C₂×#8857 #192063

order	512
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

1702 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 22 points:

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

maximal subgroup of	C₂×#208872, C₂×#208920, C₂×#192094, …
maximal normal subgroup of	C₂×#208872, C₂×#208920, C₂×#192094, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 99259);