Finite Group Databasebeta

← Prev (#72247966) Next (#72247968) →

D3×#58990 #72247967

order1536
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C215

Aliases

direct productD3×#58990

Splittings

FittingC3×#58990 ⋊ C2
SylowC3 ⋊ C2×#58990

Subgroups

subgroupG/H
center, FrattiniC23C25×D3
commutator, socle, cosocleC23×C3C26
FittingC3×#58990C2
hypercenter#58990D3
hypocenterC3C2×#58990
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #58990

50528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#7849701, D3×#7792761, D3×#7918389, …
maximal normal subgroup ofD3×#7849701, D3×#7792761, D3×#7918389, …
maximal quotient ofD3×#647656, D3×#772778

GAP

Past the SmallGroups library coverage — no SmallGroups id.