Finite Group Databasebeta

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D3×#147787 #72255324

order3072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productD3×#147787

Splittings

FittingC3×#147787 ⋊ C2
SylowC3 ⋊ C2×#147787

Subgroups

subgroupG/H
centerC22D3×#1790
commutatorC22×C3×Q8C23×C4
FrattiniC22×#41C23×D3
FittingC3×#147787C2
socleC22×C3C2×#1790
prime radicalD3×#37297C2
cosocleC22×C3×#41C24
hypercenter#147787D3
hypocenterC3C2×#147787
LCSG ▷ C22×C3×Q8 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #147787

17850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72214565
maximal normal subgroup ofD3×#72214565

GAP

Past the SmallGroups library coverage — no SmallGroups id.