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C₂×#6180 #88537

order	432
isoclinism	isoclinic class of #272
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

Splittings

H(3,𝔽₃) ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄	C₃⋊D₃
commutator, hypocenter	H(3,𝔽₃)	C₂×C₈
Frattini	C₃×C₄	C₂×C₃⋊D₃
Fitting	C₂×C₄×H(3,𝔽₃)	C₂
socle	C₂²×C₃	C₃⋊Dic₃
prime radical	C₂²×H(3,𝔽₃)	C₄
cosocle	C₄×H(3,𝔽₃)	C₂²
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃×C₄

121 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 19 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11720310, #11720311, #11720312, …
maximal normal subgroup of	#11720310, #11720311, #11720312, …
maximal quotient of	C₄×#6180, C₄⋊#6180, C₂×#88386, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 184);