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Note: Search results may be incomplete due to uncomputed quantities: Outer aut. group order (4830 objects)

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Order Exponent Nilpotency class Nilpotent
Center Commutator Central quotient Abelianization
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Perfect Direct product Semidirect product Wreath product
Automorphism group Automorphisms Transitive degree Permutation degree
Minimal degree of $\C$-irrep Minimal degree of $\Q$-irrep Minimal degree of $\C$-rep Minimal 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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Results (22 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
128.134 $C_4^2.D_4$ $2^{7}$ $2^{3}$ $17$ $C_2$ $C_2\wr C_4$ $C_2\times D_4$ $C_{2} \times C_{4}$ Nilpotent - 5
128.135 $C_4^2.D_4$ $2^{7}$ $2^{3}$ $17$ $C_2$ $C_2\wr C_4$ $C_2\times D_4$ $C_{2} \times C_{4}$ Nilpotent - 5
128.136 $C_4^2.D_4$ $2^{7}$ $2^{3}$ $17$ $C_2$ $C_2\wr C_4$ $C_2\times Q_8$ $C_{2} \times C_{4}$ Nilpotent - 5
128.137 $C_4^2.D_4$ $2^{7}$ $2^{3}$ $17$ $C_2$ $C_2\wr C_4$ $C_2\times Q_8$ $C_{2} \times C_{4}$ Nilpotent - 5
128.146 $(C_4\times C_8):C_4$ $2^{7}$ $2^{3}$ $17$ $C_2$ $C_4^2:C_4$ $C_4^2$ $C_{2} \times C_{4}$ Nilpotent - 5
128.912 $Q_{32}:C_4$ $2^{7}$ $2^{4}$ $23$ $C_2$ $D_8:C_4$ $C_8$ $C_{2}^{2} \times C_{4}$ Nilpotent - 4
128.913 $D_{16}:C_4$ $2^{7}$ $2^{4}$ $23$ $C_2$ $D_8:C_4$ $C_8$ $C_{2}^{2} \times C_{4}$ Nilpotent - 4
128.929 $C_4^2:D_4$ $2^{7}$ $2^{3}$ $20$ $C_2$ $C_2\wr C_2^2$ $C_2\times D_4$ $C_{2}^{3}$ Nilpotent - 4
128.932 $C_4^2:D_4$ $2^{7}$ $2^{3}$ $17$ $C_2$ $C_2\wr C_2^2$ $C_2\times D_4$ $C_{2}^{3}$ Nilpotent - 4
256.377 $D_{16}:C_8$ $2^{8}$ $2^{5}$ $34$ $C_2$ $D_8:C_8$ $C_{16}$ $C_{2} \times C_{8}$ Nilpotent - 5
256.445 $C_{32}:C_8$ $2^{8}$ $2^{5}$ $34$ $C_2$ $C_{16}:C_8$ $C_{16}$ $C_{2} \times C_{8}$ Nilpotent - 5
256.511 $C_2^2.C_2\wr C_4$ $2^{8}$ $2^{4}$ $19$ $C_2$ $C_4^2.D_4$ $C_4.Q_8$ $C_{2} \times C_{4}$ Nilpotent - 6
256.512 $C_2^2.C_2\wr C_4$ $2^{8}$ $2^{4}$ $19$ $C_2$ $C_4^2.D_4$ $C_4.Q_8$ $C_{2} \times C_{4}$ Nilpotent - 6
256.513 $C_2^2.C_2\wr C_4$ $2^{8}$ $2^{4}$ $19$ $C_2$ $C_4^2.D_4$ $C_4.Q_8$ $C_{2} \times C_{4}$ Nilpotent - 6
256.514 $C_2^2.C_2\wr C_4$ $2^{8}$ $2^{4}$ $19$ $C_2$ $C_4^2.D_4$ $C_4.Q_8$ $C_{2} \times C_{4}$ Nilpotent - 6
256.6665 $C_4^2.(C_2\times D_4)$ $2^{8}$ $2^{3}$ $22$ $C_2$ $C_2\wr D_4$ $C_4^2:C_2$ $C_{2}^{3}$ Nilpotent - 5
256.6666 $C_4^2.(C_2\times D_4)$ $2^{8}$ $2^{3}$ $22$ $C_2$ $C_2\wr D_4$ $C_4^2:C_2$ $C_{2}^{3}$ Nilpotent - 5
256.6667 $C_4^2.(C_2\times D_4)$ $2^{8}$ $2^{3}$ $22$ $C_2$ $C_2\wr D_4$ $C_4^2:C_2$ $C_{2}^{3}$ Nilpotent - 5
256.6668 $C_4^2.(C_2\times D_4)$ $2^{8}$ $2^{3}$ $22$ $C_2$ $C_2\wr D_4$ $C_4^2:C_2$ $C_{2}^{3}$ Nilpotent - 5
512.1743 $C_2^3.C_2\wr C_4$ $2^{9}$ $2^{4}$ $38$ $C_2$ $(C_2\times C_4^2).D_4$ $C_4.Q_8$ $C_{2} \times C_{8}$ Nilpotent - 6
512.58302 $D_{32}:C_8$ $2^{9}$ $2^{5}$ $47$ $C_2$ $D_{16}:C_8$ $C_{16}$ $C_{2}^{2} \times C_{8}$ Nilpotent - 5
2048.ctr $D_{64}:C_{16}$ $2^{11}$ $2^{6}$ $95$ $C_2$ $D_{32}:C_{16}$ $C_{32}$ $C_{2}^{2} \times C_{16}$ Nilpotent - 6
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