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C₂×#6198 #88673

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

Aliases

Splittings

H(3,𝔽₃) ⋊ C₂×D₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	((C₃⋊D₃)⋊C₃)⋊C₂
commutator, cosocle	C₂×H(3,𝔽₃)	C₂³
Frattini	C₂×C₃	C₂×D₃²
Fitting	C₂²×H(3,𝔽₃)	C₂²
socle	C₂²×C₃	D₃²
hypocenter	H(3,𝔽₃)	C₂×D₄
LCS	G ▷ C₂×H(3,𝔽₃) ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂²

205 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 3 generators on 15 points:

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

Conjugacy classes & character table

38 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11720705, #11721122, #11721126, …
maximal normal subgroup of	#11720705, #11721122, #11721126, …
maximal quotient of	C₂×#88431, #11721058, C₂×#88432, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 320);