Finite Group Databasebeta

C3×#21419253 #36381082

order22599
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C32

Aliases

direct productC3×#21419253

Splittings

SylowC31 ⋊ C3×#6875

Subgroups

subgroupG/H
centerC32(C31⋊C9)⋊C9
commutatorC9×C31C32×C9
FrattiniC3×C9C32×C31⋊C3
FittingC3×C31×C27⋊C3C3
socleC32×C31C9⋊C9
prime radicalC33×C313−1+2
cosocleC3×C9×C31C33
hypercenterC3×C27⋊C3C31⋊C3
hypocenterC31C3×#6875
LCSG ▷ C9×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C32 ◁ C32×C9 ◁ C3×C27⋊C3

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2511

Conjugacy classes & character table

1095 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 2103);