C₂×#13911 #514105

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

4594 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 512

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

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

maximal subgroup of	C₂×#674148, C₂×#612965, C₂×#534553, …
maximal normal subgroup of	C₂×#674148, C₂×#612965, C₂×#534553, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421301);