C₂²×#8310 #72319713

order	1024
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂¹³

Aliases

57497 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:

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

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

maximal subgroup of	C₂²×#208650
maximal normal subgroup of	C₂²×#208650

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

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