Finite Group Databasebeta

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D3×#18162 #72247255

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

Aliases

direct productD3×#18162

Splittings

FittingC3×#18162 ⋊ C2
SylowC3 ⋊ C2×#18162

Subgroups

subgroupG/H
centerC22C2×D3×#120
commutator, cosocleC22×C3×C4C25
FrattiniC22×C4C24×D3
FittingC3×#18162C2
socleC22×C3C22×#120
hypercenter#18162D3
hypocenterC3C2×#18162
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #18162

12240 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×#346446, #72252358
maximal normal subgroup ofD3×#346446
maximal quotient of#72252358, D3×#234591

GAP

Past the SmallGroups library coverage — no SmallGroups id.