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#44565437

order32157
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C32

Aliases

No aliases for this group.

Splittings

FittingH(3,𝔽3)×C397 ⋊ C3
SylowC397 ⋊ #732

Subgroups

subgroupG/H
centerC3C32⋊(C397⋊C3)
commutator, cosocleC32×C397C32
FrattiniC32C3×C397⋊C3
FittingH(3,𝔽3)×C397C3
socleC3×C397H(3,𝔽3)
hypercenterH(3,𝔽3)C397⋊C3
hypocenterC397#732
LCSG ▷ C32×C397 ▷ C3×C397 ▷ C397
UCSC1 ◁ C3 ◁ C32 ◁ H(3,𝔽3)

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10719

Polycyclic presentation:

3^4,397|b^3=d^2,b^a=bc,c^a=cd,e^b=e^362

Conjugacy classes & character table

1469 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32157, 34);