Finite Group Databasebeta

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D3×#24196 #72269982

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

Aliases

direct productD3×#24196

Splittings

FittingC3×#24196 ⋊ C2
SylowC3 ⋊ C2×#24196

Subgroups

subgroupG/H
centerC23C22×D3×D4
commutator, cosocleC22×C3×C4C25
FrattiniC22×C4C24×D3
FittingC3×#24196C2
socleC23×C3C23×D4
hypercenter#24196D3
hypocenterC3C2×#24196
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #24196

9736 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#6453969
maximal normal subgroup ofD3×#6453969

GAP

Past the SmallGroups library coverage — no SmallGroups id.