C₂×C₄×#344 #353154

order	512
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂×C₄³ · Schur multiplier (H₂) = C₂⁵×C₄²

Aliases

2662 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 22 points:

(1,2);(3,4,5,6);(7,8)(9,15,16,12)(10,14)(11,13)(17,21,22,19)(18,20);(7,9,10,17,11,16,18,22)(8,12,14,19,13,15,20,21)

maximal subgroup of	C₂×C₄×#1904, C₂×C₄×#2008, C₂×C₄×#1891, …
maximal normal subgroup of	C₂×C₄×#1904, C₂×C₄×#2008, C₂×C₄×#1891, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260350);