D₃×#41⋊C₃ #64277

order	288
isoclinism	isoclinic class of C₃⋊(#41⋊C₃)
automorphism	Aut(G) = C₂²×D₃×S₄ (order 576) · Inn(G) = D₃×A₄ · Out(G) = C₂³
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×#41⋊C₃
unambiguous semidirect product	(D₃×#41)⋊C₃

	subgroup	G/H
center, hypercenter	C₄	D₃×A₄
commutator, cosocle, hypocenter	C₃×Q₈	C₂²×C₃
Frattini	C₂	C₂×D₃×A₄
Fitting	C₃×#41	C₂×C₃
socle	C₂×C₃	C₂²×A₄
LCS	G ▷ C₃×Q₈
UCS	C₁ ◁ C₄

103 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 925);