Finite Group Databasebeta

C3×#73439 #11801655

order1152
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×#73439

Splittings

FittingC32×C4×C22⋊C4 ⋊ C2
SylowC32 ⋊ #2293

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×C4×C22⋊C4C2
socleC23×C32C24
prime radicalC22×C3×#67C22
cosocleC23×C3C24×C3
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×#2293
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

1433 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 35666);