Finite Group Databasebeta

C3×#85680 #11900878

order1152
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C28

Aliases

direct productC3×#85680

Splittings

FittingC22×C32×C42 ⋊ C2
SylowC32 ⋊ #3444

Subgroups

subgroupG/H
centerC3×C42C22×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC22×C32×C42C2
socleC22×C32C25
hypercenterC22×C3×C42D3
hypocenterC3C3×#3444
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C3×C42 ◁ C22×C3×C42

2673 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 134889);