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C₉×C₄²⋊C₃ #88452

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

Aliases

C₉×C₄²⋊C₃

Splittings

Fitting	C₄²×C₉ ⋊ C₃
derived, Sylow	C₄² ⋊ C₃×C₉

Subgroups

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

42 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 2 generators on 21 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

derived subgroup of	C₉⋊#857, C₉⋊#4623, C₉⋊#4626, …
maximal subgroup of	C₉×#857, C₉⋊#857, #11720742, …
maximal normal subgroup of	C₉×#857, C₉⋊#857, #11720742, …
maximal quotient of	C₉×#95⋊C₃, C₂×C₉×C₄²⋊C₃, C₂₇×C₄²⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 99);