Finite Group Databasebeta

← Prev (#72253391) Next (#72253393) →

D3×#10980 #72253392

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C210

Aliases

direct productD3×#10980

Splittings

FittingC3×#10980 ⋊ C2
SylowC3 ⋊ C2×#10980

Subgroups

subgroupG/H
centerC23C2×D3×C22⋊C4
commutatorC24×C3C23×C4
FrattiniC25C23×D3
FittingC3×#10980C2
socleC23×C3C22×C22⋊C4
prime radicalC22×D3×#121C2
cosocleC25×C3C24
hypercenter#10980D3
hypocenterC3C2×#10980
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ #10980

14068 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#449469
maximal normal subgroup ofD3×#449469
maximal quotient ofD3×#111516

GAP

Past the SmallGroups library coverage — no SmallGroups id.