Finite Group Databasebeta

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C3⋊D3×#10620789 #72269445

order12096
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C27×C3

Aliases

direct productC3⋊D3×#10620789

Splittings

FittingC24×C32×C7 ⋊ C22×C3
HallC32×ΓL(1,𝔽8) ⋊ C2×#120
SylowC7 ⋊ C3×C3⋊D3×#120

Subgroups

subgroupG/H
center, FrattiniC22C22×C3⋊D3×AGL(1,𝔽7)
commutator, socle, cosocleC22×C32×C7C24×C3
FittingC24×C32×C7C22×C3
hypercenterC24C3⋊D3×AGL(1,𝔽7)
hypocenterC32×C7C2×C3×#120
LCSG ▷ C22×C32×C7 ▷ C32×C7
UCSC1 ◁ C22 ◁ C24

8984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 504

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.