D₅×Dic₁₀ #87869

order	400
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

direct product	D₅×Dic₁₀
unambiguous semidirect product	(C₅×D₅)⋊Q₈

C₅² ⋊ C₂×Q₈

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 163);