Finite Group Databasebeta

← Prev (#72249045) Next (#72249047) →

D3×#106766 #72249046

order3072
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C210

Aliases

direct productD3×#106766

Splittings

FittingC3×#106766 ⋊ C2
SylowC3 ⋊ C2×#106766

Subgroups

subgroupG/H
centerC22D3×C22⋊#95
commutatorC24×C3C22×C42
FrattiniC26C23×D3
FittingC3×#106766C2
socleC22×C3C2×C22⋊#95
prime radicalC24×D3×D4C22
cosocleC26×C3C24
hypercenter#106766D3
hypocenterC3C2×#106766
LCSG ▷ C24×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C26 ◁ #106766

At least 8334 conjugacy classes of subgroups; only the 1355 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72210600, D3×#72210462, D3×#72213274
maximal normal subgroup ofD3×#72210600, D3×#72210462, D3×#72213274
maximal quotient ofD3×#72210462, D3×#72213396

GAP

Past the SmallGroups library coverage — no SmallGroups id.