Finite Group Databasebeta

C32×C32⋊(C43⋊C9) #44534636

order31347
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C37

Aliases

direct productC32×C32⋊(C43⋊C9)

Splittings

SylowC43 ⋊ C32×C32⋊C9

Subgroups

subgroupG/H
centerC34C3×C43⋊C3
commutatorC3×C43C33×C9
FrattiniC32C33×C43⋊C3
Fitting, prime radicalC35×C43C3
socleC34×C43C32
cosocleC32×C43C34
hypercenterC35C43⋊C3
hypocenterC43C32×C32⋊C9
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C34 ◁ C35

2996 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, 3259);