Finite Group Databasebeta

#47975076

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

Aliases

No aliases for this group.

Splittings

SylowC433 ⋊ #731

Subgroups

subgroupG/H
centerC3C32⋊(C433⋊C3)
commutator, cosocleC32×C433C32
FrattiniC32C3×C433⋊C3
Fitting, prime radicalH(3,𝔽3)×C433C3
socleC3×C433H(3,𝔽3)
hypercenterH(3,𝔽3)C433⋊C3
hypocenterC433#731
LCSG ▷ C32×C433 ▷ C3×C433 ▷ C433
UCSC1 ◁ C3 ◁ C32 ◁ H(3,𝔽3)

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11691

Polycyclic presentation:

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

Conjugacy classes & character table

1601 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35073, 31);