Finite Group Databasebeta

C3×C32⋊#11758281 #40996989

order26487
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productC3×C32⋊#11758281
unambiguous semidirect product(C109⋊C3)⋊(C32⋊C9)
unambiguous semidirect product(C3×#11758281)⋊C32

Splittings

FittingC33×C109 ⋊ C9
SylowC109 ⋊ C3×C32⋊C9

Subgroups

subgroupG/H
centerC32C3×#11758281
commutatorC3×C109C32×C9
FrattiniC3C32×#11758281
FittingC33×C109C9
socleC32×C109C3×C9
prime radicalC33×C109⋊C3C3
cosocleC3×C109⋊C3C33
hypercenterC33#11758281
hypocenterC109C3×C32⋊C9
LCSG ▷ C3×C109 ▷ C109
UCSC1 ◁ C32 ◁ C33

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2943

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26487, 347);