C₂×C₃⋊#226 #64262

order	288
isoclinism	isoclinic class of C₃⋊#226
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃⋊#226
unambiguous semidirect product	(C₂×C₃)⋊#226

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊S₄
commutator, cosocle, hypocenter	C₃×SL(2,𝔽₃)	C₂²
Frattini	C₂	C₂×C₃⋊S₄
Fitting	C₂×C₃×Q₈	D₃
socle	C₂²×C₃	S₄
prime radical	C₂×C₃×SL(2,𝔽₃)	C₂
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂²

104 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2)(4,5)(6,11,15,18,10,20,17,12)(7,16,19,9,13,8,21,14);(1,2)(3,4,5);(8,14,17)(9,15,16)(11,18,21)(12,19,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 910);