Finite Group Databasebeta

C3×#78548 #11857217

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×#78548

Splittings

FittingC32×#405 ⋊ C2
SylowC32 ⋊ #2873

Subgroups

subgroupG/H
centerC2×C3×C4C23×D3
commutatorC2×C3C22×C3×C42
FrattiniC2×C4C23×C3×D3
FittingC32×#405C2
socleC22×C32C23×C4
prime radicalC23×C3×D3C2×C4
cosocleC2×C3×C4C24×C3
hypercenterC3×#405D3
hypocenterC3C3×#2873
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×#405

1193 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 91228);