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C₂×#6249⋊C₂ #11724030

order	864
isoclinism	isoclinic class of #6249⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

solvable

Aliases

direct product	C₂×#6249⋊C₂
unambiguous semidirect product	#6249⋊C₂²
unambiguous semidirect product	SU(3,𝔽₂)⋊C₂²

Splittings

Fitting	C₂×H(3,𝔽₃) ⋊ SD₁₆
Sylow	H(3,𝔽₃) ⋊ C₂×SD₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₂	#6249⋊C₂
commutator, cosocle	#1088	C₂³
Frattini	C₃	C₂×AΓL(1,𝔽₉)
Fitting	C₂×H(3,𝔽₃)	SD₁₆
socle	C₂×C₃	AΓL(1,𝔽₉)
prime radical	C₂×#1088⋊C₂	C₂
hypocenter	H(3,𝔽₃)	C₂×SD₁₆
LCS	G ▷ #1088 ▷ #272 ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 54

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×#6249⋊C₂, #13164088, #13164089, …
maximal normal subgroup of	C₄×#6249⋊C₂, #13164088, #13164089, …
maximal quotient of	#6249⋊Q₈, (#1088⋊C₂)⋊Q₈, #13164084, …
automorphism group of	C₂×#6249

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 3997);