C₂×#8852 #192030

order	512
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

1424 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 18 points:

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

maximal subgroup of	C₂×#192050, C₂×#192042, C₂×#208820, …
maximal normal subgroup of	C₂×#192050, C₂×#192042, C₂×#208820, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 99226);