C₂²×#14130 #72324205

order	1024
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁶

Aliases

82037 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 6 generators on 20 points:

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

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

maximal subgroup of	C₂²×#759305, C₂²×#648046, C₂²×#520270, …
maximal normal subgroup of	C₂²×#759305, C₂²×#648046, C₂²×#520270, …

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

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