Finite Group Databasebeta

C3⋊D3×#2171 #72255424

order2304
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C3

Aliases

direct productC3⋊D3×#2171

Splittings

FittingC32×#2171 ⋊ C2
SylowC32 ⋊ C2×#2171

Subgroups

subgroupG/H
centerC8C2×D4×C3⋊D3
commutatorC32×C4C23×C8
FrattiniC2×C8C23×C3⋊D3
FittingC32×#2171C2
socleC2×C32C2×C8×D4
prime radicalC3⋊D3×#135C4
cosocleC2×C32×C8C24
hypercenter#2171C3⋊D3
hypocenterC32C2×#2171
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C16 ◁ #2171

1962 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3⋊D3×#12068
maximal normal subgroup ofC3⋊D3×#12068

GAP

Past the SmallGroups library coverage — no SmallGroups id.