C₂²×#519563 #72289306

order	2048
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₄ · Schur multiplier (H₂) = C₂²²

Aliases

1215520 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 7 generators on 20 points:

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

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

maximal subgroup of	C₂²×#72219693
maximal normal subgroup of	C₂²×#72219693

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

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