C₂²×#12903 #72313788

order	1024
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

5077 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)(10,14,15,20)(11,17)(12,19)(16,23,22,21)(18,24);(1,2);(3,4);(5,6,7,8);(9,10,11,14,12,16,17,21,13,15,18,20,19,22,24,23)

maximal subgroup of	C₂²×#497864, C₂²×#496124, C₂²×D₄×#365
maximal normal subgroup of	C₂²×#497864, C₂²×#496124, C₂²×D₄×#365

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

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