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C₃×C₄²⋊C₉ #88454

order	432
isoclinism	isoclinic class of C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₃×C₄

Aliases

direct product	C₃×C₄²⋊C₉
unambiguous semidirect product	(C₃×C₄²)⋊C₉

Splittings

C₄² ⋊ C₃×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃²	C₄²⋊C₃
commutator, hypocenter	C₄²	C₃×C₉
Frattini	C₂²×C₃	C₃×A₄
Fitting	C₃²×C₄²	C₃
socle, prime radical	C₂²×C₃²	A₄
cosocle	C₃×C₄²	C₃²
LCS	G ▷ C₄²
UCS	C₁ ◁ C₃²

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,5)(3,6,10)(4,7,9)(8,11,12)(16,17,19,18,20,22,21,23,24);(1,8,4,3)(5,10,9,12)(13,14,15)

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

derived subgroup of	C₃⋊#63419, C₃⋊#10588303, C₃⋊#10588306, …
maximal subgroup of	C₃×#63419, C₃⋊#63419, C₃⋊(#127⋊C₉), …
maximal normal subgroup of	C₃×#63419, C₃⋊#63419, C₃⋊(#127⋊C₉), …
maximal quotient of	C₃×#95⋊C₉, C₂×C₃×C₄²⋊C₉, C₃×C₄²⋊C₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 101);