Finite Group Databasebeta

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D3×#10590410 #72258292

order3456
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD3×#10590410

Splittings

FittingC33×C22⋊C4 ⋊ C23
SylowC33 ⋊ C2×B(4,𝔽2)

Subgroups

subgroupG/H
centerC2D3×#63923
commutator, cosocleC23×C33C24
FrattiniC23C2×D33
FittingC33×C22⋊C4C23
socleC2×C33C2×#120
hypercenterC22⋊C4D33
hypocenterC33C2×B(4,𝔽2)
LCSG ▷ C23×C33 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C23 ◁ C22⋊C4

5260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#11865254
maximal normal subgroup ofD3×#11865254

GAP

Past the SmallGroups library coverage — no SmallGroups id.