C₂×#20714 #6370916

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

7570 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);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,16,17,19,18,20,21,22);(8,11)(12,14);(4,6);(7,9,10,13)(8,12,11,14)

maximal subgroup of	#72302880, C₂×#184859, C₂×#105483, …
maximal normal subgroup of	#72302880, C₂×#184859, C₂×#105483, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278112);