A₄×D₁₅ #67214

order	360
isoclinism	isoclinic class of A₄×D₁₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×D₁₅
unambiguous semidirect product	C₃⋊(D₅×A₄)
unambiguous semidirect product	C₅⋊(D₃×A₄)
unambiguous semidirect product	(C₂²×D₁₅)⋊C₃

Fitting, socle, derived	C₂²×C₃×C₅ ⋊ C₂×C₃
Sylow	C₅ ⋊ D₃×A₄

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₃×C₅	C₂×C₃
LCS	G ▷ C₂²×C₃×C₅
UCS	C₁

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 12 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 144);