Finite Group Databasebeta

C3⋊D3×#13654 #72269656

order4608
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC3⋊D3×#13654

Splittings

FittingC32×#13654 ⋊ C2
SylowC32 ⋊ C2×#13654

Subgroups

subgroupG/H
centerC22C2×C3⋊D3×D16
commutatorC32×C16C23×C4
FrattiniC2×C16C23×C3⋊D3
FittingC32×#13654C2
socleC22×C32C22×D16
prime radicalC2×C3⋊D3×D32C2
cosocleC2×C32×C16C24
hypercenter#13654C3⋊D3
hypocenterC32C2×#13654
LCSG ▷ C32×C16 ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×C16 ◁ #13654

2964 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3⋊D3×#151085
maximal normal subgroup ofC3⋊D3×#151085

GAP

Past the SmallGroups library coverage — no SmallGroups id.