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C₃×#3788 #88982

order	432
isoclinism	isoclinic class of #3788
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₃

Aliases

Splittings

C₃³ ⋊ M₁₆

Subgroups

	subgroup	G/H
center	C₂×C₃	C₂×#157
commutator	C₂×C₃²	C₂×C₃×C₄
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
hypercenter	C₃×C₄	#157
hypocenter	C₃²	C₃×M₁₆
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

84 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)(10,17,13,12)(11,15,16,14);(4,5)(6,7,9,8)(10,15,17,11,13,14,12,16)

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11722710, #11722712, #11722716, …
maximal normal subgroup of	#11722710, #11722712, #11722716, …
maximal quotient of	C₃×C₄⋊#622, C₃×#63777, C₃×#63778, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 629);