C₂×C₄×#483 #6373029

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

Aliases

2910 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)(9,12)(10,11)(13,14)(15,16,18,21)(17,19,22,20);(8,11)(12,14);(7,9,10,13)(8,12,11,14)(16,19)(17,22)(20,21)

maximal subgroup of	C₂×#6578604, C₂×C₄×#3114, C₂×D₄×#483, …
maximal normal subgroup of	C₂×#6578604, C₂×C₄×#3114, C₂×D₄×#483, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280225);