Finite Group Databasebeta

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D3×#89804⋊C3 #72269447

order8064
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C27

Aliases

direct productD3×#89804⋊C3

Splittings

FittingC3×C7×#120 ⋊ C22×C3
HallC3×ΓL(1,𝔽8) ⋊ C2×B(4,𝔽2)
SylowC7 ⋊ C3×D3×B(4,𝔽2)

Subgroups

subgroupG/H
centerC2D3×#6500⋊C3
commutator, cosocleC23×C3×C7C24×C3
FrattiniC23C22×D3×AGL(1,𝔽7)
FittingC3×C7×#120C22×C3
socleC2×C3×C7C2×C3×#120
hypercenter#120D3×AGL(1,𝔽7)
hypocenterC3×C7C2×C3×B(4,𝔽2)
LCSG ▷ C23×C3×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C23 ◁ #120

4270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽7)×B(4,𝔽2)
maximal normal subgroup ofD3×AGL(1,𝔽7)×B(4,𝔽2)

GAP

Past the SmallGroups library coverage — no SmallGroups id.