Finite Group Databasebeta

C31⋊C3×#6855 #36379834

order22599
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C35

Aliases

direct productC31⋊C3×#6855

Splittings

FittingC31×#6855 ⋊ C3
SylowC31 ⋊ C3×#6855

Subgroups

subgroupG/H
center, FrattiniC33C32×C31⋊C3
commutatorC3×C31C3×C92
FittingC31×#6855C3
socle, cosocleC33×C31C33
prime radicalC33×C31⋊C3C32
hypercenter#6855C31⋊C3
hypocenterC31C3×#6855
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C33 ◁ #6855

1052 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 855);