C₅×#627 #67146

order	360
isoclinism	isoclinic class of #625
automorphism	Aut(G) = C₄×#64241 (order 1152) · Inn(G) = D₃² · Out(G) = C₄×D₄
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃²×C₅ ⋊ Q₈
Sylow	C₃² ⋊ C₅×Q₈

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 76);