C₃×#95⋊C₃ #63582

order	288
isoclinism	isoclinic class of #95⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×#95⋊C₃
unambiguous semidirect product	#95⋊C₃²
unambiguous semidirect product	(C₃×#95)⋊C₃

Fitting	C₃×#95 ⋊ C₃
derived, Sylow	#95 ⋊ C₃²

	subgroup	G/H
center, hypercenter	C₂×C₃	C₄²⋊C₃
commutator, cosocle, hypocenter	#95	C₃²
Frattini	C₂³	C₃×A₄
Fitting	C₃×#95	C₃
socle	C₂³×C₃	A₄
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₃

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 36

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 230);