Finite Group Databasebeta

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D3×#13104909 #72259657

order9600
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4×C5

Aliases

direct productD3×#13104909

Splittings

FittingC2×C3×C52×D4 ⋊ C2×C4
HallC3×C52 ⋊ C2×#418
SylowC52 ⋊ D3×#418
SylowC3 ⋊ C2×#13104909

Subgroups

subgroupG/H
centerC2C2×D3×C22⋊#1044
commutatorC3×C4×C52C23×C4
FrattiniC4C22×D3×#1044
FittingC2×C3×C52×D4C2×C4
socleC2×C3×C52C22×C22⋊C4
prime radicalC2×D3×D4×C5⋊D5C2
cosocleC3×C4×C5⋊D5C24
hypercenterC2×D4D3×#1044
hypocenterC3×C52C2×#418
LCSG ▷ C3×C4×C52 ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

6756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

246 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.