Finite Group Databasebeta

C3×#69074 #11797355

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C4

Aliases

direct productC3×#69074

Splittings

FittingC32×#346 ⋊ C2
SylowC32 ⋊ #2164

Subgroups

subgroupG/H
centerC2×C3×C8C22×D3
commutatorC22×C3C22×C3×C8
FrattiniC2×C8C22×C3×D3
FittingC32×#346C2
socleC22×C32C22×C8
prime radicalC22×C3×D3C2×C8
cosocleC2×C3×C8C23×C3
hypercenterC3×#346D3
hypocenterC3C3×#2164
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C8 ◁ C3×#346

303 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, 31366);