Finite Group Databasebeta

(C211⋊C9)⋊C9 #30685257

order17091
automorphism?
homologyAbelianization (H1) = C3×C9 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect product(C211⋊C9)⋊C9

Splittings

SylowC211 ⋊ C9⋊C9

Subgroups

subgroupG/H
center, FrattiniC32C3×C211⋊C3
commutatorC3×C211C3×C9
FittingC3×C9×C211C3
socle, prime radical, cosocleC32×C211C32
hypercenterC3×C9C211⋊C3
hypocenterC211C9⋊C9
LCSG ▷ C3×C211 ▷ C211
UCSC1 ◁ C32 ◁ C3×C9

34 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17091

Polycyclic presentation:

3^4,211|a^3=d,b^3=c,b^a=bc,e^b=e^196

Conjugacy classes & character table

1923 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17091, 20);