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C₃×#3701 #88718

order	432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Fitting	C₃×Q₈×C₉ ⋊ C₂
Sylow	C₃×C₉ ⋊ #41

Subgroups

	subgroup	G/H
center	C₂×C₃	C₂²×D₉
commutator, cosocle	C₂×C₉	C₂³×C₃
Frattini	C₂×C₃	C₂²×C₃×D₃
Fitting	C₃×Q₈×C₉	C₂
socle	C₂×C₃²	C₂²×D₃
hypercenter	C₃×Q₈	D₉
hypocenter	C₉	C₃×#41
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₃×Q₈

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11721211, #11721215, #11721219, …
maximal normal subgroup of	#11721211, #11721215, #11721219, …
maximal quotient of	C₃×#63452, C₃×#63454, C₃×#63455, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 365);