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D₉×C₃⋊C₈ #88411

order	432
isoclinism	isoclinic class of D₃×D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₉×C₃⋊C₈
unambiguous semidirect product	(C₃×D₉)⋊C₈

Splittings

C₃×C₉ ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₄	D₃×D₉
commutator, hypocenter	C₃×C₉	C₂×C₈
Frattini	C₃×C₄	D₃²
Fitting, cosocle	C₃×C₄×C₉	C₂²
socle	C₂×C₃²	C₄×D₃
prime radical	C₂×C₃×D₉	C₄
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₄

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 2 generators on 20 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×C₈×D₉, D₉×ΓL(1,𝔽₂₅), #11720808, …
maximal normal subgroup of	D₃×C₈×D₉, D₉×ΓL(1,𝔽₂₅), #11720808, …
maximal quotient of	D₉×C₃⋊C₁₆, #11720230, C₃⋊C₈×Dic₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 58);