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C₂×#6196 #88669

order	432
isoclinism	isoclinic class of #6196
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

H(3,𝔽₃) ⋊ C₂×Q₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	((C₃⋊D₃)⋊C₃)⋊C₂
commutator, cosocle	C₂×H(3,𝔽₃)	C₂³
Frattini	C₂×C₃	C₂×D₃²
Fitting, prime radical	C₂²×H(3,𝔽₃)	C₂²
socle	C₂²×C₃	D₃²
hypocenter	H(3,𝔽₃)	C₂×Q₈
LCS	G ▷ C₂×H(3,𝔽₃) ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂²

149 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)(3,5,6,10)(4,7,8,9)(12,18,16,14,15,19)(13,17);(3,4,6,8)(5,9,10,7)(11,12,14)(13,15,18,17,16,19);(1,2)

Conjugacy classes & character table

38 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11720702, #11721077, #11721078, …
maximal normal subgroup of	#11720702, #11721077, #11721078, …
maximal quotient of	#11721093, #11721095, C₄×#6196, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 316);