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C₃×#3746 #88837

order	432
isoclinism	isoclinic class of #3744
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₃

Aliases

Splittings

C₃³ ⋊ Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₃	C₄⋊(C₃⋊D₃)
commutator, cosocle	C₃²×C₄	C₂²×C₃
Frattini	C₄	C₂×C₃×C₃⋊D₃
Fitting	C₃³×C₈	C₂
socle, prime radical	C₂×C₃³	D₄
hypercenter	C₃×C₈	C₃⋊D₃
hypocenter	C₃²	C₃×Q₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 25 points:

(1,14,4,3,5,11,10,12)(2,16,7,6,8,9,13,15)(17,18,19)(23,24,25);(1,8,5,2)(3,16,12,9)(4,7,10,13)(6,11,15,14)(21,22)(24,25);(20,21,22)

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#63548, C₃×#63551, #11722007, …
maximal normal subgroup of	C₃×#63548, C₃×#63551, #11722007, …
maximal quotient of	C₃×#63643, C₃×#63645, C₂×C₃×#3746, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 484);