Finite Group Databasebeta

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D3×#495739 #72270324

order3072
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD3×#495739

Splittings

FittingC3×#495739 ⋊ C2
SylowC3 ⋊ C2×#495739

Subgroups

subgroupG/H
centerC2D3×#21452
commutatorC2×C3×C8C24×C4
FrattiniC22×C8C24×D3
FittingC3×#495739C2
socleC2×C3C2×#21452
prime radicalD3×#33539C2
cosocleC22×C3×C8C25
hypercenter#495739D3
hypocenterC3C2×#495739
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2875 ◁ #495739

15126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.