D₃×C₄²⋊C₃ #63759

order	288
isoclinism	isoclinic class of D₃×C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₄

Aliases

direct product	D₃×C₄²⋊C₃
unambiguous semidirect product	C₃⋊(C₂×C₄²⋊C₃)
unambiguous semidirect product	(C₄²×D₃)⋊C₃

C₃×C₄² ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₄²	C₂×C₃
Frattini	C₂²	D₃×A₄
socle	C₂²×C₃	C₂×A₄
LCS	G ▷ C₃×C₄²
UCS	C₁

59 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)(3,6,10)(4,7,9)(8,11,12)(14,15);(1,3,4,8)(5,12,9,10)(13,14,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 407);