Finite Group Databasebeta

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D3×#10989 #72253535

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productD3×#10989

Splittings

FittingC3×#10989 ⋊ C2
SylowC3 ⋊ C2×#10989

Subgroups

subgroupG/H
centerC22D3×#386
commutatorC22×C3×C4C23×C4
FrattiniC23×C4C23×D3
FittingC3×#10989C2
socleC22×C3C2×#386
prime radicalC2×D3×#535C2
cosocleC23×C3×C4C24
hypercenter#10989D3
hypocenterC3C2×#10989
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #10989

10460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#359509, D3×#133356, D3×#393975
maximal normal subgroup ofD3×#359509, D3×#133356, D3×#393975

GAP

Past the SmallGroups library coverage — no SmallGroups id.