C₂⁵×AGL(1,ℤ/8) #72280400

order	1024
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁸ · Schur multiplier (H₂) = C₂²⁷

Aliases

	subgroup	G/H
center, socle	C₂⁶	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂⁸
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁶ ◁ C₂⁶×C₄ ◁ G
LECS	G ▷ C₄ ▷ C₂ ▷ C₁

1012373 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 8 generators on 18 points:

(1,2);(3,4);(5,6);(12,15)(13,17)(16,18);(11,12,14,16)(13,18,17,15);(1,2)(3,4)(5,6)(7,8)(9,10)(12,16)(15,18);(7,8);(9,10)

352 conjugacy classes. The character table is too large to display.

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2), (3,4), (5,6), (12,15)(13,17)(16,18), (11,12,14,16)(13,18,17,15), (1,2)(3,4)(5,6)(7,8)(9,10)(12,16)(15,18), (7,8), (9,10));