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C₃×#3713 #88771

order	432
isoclinism	isoclinic class of #3713
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

Splittings

C₃³ ⋊ D₈

Subgroups

	subgroup	G/H
center	C₂×C₃	#625
commutator, cosocle	C₃²×C₄	C₂²×C₃
Frattini	C₄	C₃×D₃²
Fitting	C₃³×C₄	C₂²
socle	C₂×C₃³	D₄
hypercenter	C₃×C₄	D₃²
hypocenter	C₃²	C₃×D₈
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 17 points:

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#63734, C₃×#63735, #11722765, …
maximal normal subgroup of	C₃×#63734, C₃×#63735, #11722765, …
maximal quotient of	C₃×#63545, C₃×#63547, C₃×#63550, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 418);