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D₃×#6512⋊C₃ #72245652

order	4032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁵

Aliases

D₃×#6512⋊C₃

Splittings

Fitting	C₃×C₇×#41 ⋊ C₂²×C₃
Hall	C₃×ΓL(1,𝔽₈) ⋊ C₂×AGL(1,ℤ/8)
Sylow	C₇ ⋊ C₃×D₃×AGL(1,ℤ/8)

Subgroups

	subgroup	G/H
center	C₂	C₂×D₃×(C₂²⋊D₇)⋊C₃
commutator, cosocle	C₃×C₄×C₇	C₂⁴×C₃
Frattini	C₄	C₂²×D₃×AGL(1,𝔽₇)
Fitting	C₃×C₇×#41	C₂²×C₃
socle	C₂×C₃×C₇	C₂²×C₃×D₄
hypercenter	#41	D₃×AGL(1,𝔽₇)
hypocenter	C₃×C₇	C₂×C₃×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄×C₇ ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #41

1260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 168

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×AGL(1,ℤ/8)×AGL(1,𝔽₇), D₃×#89594⋊C₃, D₃×#90013⋊C₃, …
maximal normal subgroup of	D₃×AGL(1,ℤ/8)×AGL(1,𝔽₇), D₃×#89594⋊C₃, D₃×#90013⋊C₃
maximal quotient of	#72269413

GAP

Past the SmallGroups library coverage — no SmallGroups id.