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#34063264

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

Aliases

No aliases for this group.

Splittings

FittingC3×3−1+2×C79 ⋊ C3
SylowC79 ⋊ #6893

Subgroups

subgroupG/H
center, FrattiniC32C32×C79⋊C3
commutator, socle, cosocleC32×C79C33
FittingC3×3−1+2×C79C3
prime radicalC3×C32⋊(C79⋊C3)C3
hypercenterC3×3−1+2C79⋊C3
hypocenterC79#6893
LCSG ▷ C32×C79 ▷ C79
UCSC1 ◁ C32 ◁ C3×3−1+2

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6399

Polycyclic presentation:

3^5,79|c^3=d,b^a=bd,c^a=ce,f^a=f^55,f^c=f^23

Conjugacy classes & character table

909 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19197, 193);