Finite Group Databasebeta

C3×#68668 #11787131

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C25

Aliases

direct productC3×#68668

Splittings

FittingC32×#336 ⋊ C2
SylowC32 ⋊ #1869

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC32×#336C2
socleC23×C32C22×C4
prime radicalC22×C3×D12C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#336D3
hypocenterC3C3×#1869
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×#336

923 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, 21142);