Finite Group Databasebeta

C3×D3×#805 #13157408

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×D3×#805

Splittings

FittingC33×C42 ⋊ C22
SylowC33 ⋊ C2×#104

Subgroups

subgroupG/H
centerC3×C4D3×D12
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC33×C42C22
socleC2×C33C2×C22⋊C4
prime radicalC3×D3×#235C2
cosocleC2×C32×C4C23×C3
hypercenterC3×C42D32
hypocenterC32C2×C3×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×C42

906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×#10590393, C3×D3×#5077, D3×#10590397
maximal normal subgroup ofD3×#10590393, C3×D3×#5077, D3×#10590397

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 23471);