C₂×#22487 #6379271

order	512
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

4106 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);(3,4,5,6)(8,11)(12,14)(16,19)(17,21)(20,22);(7,8)(9,12)(10,11)(13,14);(7,9,10,13)(8,12,11,14)(15,16,18,20)(17,22,21,19);(8,11)(12,14)

maximal subgroup of	C₂×#6596621, C₂×#6384086, C₂×#6605573
maximal normal subgroup of	C₂×#6596621, C₂×#6384086, C₂×#6605573

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6286467);