D₄×#352 #497289

order	512
nilpotency class	4
isoclinism	isoclinic class of #480860
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

1424 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 20 points:

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

maximal subgroup of	D₄×#2200, #72311129, #72311171, …
maximal normal subgroup of	D₄×#2200, #72311129, #72311171, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 404485);