C₄×#7179 #72242510

order	1024
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₄²×C₈ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

1773 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4)(9,10)(11,15)(12,23)(13,18)(14,19)(16,20)(17,22)(21,24);(10,15,18,24,19,17,23,16);(5,6,7,8)

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

maximal subgroup of	C₄×#136361
maximal normal subgroup of	C₄×#136361

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

gap> G := Group((1,2,3,4)(9,10)(11,15)(12,23)(13,18)(14,19)(16,20)(17,22)(21,24), (10,15,18,24,19,17,23,16), (5,6,7,8));