C₂×C₅×C₂²⋊D₅ #87896

order	400
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×C₅×C₂²⋊D₅
unambiguous semidirect product	C₂³⋊(C₅×D₅)

Fitting	C₂³×C₅² ⋊ C₂
Sylow	C₅² ⋊ C₂×D₄

140 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 190);