Finite Group Databasebeta

← Prev (#46798682) Next (#46798684) →

#46798683

order33777
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

No aliases for this group.

Splittings

FittingC3×3−1+2×C139 ⋊ C3
SylowC139 ⋊ 3−1+4

Subgroups

subgroupG/H
center, FrattiniC3C33×C139⋊C3
commutator, socle, cosocleC3×C139C34
FittingC3×3−1+2×C139C3
prime radicalC3×C32⋊(C139⋊C3)C3
hypercenterC3×3−1+2C139⋊C3
hypocenterC1393−1+4
LCSG ▷ C3×C139 ▷ C139
UCSC1 ◁ C3 ◁ C3×3−1+2

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3753

Polycyclic presentation:

3^5,139|a^3=e,b^a=be,d^a=de,c^b=ce,f^c=f^96

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(33777, 307);