C₂×#21930 #6374843

order	512
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁹

Aliases

4266 conjugacy classes of subgroups.

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

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

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

maximal subgroup of	#72316241, #72316245, C₂×#6500552, …
maximal normal subgroup of	#72316241, #72316245, C₂×#6500552, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6282039);