C₉×C₄⋊Dic₅ #10623573

order	720
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₉×C₄⋊Dic₅
unambiguous semidirect product	C₄⋊(C₉×Dic₅)

Hall	C₅×C₉ ⋊ C₄⋊C₄
Sylow	C₅ ⋊ C₉×C₄⋊C₄

78 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 42);