Finite Group Databasebeta

← Prev (#88827) Next (#88829) →

C₃²×#213 #88828

order	432
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

C₃²×#213

Splittings

Fitting	C₃³×D₄ ⋊ C₂
Sylow	C₃³ ⋊ D₈

Subgroups

	subgroup	G/H
center	C₂×C₃²	#67
commutator, cosocle	C₃×C₄	C₂²×C₃²
Frattini	C₄	C₂×C₃²×D₃
Fitting	C₃³×D₄	C₂
socle	C₂×C₃³	D₄
hypercenter	C₃²×D₄	D₃
hypocenter	C₃	C₃²×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃² ◁ C₃²×C₄ ◁ C₃²×D₄

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 72

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

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

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×D₃×#213, C₃×#63925, C₃×#63926, …
maximal normal subgroup of	C₃×D₃×#213, C₃×#63925, C₃×#63926, …
maximal quotient of	C₃²×#807, C₃²×#809, C₃²×#826, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 475);