Finite Group Databasebeta

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D3×#11058 #72253364

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD3×#11058

Splittings

FittingC3×#11058 ⋊ C2
SylowC3 ⋊ C2×#11058

Subgroups

subgroupG/H
centerC22D3×#386
commutatorC22×C3×C4C23×C4
FrattiniC23×C4C23×D3
FittingC3×#11058C2
socleC22×C3C2×#386
prime radicalC23×D3×D4C22
cosocleC23×C3×C4C24
hypercenter#11058D3
hypocenterC3C2×#11058
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #11058

6324 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×#418876, D3×#454694, D3×#364468
maximal normal subgroup ofD3×#418876, D3×#454694, D3×#364468

GAP

Past the SmallGroups library coverage — no SmallGroups id.