Finite Group Databasebeta

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#16836729⋊C9 #46798547

order33777
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C32

Aliases

unambiguous semidirect product#16836729⋊C9

Splittings

FittingC9⋊C9×C139 ⋊ C3
SylowC139 ⋊ C9×3−1+2

Subgroups

subgroupG/H
center, FrattiniC32C32×C139⋊C3
commutatorC3×C139C32×C9
FittingC9⋊C9×C139C3
socle, cosocleC32×C139C33
prime radicalC32×C139⋊C3C32
hypercenterC9⋊C9C139⋊C3
hypocenterC139C9×3−1+2
LCSG ▷ C3×C139 ▷ C139
UCSC1 ◁ C32 ◁ C9⋊C9

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11259

Polycyclic presentation:

3^5,139|a^3=e,b^3=d,c^3=e,b^a=bd,f^c=f^42

Conjugacy classes & character table

1617 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33777, 171);