Finite Group Databasebeta

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D3×#23990 #72258113

order1536
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productD3×#23990

Splittings

FittingC3×#23990 ⋊ C2
SylowC3 ⋊ C2×#23990

Subgroups

subgroupG/H
centerC2D3×#2404
commutator, cosocleC22×C3×C4C25
FrattiniC22×C4C24×D3
FittingC3×#23990C2
socleC2×C3C2×#2404
hypercenter#23990D3
hypocenterC3C2×#23990
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C22×C4 ◁ #23990

8432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#6499855
maximal normal subgroup ofD3×#6499855

GAP

Past the SmallGroups library coverage — no SmallGroups id.