Finite Group Databasebeta

C3×#73322 #11800898

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

Aliases

direct productC3×#73322

Splittings

FittingC2×C32×#95 ⋊ C2
SylowC32 ⋊ #2275

Subgroups

subgroupG/H
centerC23×C3C23×D3
commutatorC2×C3C22×C3×C42
FrattiniC23C23×C3×D3
FittingC2×C32×#95C2
socleC23×C32C24
prime radicalC22×C3×#67C22
cosocleC23×C3C24×C3
hypercenterC2×C3×#95D3
hypocenterC3C3×#2275
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#95

1725 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, 34909);