C₅×(C₂²⋊C₉)⋊C₄ #10623635

order	720
isoclinism	isoclinic class of (C₂²⋊C₉)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×(C₂²⋊C₉)⋊C₄
unambiguous semidirect product	(C₂²⋊C₉)⋊(C₄×C₅)

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 180

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 104);