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C₃×#3787 #88981

order	432
isoclinism	isoclinic class of #157
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₂×C₃

Aliases

Splittings

derived	C₃² ⋊ C₂×C₃×C₈
Sylow	C₃³ ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄	#157
commutator, hypocenter	C₃²	C₂×C₃×C₈
Frattini	C₂	C₂×C₃×#157
Fitting	C₃³×C₄	C₄
socle	C₂×C₃³	C₂×C₄
prime radical	C₂×C₃×C₃⋊D₃	C₄
cosocle	C₃⋊Dic₃	C₂²×C₃
LCS	G ▷ C₃²
UCS	C₁ ◁ C₃×C₄

88 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:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11722703, #11722705, #11722707, …
maximal normal subgroup of	#11722703, #11722705, #11722707, …
maximal quotient of	C₃×#63764, C₃×#63765, C₃×C₄×#622, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 628);