Finite Group Databasebeta

#44534665

order31347
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C35

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #10624862

Subgroups

subgroupG/H
center, FrattiniC32C33×C43⋊C3
commutatorC3×C43C33×C9
Fitting, prime radicalC32×H(3,𝔽3)×C43C3
socle, cosocleC32×C43C34
hypercenterC32×H(3,𝔽3)C43⋊C3
hypocenterC43#10624862
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C32×H(3,𝔽3)

1178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3483

Polycyclic presentation:

3^6,43|a^3=f,b^a=be,d^a=de,g^a=g^36,c^b=ce

Conjugacy classes & character table

1635 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 3288);