C₅×#622 #67125

order	360
isoclinism	isoclinic class of #157
automorphism	Aut(G) = C₂×C₄×AΓL(1,𝔽₉) (order 1152) · Inn(G) = #157 · Out(G) = C₂³×C₄
homology	Abelianization (H₁) = C₅×C₈ · Schur multiplier (H₂) = C₃

Aliases

derived, Sylow	C₃² ⋊ C₅×C₈
Hall	C₃²×C₅ ⋊ C₈

28 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 55);