Finite Group Databasebeta

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D3×#11717451 #72230641

order4800
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4×C5

Aliases

direct productD3×#11717451

Splittings

FittingC2×C3×C4×C52 ⋊ C2×C4
HallC3×C52 ⋊ C2×#117
SylowC52 ⋊ D3×#117
SylowC3 ⋊ C2×#11717451

Subgroups

subgroupG/H
centerC4C2×D3×#1044
commutator, socleC2×C3×C52C23×C4
FrattiniC2C22×D3×#1044
FittingC2×C3×C4×C52C2×C4
prime radicalC22×D3×C5⋊D5C22
cosocleC2×C3×C5⋊D5C24
hypercenterC2×C4D3×#1044
hypocenterC3×C52C2×#117
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C4 ◁ C2×C4

1792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#13107559, D3×#13103962, D3×#13104909
maximal normal subgroup ofD3×#13107559, D3×#13103962, D3×#13104909

GAP

Past the SmallGroups library coverage — no SmallGroups id.