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C₃×#3718 #88776

order	432
isoclinism	isoclinic class of #3713
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

Splittings

C₃³ ⋊ Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₃	#625
commutator, cosocle	C₃²×C₄	C₂²×C₃
Frattini	C₄	C₃×D₃²
Fitting	C₃³×C₄	C₂²
socle, prime radical	C₂×C₃³	D₄
hypercenter	C₃×C₄	D₃²
hypocenter	C₃²	C₃×Q₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 25 points:

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#63735, C₃×#63736, #11722766, …
maximal normal subgroup of	C₃×#63735, C₃×#63736, #11722766, …
maximal quotient of	C₃×#63565, C₃×#63576, C₂×C₃×#3718, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 423);