Finite Group Databasebeta

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C3×#20264264 #34063374

order19197
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC3×#20264264

Splittings

FittingC3×3−1+2×C79 ⋊ C3
SylowC79 ⋊ C3×#737

Subgroups

subgroupG/H
centerC32C32×C79⋊C3
commutator, cosocleC3×C79C34
FrattiniC3C33×C79⋊C3
FittingC3×3−1+2×C79C3
socleC32×C79C33
prime radicalC3×C32⋊(C79⋊C3)C3
hypercenterC3×3−1+2C79⋊C3
hypocenterC79C3×#737
LCSG ▷ C3×C79 ▷ C79
UCSC1 ◁ C32 ◁ C3×3−1+2

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6399

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19197, 303);