Finite Group Databasebeta

← Prev (#72255440) Next (#72255442) →

C₃⋊D₃×#13658 #72255441

order	4608
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

C₃⋊D₃×#13658

Splittings

Fitting	C₃²×#13658 ⋊ C₂
Sylow	C₃² ⋊ C₂×#13658

Subgroups

	subgroup	G/H
center	C₂	C₃⋊D₃×#2177
commutator	C₃²×C₁₆	C₂³×C₄
Frattini	C₂×C₁₆	C₂³×C₃⋊D₃
Fitting	C₃²×#13658	C₂
socle	C₂×C₃²	C₂×#2177
prime radical	C₃⋊D₃×#2263	C₂
cosocle	C₂×C₃²×C₁₆	C₂⁴
hypercenter	#13658	C₃⋊D₃
hypocenter	C₃²	C₂×#13658
LCS	G ▷ C₃²×C₁₆ ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346 ◁ #13658

2700 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)
maximal quotient of	C₃⋊D₃×#151085

GAP

Past the SmallGroups library coverage — no SmallGroups id.