C₂²×#13255 #72310271

order	1024
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

9861 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 24 points:

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

maximal subgroup of	C₂²×#498578, C₂²×#495843, C₂²×D₄×#360
maximal normal subgroup of	C₂²×#498578, C₂²×#495843, C₂²×D₄×#360

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

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