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#99×((C₃⋊D₃)⋊C₃)⋊C₂ #72253008

order	3456
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

#99×((C₃⋊D₃)⋊C₃)⋊C₂

Splittings

Fitting	H(3,𝔽₃)×#99 ⋊ C₂²
Sylow	H(3,𝔽₃) ⋊ C₂²×#99

Subgroups

	subgroup	G/H
center	C₂	C₂²⋊C₄×((C₃⋊D₃)⋊C₃)⋊C₂
commutator	C₂²×H(3,𝔽₃)	C₂³×C₄
Frattini	C₂³×C₃	C₂²×D₃²
Fitting	H(3,𝔽₃)×#99	C₂²
socle	C₂×C₃	D₃²×C₂²⋊C₄
prime radical	C₂×D₄×((C₃⋊D₃)⋊C₃)⋊C₂	C₂
cosocle	C₂³×H(3,𝔽₃)	C₂⁴
hypercenter	#99	((C₃⋊D₃)⋊C₃)⋊C₂
hypocenter	H(3,𝔽₃)	C₂²×#99
LCS	G ▷ C₂²×H(3,𝔽₃) ▷ C₂×H(3,𝔽₃) ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ #99

4102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 72

Conjugacy classes & character table

121 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#99×AGL(2,𝔽₃), B(4,𝔽₂)×((C₃⋊D₃)⋊C₃)⋊C₂
maximal normal subgroup of	B(4,𝔽₂)×((C₃⋊D₃)⋊C₃)⋊C₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.