Finite Group Databasebeta

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C₃×#3745 #88836

order	432
isoclinism	isoclinic class of #3744
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

Splittings

Fitting	C₃³×C₈ ⋊ C₂
Sylow	C₃³ ⋊ D₈

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	C₂×C₃³	D₄
hypercenter	C₃×C₈	C₃⋊D₃
hypocenter	C₃²	C₃×D₈
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 17 points:

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

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#63546, C₃×#63549, #11722004, …
maximal normal subgroup of	C₃×#63546, C₃×#63549, #11722004, …
maximal quotient of	C₃×#63626, C₃×#63627, C₃×#63628, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 483);