Finite Group Databasebeta

C32×#16812503 #44535264

order31347
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C35

Aliases

direct productC32×#16812503

Splittings

FittingC32×C27×C43 ⋊ C3
SylowC43 ⋊ C32×C27⋊C3

Subgroups

subgroupG/H
centerC32×C9C3×C43⋊C3
commutatorC3×C43C33×C9
FrattiniC9C33×C43⋊C3
FittingC32×C27×C43C3
socleC33×C43C3×C9
prime radicalC33×C43⋊C3C9
cosocleC9×C43C34
hypercenterC32×C27C43⋊C3
hypocenterC43C32×C27⋊C3
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C32×C9 ◁ C32×C27

944 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10449

Conjugacy classes & character table

3699 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 3887);