Finite Group Databasebeta

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#97×((C₃⋊D₃)⋊C₃)⋊C₂ #72268965

order	3456
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶

Aliases

#97×((C₃⋊D₃)⋊C₃)⋊C₂

Splittings

Fitting	H(3,𝔽₃)×#97 ⋊ C₂²
Sylow	H(3,𝔽₃) ⋊ C₂²×#97

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂²×((C₃⋊D₃)⋊C₃)⋊C₂
commutator	C₂×H(3,𝔽₃)	C₂²×C₄²
Frattini	C₂×C₃×C₄	C₂²×D₃²
Fitting	H(3,𝔽₃)×#97	C₂²
socle	C₂²×C₃	C₂×C₄×D₃²
prime radical	C₂²×((C₃⋊D₃)⋊C₃)⋊C₂	C₂×C₄
cosocle	C₂×C₄×H(3,𝔽₃)	C₂⁴
hypercenter	#97	((C₃⋊D₃)⋊C₃)⋊C₂
hypocenter	H(3,𝔽₃)	C₂²×#97
LCS	G ▷ C₂×H(3,𝔽₃) ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₄ ◁ #97

2526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 288

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

#97×AGL(2,𝔽₃)

GAP

Past the SmallGroups library coverage — no SmallGroups id.