Finite Group Databasebeta

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C₂×D₇×D₁₃⋊C₃ #72247771

order	2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₇×D₁₃⋊C₃

Splittings

Fitting, socle	C₂×C₇×C₁₃ ⋊ C₂²×C₃
derived, Hall	C₇×C₁₃ ⋊ C₂³×C₃
Hall	C₂×D₇×D₁₃ ⋊ C₃
Hall	C₇×C₁₃⋊C₃ ⋊ C₂³
Hall	C₁₃⋊C₃ ⋊ C₂²×D₇
Sylow	C₁₃ ⋊ C₂²×C₃×D₇
Sylow	C₇ ⋊ C₂²×D₁₃⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₇×D₁₃⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₃	C₂³×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃	C₂²×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 182

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₇×AGL(1,𝔽₁₃), C₂×AGL(1,𝔽₇)×D₁₃⋊C₃
maximal normal subgroup of	C₂×D₇×AGL(1,𝔽₁₃), C₂×AGL(1,𝔽₇)×D₁₃⋊C₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.