Finite Group Databasebeta

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C₃⋊D₃×#10620710 #72246454

order	12096
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁵×C₃×C₄

Aliases

C₃⋊D₃×#10620710

Splittings

Fitting	C₃²×C₄²×C₇ ⋊ C₂²×C₃
Hall	C₃²×ΓL(1,𝔽₈) ⋊ C₂×#127
Sylow	C₇ ⋊ C₃×C₃⋊D₃×#127

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×C₃⋊D₃×AGL(1,𝔽₇)
commutator, socle, cosocle	C₂²×C₃²×C₇	C₂⁴×C₃
Fitting	C₃²×C₄²×C₇	C₂²×C₃
hypercenter	C₄²	C₃⋊D₃×AGL(1,𝔽₇)
hypocenter	C₃²×C₇	C₂×C₃×#127
LCS	G ▷ C₂²×C₃²×C₇ ▷ C₃²×C₇
UCS	C₁ ◁ C₂² ◁ C₄²

6840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1008

Conjugacy classes & character table

348 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃⋊D₃×#127×AGL(1,𝔽₇)
maximal normal subgroup of	C₃⋊D₃×#127×AGL(1,𝔽₇)

GAP

Past the SmallGroups library coverage — no SmallGroups id.