C₂×#13915 #514110

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁷×C₄²

Aliases

5626 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 22 points:

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

maximal subgroup of	C₂×#845567, C₂×#655741, C₂×#824899, …
maximal normal subgroup of	C₂×#845567, C₂×#655741, C₂×#824899, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421306);