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#30685271

order17091
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C32

Aliases

No aliases for this group.

Splittings

FittingH(3,𝔽3)×C211 ⋊ C3
SylowC211 ⋊ #732

Subgroups

subgroupG/H
centerC3C32⋊(C211⋊C3)
commutator, cosocleC32×C211C32
FrattiniC32C3×C211⋊C3
FittingH(3,𝔽3)×C211C3
socleC3×C211H(3,𝔽3)
hypercenterH(3,𝔽3)C211⋊C3
hypocenterC211#732
LCSG ▷ C32×C211 ▷ C3×C211 ▷ C211
UCSC1 ◁ C3 ◁ C32 ◁ H(3,𝔽3)

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5697

Polycyclic presentation:

3^4,211|b^3=d^2,b^a=bc,c^a=cd,e^b=e^196

Conjugacy classes & character table

787 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17091, 34);