C₂×C₄×#481 #6373028

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

3202 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)(17,19)(18,20)(21,22);(8,11)(12,14)(16,19)(20,21);(7,9,10,13)(8,12,11,14)(16,20)(18,22)(19,21)

maximal subgroup of	C₂×C₄×#3109, C₂×#6578588, C₂×D₄×#481, …
maximal normal subgroup of	C₂×C₄×#3109, C₂×#6578588, C₂×D₄×#481, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280224);