Finite Group Databasebeta

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D3×#20739 #72269999

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productD3×#20739

Splittings

FittingC3×#20739 ⋊ C2
SylowC3 ⋊ C2×#20739

Subgroups

subgroupG/H
centerC23C22×D3×D4
commutatorC2×C3×C4C24×C4
FrattiniC22×C4C24×D3
FittingC3×#20739C2
socleC23×C3C23×D4
prime radicalC23×D3×D4C22
cosocleC22×C3×C4C25
hypercenter#20739D3
hypocenterC3C2×#20739
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C42 ◁ #20739

12692 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#6453969
maximal normal subgroup ofD3×#6453969
maximal quotient ofD3×#494058

GAP

Past the SmallGroups library coverage — no SmallGroups id.