Finite Group Databasebeta

#38733323

order24867
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3

Aliases

No aliases for this group.

Splittings

SylowC307 ⋊ #731

Subgroups

subgroupG/H
centerC3C32⋊(C307⋊C3)
commutator, cosocleC32×C307C32
FrattiniC32C3×C307⋊C3
Fitting, prime radicalH(3,𝔽3)×C307C3
socleC3×C307H(3,𝔽3)
hypercenterH(3,𝔽3)C307⋊C3
hypocenterC307#731
LCSG ▷ C32×C307 ▷ C3×C307 ▷ C307
UCSC1 ◁ C3 ◁ C32 ◁ H(3,𝔽3)

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8289

Polycyclic presentation:

3^4,307|b^3=d,b^a=bc,c^a=cd,e^b=e^289

Conjugacy classes & character table

1139 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24867, 31);