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#34063141

order19197
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C32

Aliases

No aliases for this group.

Splittings

FittingC3×H(3,𝔽3)×C79 ⋊ C3
SylowC79 ⋊ #6856

Subgroups

subgroupG/H
centerC32C32⋊(C79⋊C3)
commutator, cosocleC33×C79C32
FrattiniC33C3×C79⋊C3
FittingC3×H(3,𝔽3)×C79C3
socleC32×C79H(3,𝔽3)
hypercenterC3×H(3,𝔽3)C79⋊C3
hypocenterC79#6856
LCSG ▷ C33×C79 ▷ C32×C79 ▷ C79
UCSC1 ◁ C32 ◁ C33 ◁ C3×H(3,𝔽3)

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6399

Polycyclic presentation:

3^5,79|b^a=bc,c^a=cd,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, 70);