C₅×#626 #67145

order	360
isoclinism	isoclinic class of #625
automorphism	Aut(G) = C₂²×C₄×D₃² (order 576) · Inn(G) = D₃² · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃²×C₅ ⋊ D₄
Sylow	C₃² ⋊ C₅×D₄

74 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 75);