D₄×#432 #6380832

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄×#120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

2710 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 5 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6288028);