable - 2
80.7 $D_{40}$ $2^{4} \cdot 5$ $2^{3} \cdot 5$ 23 $C_2$ $D_{20}$ $C_{20}$ $C_{2}^{2}$ Solvable - 2
82.1 $D_{41}$ $2 \cdot 41$ $2 \cdot 41$ 22 $C_1$ $D_{41}$ $C_{41}$ $C_{2}$ Solvable - 2
84.14 $D_{42}$ $2^{2} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ 24 $C_2$ $D_{21}$ $C_{21}$ $C_{2}^{2}$ Solvable - 2
86.1 $D_{43}$ $2 \cdot 43$ $2 \cdot 43$ 23 $C_1$ $D_{43}$ $C_{43}$ $C_{2}$ Solvable - 2
88.5 $D_{44}$ $2^{3} \cdot 11$ $2^{2} \cdot 11$ 25 $C_2$ $D_{22}$ $C_{22}$ $C_{2}^{2}$ Solvable - 2
90.3 $D_{45}$ $2 \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ 24 $C_1$ $D_{45}$ $C_{45}$ $C_{2}$ Solvable - 2
92.3 $D_{46}$ $2^{2} \cdot 23$ $2 \cdot 23$ 26 $C_2$ $D_{23}$ $C_{23}$ $C_{2}^{2}$ Solvable - 2
94.1 $D_{47}$ $2 \cdot 47$ $2 \cdot 47$ 25 $C_1$ $D_{47}$ $C_{47}$ $C_{2}$ Solvable - 2
96.6 $D_{48}$ $2^{5} \cdot 3$ $2^{4} \cdot 3$ 27 $C_2$ $D_{24}$ $C_{24}$ $C_{2}^{2}$ Solvable - 2
98.1 $D_{49}$ $2 \cdot 7^{2}$ $2 \cdot 7^{2}$ 26 $C_1$ $D_{49}$ $C_{49}$ $C_{2}$ Solvable - 2
100.4 $D_{50}$ $2^{2} \cdot 5^{2}$ $2 \cdot 5^{2}$ 28 $C_2$ $D_{25}$ $C_{25}$ $C_{2}^{2}$ Solvable - 2
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