Finite Group Databasebeta

← Prev (#72231351) Next (#72231353) →

D3×#8534 #72231352

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productD3×#8534

Splittings

FittingC3×#8534 ⋊ C2
SylowC3 ⋊ C2×#8534

Subgroups

subgroupG/H
centerC22D3×#379
commutatorC24×C3C23×C4
FrattiniC25C23×D3
FittingC3×#8534C2
socleC22×C3C2×#379
prime radicalD3×#3484C2
cosocleC25×C3C24
hypercenter#8534D3
hypocenterC3C2×#8534
LCSG ▷ C24×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C25 ◁ #8534

9744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#347042, D3×#133839, D3×#139743, …
maximal normal subgroup ofD3×#347042, D3×#133839, D3×#139743, …
maximal quotient ofC2×D3×#8534, D3×#133356

GAP

Past the SmallGroups library coverage — no SmallGroups id.