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#34063346

order19197
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C34

Aliases

No aliases for this group.

Splittings

FittingC3×H(3,𝔽3)×C79 ⋊ C3
SylowC79 ⋊ #6911

Subgroups

subgroupG/H
centerC3C3×C32⋊(C79⋊C3)
commutator, cosocleC32×C79C33
FrattiniC32C32×C79⋊C3
FittingC3×H(3,𝔽3)×C79C3
socleC3×C79C3×H(3,𝔽3)
hypercenterC3×H(3,𝔽3)C79⋊C3
hypocenterC79#6911
LCSG ▷ C32×C79 ▷ C3×C79 ▷ C79
UCSC1 ◁ C3 ◁ C33 ◁ C3×H(3,𝔽3)

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2133

Polycyclic presentation:

3^5,79|b^3=e^2,b^a=bd,d^a=de,c^b=ce,f^b=f^23

Conjugacy classes & character table

893 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19197, 275);