Finite Group Databasebeta

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D3×#13103931 #72259608

order9600
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD3×#13103931

Splittings

HallC3×C52 ⋊ C2×#417
SylowC52 ⋊ D3×#417
SylowC3 ⋊ C2×#13103931

Subgroups

subgroupG/H
centerC2C2×D3×#87831
commutatorC3×C4×C52C23×C4
FrattiniC4C2×D3×D5⋊AGL(1,𝔽5)
FittingC2×C3×C4×C52C22×C4
socleC2×C3×C52C22×C22⋊C4
prime radicalD3×#11717471C2
cosocleC3×C4×C5⋊D5C24
hypercenterC2×C4D3×D5⋊AGL(1,𝔽5)
hypocenterC3×C52C2×#417
LCSG ▷ C3×C4×C52 ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ C2×C4

4100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72213282
maximal normal subgroup ofD3×#72213282

GAP

Past the SmallGroups library coverage — no SmallGroups id.