C₂×C₃×Q₈⋊C₉ #88687

order	432
isoclinism	isoclinic class of SL(2,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂×C₃×Q₈⋊C₉
unambiguous semidirect product	(C₂×C₃×Q₈)⋊C₉

derived	Q₈ ⋊ C₂×C₃×C₉
Sylow	C₂×Q₈ ⋊ C₃×C₉

	subgroup	G/H
center, socle, prime radical, hypercenter	C₂²×C₃²	A₄
commutator, hypocenter	Q₈	C₂×C₃×C₉
Frattini	C₂×C₃	C₂×C₃×A₄
Fitting	C₂×C₃²×Q₈	C₃
cosocle	C₃×Q₈	C₂×C₃²
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂²×C₃²

94 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 432

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2)(7,8,10)(11,13,12)(14,18,22,16,21,17,19,15,20);(3,4,5)(6,10,9,12)(7,13,11,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 334);