Finite Group Databasebeta

← Prev (#72230534) Next (#72230536) →

D3×#13103905 #72230535

order9600
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productD3×#13103905

Splittings

HallC3×C52 ⋊ C2×C4×M16
SylowC52 ⋊ C4×D3×M16
SylowC3 ⋊ C2×#13103905

Subgroups

subgroupG/H
center, FrattiniC4C2×D3×D5⋊AGL(1,𝔽5)
commutator, socleC2×C3×C52C22×C42
FittingC2×C3×C4×C52C22×C4
prime radicalC22×D3×C5⋊D5C2×C4
cosocleC3×C4×C5⋊D5C24
hypercenterC2×C4D3×D5⋊AGL(1,𝔽5)
hypocenterC3×C52C2×C4×M16
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C4 ◁ C2×C4

3620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

228 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.