Finite Group Databasebeta

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C₃×C₃⋊D₃×C₁₃⋊C₃ #72276998

order	2106
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃²

Aliases

C₃×C₃⋊D₃×C₁₃⋊C₃

Splittings

Fitting, socle	C₃³×C₁₃ ⋊ C₂×C₃
derived	C₃²×C₁₃ ⋊ C₂×C₃²
Hall	C₃³×C₁₃⋊C₃ ⋊ C₂
Sylow	C₁₃ ⋊ C₃²×C₃⋊D₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₃⋊D₃×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃³×C₁₃	C₂×C₃
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₃

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 234

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×C₃⋊D₃×D₁₃⋊C₃, D₃×C₃⋊D₃×C₁₃⋊C₃, C₃⋊D₃×C₃⋊(D₁₃⋊C₃)
maximal normal subgroup of	C₃×C₃⋊D₃×D₁₃⋊C₃, D₃×C₃⋊D₃×C₁₃⋊C₃, C₃⋊D₃×C₃⋊(D₁₃⋊C₃)

GAP

Past the SmallGroups library coverage — no SmallGroups id.