Finite Group Databasebeta

#47975063

order35073
automorphism?
homologyAbelianization (H1) = C3×C9 · Schur multiplier (H2) = C32

Aliases

No aliases for this group.

Splittings

FittingC3×C9×C433 ⋊ C3
SylowC433 ⋊ C32⋊C9

Subgroups

subgroupG/H
center, FrattiniC32C3×C433⋊C3
commutatorC3×C433C3×C9
FittingC3×C9×C433C3
socle, cosocleC32×C433C32
prime radicalC32×C433⋊C3C3
hypercenterC3×C9C433⋊C3
hypocenterC433C32⋊C9
LCSG ▷ C3×C433 ▷ C433
UCSC1 ◁ C32 ◁ C3×C9

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11691

Polycyclic presentation:

3^4,433|a^3=d,b^a=bc,e^b=e^198

Conjugacy classes & character table

3921 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35073, 18);