Finite Group Databasebeta

C3×#67731 #11772451

order1152
isoclinismisoclinic class of #4487
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C22

Aliases

direct productC3×#67731

Splittings

SylowC32 ⋊ #1385

Subgroups

subgroupG/H
centerC3×C4#808
commutatorC3×C8C3×C42
FrattiniC22×C8C2×C3×D3
FittingC2×C32×#108C2
socleC2×C32#340
prime radicalC23×C32Q16
cosocleC22×C3×C8C22×C3
hypercenterC2×C3×#108D3
hypocenterC3C3×#1385
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×#108

301 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 6462);