Finite Group Databasebeta

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C₃⋊D₃×#7390 #72255457

order	4608
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₃⋊D₃×#7390

Splittings

Fitting	C₃²×#7390 ⋊ C₂
Sylow	C₃² ⋊ C₂×#7390

Subgroups

	subgroup	G/H
center	C₂	C₃⋊D₃×#1333
commutator	C₃²×C₁₆	C₂²×C₈
Frattini	#346	C₂²×C₃⋊D₃
Fitting	C₃²×#7390	C₂
socle	C₂×C₃²	C₂×#1333
prime radical	C₂×C₃⋊D₃×D₁₆	C₄
cosocle	C₃²×#346	C₂³
hypercenter	#7390	C₃⋊D₃
hypocenter	C₃²	C₂×#7390
LCS	G ▷ C₃²×C₁₆ ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346 ◁ #7390

1668 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 288

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃⋊D₃×AGL(1,ℤ/32)
maximal normal subgroup of	C₃⋊D₃×AGL(1,ℤ/32)

GAP

Past the SmallGroups library coverage — no SmallGroups id.