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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
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Num. of char. subgroups Num. of aut. classes Number of divisions
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Results (1-50 of 8418 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
32.18 $D_{16}$ $2^{5}$ $2^{4}$ 11 $C_2$ $D_8$ $C_8$ $C_{2}^{2}$ Nilpotent - 4
32.19 $\SD_{32}$ $2^{5}$ $2^{4}$ 11 $C_2$ $D_8$ $C_8$ $C_{2}^{2}$ Nilpotent - 4
32.20 $Q_{32}$ $2^{5}$ $2^{4}$ 11 $C_2$ $D_8$ $C_8$ $C_{2}^{2}$ Nilpotent - 4
64.32 $C_2\wr C_4$ $2^{6}$ $2^{3}$ 13 $C_2$ $C_2^3:C_4$ $C_2^3$ $C_{2} \times C_{4}$ Nilpotent - 4
64.33 $C_2^3.D_4$ $2^{6}$ $2^{3}$ 13 $C_2$ $C_2^3:C_4$ $C_2^3$ $C_{2} \times C_{4}$ Nilpotent - 4
64.34 $C_4^2:C_4$ $2^{6}$ $2^{2}$ 13 $C_2$ $C_2^3:C_4$ $C_2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 4
64.35 $C_4^2:C_4$ $2^{6}$ $2^{2}$ 13 $C_2$ $C_2^3:C_4$ $C_2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 4
64.36 $C_4^2.C_4$ $2^{6}$ $2^{3}$ 13 $C_2$ $C_2^3:C_4$ $C_2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 4
64.37 $C_4^2.C_4$ $2^{6}$ $2^{3}$ 13 $C_2$ $C_2^3:C_4$ $C_2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 4
64.38 $D_8:C_4$ $2^{6}$ $2^{4}$ 22 $C_2^2$ $D_8$ $C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
64.39 $Q_{16}:C_4$ $2^{6}$ $2^{4}$ 22 $C_2^2$ $D_8$ $C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
64.40 $C_4.D_8$ $2^{6}$ $2^{4}$ 22 $C_4$ $D_8$ $C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
64.41 $D_8:C_4$ $2^{6}$ $2^{4}$ 16 $C_2$ $D_4:C_4$ $C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
64.42 $\OD_{32}:C_2$ $2^{6}$ $2^{4}$ 16 $C_2$ $D_4:C_4$ $C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
64.43 $C_4.D_8$ $2^{6}$ $2^{4}$ 16 $C_2$ $D_4:C_4$ $C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
64.46 $C_{16}:C_4$ $2^{6}$ $2^{4}$ 16 $C_2$ $C_8:C_4$ $C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
64.47 $C_{16}:C_4$ $2^{6}$ $2^{4}$ 22 $C_2^2$ $D_8$ $C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
64.48 $C_{16}:C_4$ $2^{6}$ $2^{4}$ 22 $C_2^2$ $D_8$ $C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
64.49 $C_{16}.C_4$ $2^{6}$ $2^{4}$ 22 $C_4$ $D_8$ $C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
64.186 $C_2\times D_{16}$ $2^{6}$ $2^{4}$ 22 $C_2^2$ $D_8$ $C_8$ $C_{2}^{3}$ Nilpotent - 4
64.187 $C_2\times \SD_{32}$ $2^{6}$ $2^{4}$ 22 $C_2^2$ $D_8$ $C_8$ $C_{2}^{3}$ Nilpotent - 4
64.188 $C_2\times Q_{32}$ $2^{6}$ $2^{4}$ 22 $C_2^2$ $D_8$ $C_8$ $C_{2}^{3}$ Nilpotent - 4
64.189 $D_{16}:C_2$ $2^{6}$ $2^{4}$ 22 $C_4$ $D_8$ $C_8$ $C_{2}^{3}$ Nilpotent - 4
64.190 $D_{16}:C_2$ $2^{6}$ $2^{4}$ 16 $C_2$ $C_2\times D_8$ $C_8$ $C_{2}^{3}$ Nilpotent - 4
64.191 $Q_{32}:C_2$ $2^{6}$ $2^{4}$ 16 $C_2$ $C_2\times D_8$ $C_8$ $C_{2}^{3}$ Nilpotent - 4
96.61 $C_3\times D_{16}$ $2^{5} \cdot 3$ $2^{4} \cdot 3$ 33 $C_6$ $D_8$ $C_8$ $C_{2} \times C_{6}$ Nilpotent - 4
96.62 $C_3\times \SD_{32}$ $2^{5} \cdot 3$ $2^{4} \cdot 3$ 33 $C_6$ $D_8$ $C_8$ $C_{2} \times C_{6}$ Nilpotent - 4
96.63 $C_3\times Q_{32}$ $2^{5} \cdot 3$ $2^{4} \cdot 3$ 33 $C_6$ $D_8$ $C_8$ $C_{2} \times C_{6}$ Nilpotent - 4
128.48 $C_2^4:C_8$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2^3:C_4$ $C_2^3$ $C_{2} \times C_{8}$ Nilpotent - 4
128.49 $C_2^3.\OD_{16}$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2^3:C_4$ $C_2^3$ $C_{2} \times C_{8}$ Nilpotent - 4
128.50 $(C_2\times D_4):C_8$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2^3:C_4$ $C_2\times C_4$ $C_{2} \times C_{8}$ Nilpotent - 4
128.51 $(C_2\times Q_8):C_8$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2^3:C_4$ $C_2\times C_4$ $C_{2} \times C_{8}$ Nilpotent - 4
128.52 $C_2^4.C_8$ $2^{7}$ $2^{4}$ 26 $C_4$ $C_2^3:C_4$ $C_2^3$ $C_{2} \times C_{8}$ Nilpotent - 4
128.53 $C_2^3.\OD_{16}$ $2^{7}$ $2^{4}$ 26 $C_4$ $C_2^3:C_4$ $C_2\times C_4$ $C_{2} \times C_{8}$ Nilpotent - 4
128.56 $C_4^2:C_8$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2^3:C_4$ $C_2\times C_4$ $C_{2} \times C_{8}$ Nilpotent - 4
128.57 $C_4^2:C_8$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2^3:C_4$ $C_2\times C_4$ $C_{2} \times C_{8}$ Nilpotent - 4
128.58 $C_2^3.\OD_{16}$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2^3:C_4$ $C_2^3$ $C_{2} \times C_{8}$ Nilpotent - 4
128.59 $C_4^2.C_8$ $2^{7}$ $2^{4}$ 26 $C_4$ $C_2^3:C_4$ $C_2\times C_4$ $C_{2} \times C_{8}$ Nilpotent - 4
128.60 $(C_2\times C_8).D_4$ $2^{7}$ $2^{4}$ 26 $C_4$ $C_2^3:C_4$ $C_2^3$ $C_{2} \times C_{8}$ Nilpotent - 4
128.63 $D_8:C_8$ $2^{7}$ $2^{4}$ 44 $C_2\times C_4$ $D_8$ $C_8$ $C_{2} \times C_{8}$ Nilpotent - 4
128.64 $Q_{16}:C_8$ $2^{7}$ $2^{4}$ 44 $C_2\times C_4$ $D_8$ $C_8$ $C_{2} \times C_{8}$ Nilpotent - 4
128.65 $D_8:C_8$ $2^{7}$ $2^{4}$ 32 $C_2^2$ $D_4:C_4$ $C_8$ $C_{2} \times C_{8}$ Nilpotent - 4
128.66 $Q_{16}:C_8$ $2^{7}$ $2^{4}$ 32 $C_2^2$ $D_4:C_4$ $C_8$ $C_{2} \times C_{8}$ Nilpotent - 4
128.67 $C_8\wr C_2$ $2^{7}$ $2^{4}$ 44 $C_8$ $D_8$ $C_8$ $C_{2} \times C_{8}$ Nilpotent - 4
128.68 $D_8:C_8$ $2^{7}$ $2^{4}$ 32 $C_4$ $D_4:C_4$ $C_8$ $C_{2} \times C_{8}$ Nilpotent - 4
128.71 $C_2^3.D_8$ $2^{7}$ $2^{4}$ 20 $C_2$ $C_2^2.D_8$ $C_2\times C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
128.72 $C_2^3.D_8$ $2^{7}$ $2^{4}$ 20 $C_2$ $C_2^2.D_8$ $C_2\times C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
128.73 $C_2^3.\SD_{16}$ $2^{7}$ $2^{4}$ 20 $C_2$ $C_2^2.D_8$ $C_2\times C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
128.74 $C_2^3.\SD_{16}$ $2^{7}$ $2^{4}$ 20 $C_2$ $C_2^2.D_8$ $C_2\times C_8$ $C_{2} \times C_{4}$ Nilpotent - 4
128.75 $C_2^3.D_8$ $2^{7}$ $2^{3}$ 23 $C_2^2$ $C_2^3:C_4$ $C_2^2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 4
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