Finite Group Databasebeta

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C₂×D₃×(C₂²⋊D₇)⋊C₃ #72244114

order	2016
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×D₃×(C₂²⋊D₇)⋊C₃

Splittings

Fitting	C₂³×C₃×C₇ ⋊ C₂²×C₃
Hall	C₃×ΓL(1,𝔽₈) ⋊ C₂²×D₄
Sylow	C₇ ⋊ C₂×C₃×D₃×D₄

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×AGL(1,𝔽₇)
commutator, cosocle	C₂×C₃×C₇	C₂⁴×C₃
Frattini	C₂	C₂²×D₃×AGL(1,𝔽₇)
Fitting	C₂³×C₃×C₇	C₂²×C₃
socle	C₂²×C₃×C₇	C₂³×C₃
hypercenter	C₂³	D₃×AGL(1,𝔽₇)
hypocenter	C₃×C₇	C₂²×C₃×D₄
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂² ◁ C₂³

998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 168

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×D₄×AGL(1,𝔽₇), D₃×#6500⋊C₃, D₃×#10620789, …
maximal normal subgroup of	C₂×D₃×D₄×AGL(1,𝔽₇), D₃×#6500⋊C₃, D₃×#10620789, …
maximal quotient of	D₃×#6500⋊C₃, D₃×#10620789, D₃×#6503⋊C₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.