C₂×C₄×#478 #6373147

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

2802 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);(7,8,10,12)(9,13,14,11)(15,16,17,19)(18,20,22,21);(7,9,10,14)(8,11,12,13)(16,19)(20,21);(16,20)(18,22)(19,21)

maximal subgroup of	C₂×D₄×#478, C₂×C₄×#3114, C₂×#6578236, …
maximal normal subgroup of	C₂×D₄×#478, C₂×C₄×#3114, C₂×#6578236, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280343);