Finite Group Databasebeta

C3⋊D3×#1367 #72245508

order2304
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23×C3

Aliases

direct productC3⋊D3×#1367

Splittings

FittingC32×#1367 ⋊ C2
SylowC32 ⋊ C2×#1367

Subgroups

subgroupG/H
centerC2×C8D4×C3⋊D3
commutatorC32×C4C22×C16
FrattiniC4×C8C22×C3⋊D3
FittingC32×#1367C2
socleC22×C32C2×C4⋊C8
prime radicalC22×C3⋊D3C4⋊C8
cosocleC32×C4×C8C23
hypercenter#1367C3⋊D3
hypocenterC32C2×#1367
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ #1367

858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

Conjugacy classes & character table

336 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3⋊D3×#7099
maximal normal subgroup ofC3⋊D3×#7099
maximal quotient ofC3⋊D3×#7099

GAP

Past the SmallGroups library coverage — no SmallGroups id.