C₂×#10790 #353373

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁹

Aliases

4858 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 18 points:

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

maximal subgroup of	C₂×#394048, C₂×#394051, C₂×#353374, …
maximal normal subgroup of	C₂×#394048, C₂×#394051, C₂×#353374, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260569);