C₂²×#13257 #72313728

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

Aliases

12197 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:

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

maximal subgroup of	C₂²×#495837, C₂²×#498578, C₂²×D₄×#361
maximal normal subgroup of	C₂²×#495837, C₂²×#498578, C₂²×D₄×#361

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

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