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C₈×C₃⋊D₉ #88522

order	432
isoclinism	isoclinic class of C₃⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₈×C₃⋊D₉

Splittings

Fitting	C₃×C₈×C₉ ⋊ C₂
derived, Sylow	C₃×C₉ ⋊ C₂×C₈

Subgroups

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

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 216

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₃⋊D₉)⋊C₁₆, #11720231, C₁₆×C₃⋊D₉, …
maximal normal subgroup of	(C₃⋊D₉)⋊C₁₆, #11720231, C₁₆×C₃⋊D₉, …
maximal quotient of	C₁₆×C₃⋊D₉, #11720506, C₈×C₃⋊Dic₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 169);