Finite Group Databasebeta

C3×#73413 #11801124

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

Aliases

direct productC3×#73413

Splittings

FittingC32×#376 ⋊ C2
SylowC32 ⋊ #2283

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#376C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#376D3
hypocenterC3C3×#2283
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×#376

1225 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

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, 35135);