Finite Group Databasebeta

C32×C32⋊(C31⋊C9) #36382238

order22599
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C37

Aliases

direct productC32×C32⋊(C31⋊C9)

Splittings

SylowC31 ⋊ C32×C32⋊C9

Subgroups

subgroupG/H
centerC34C3×C31⋊C3
commutatorC3×C31C33×C9
FrattiniC32C33×C31⋊C3
Fitting, prime radicalC35×C31C3
socleC34×C31C32
cosocleC32×C31C34
hypercenterC35C31⋊C3
hypocenterC31C32×C32⋊C9
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C34 ◁ C35

2996 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

Conjugacy classes & character table

2727 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 3259);