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C₃×C₄⋊#157 #88984

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

Aliases

direct product	C₃×C₄⋊#157
unambiguous semidirect product	C₄⋊(C₃×#157)

Splittings

Fitting	C₃³×C₄ ⋊ C₄
Sylow	C₃³ ⋊ C₄⋊C₄

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	C₂²
cosocle	C₂×C₃⋊D₃	C₂²×C₃
hypercenter	C₃×C₄	#157
hypocenter	C₃²	C₃×C₄⋊C₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 13 points:

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11722706, #11722708, #11722714, …
maximal normal subgroup of	#11722706, #11722708, #11722714, …
maximal quotient of	C₃×#63768, C₃×#63769, C₃×#63770, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 631);