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C3×#20238272 #31801397

order17739
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productC3×#20238272

Splittings

FittingC3×3−1+2×C73 ⋊ C3
SylowC73 ⋊ C3×#731

Subgroups

subgroupG/H
centerC32C32⋊(C73⋊C3)
commutator, cosocleC32×C73C33
FrattiniC32C32×C73⋊C3
FittingC3×3−1+2×C73C3
socleC32×C73H(3,𝔽3)
prime radicalC3×C32⋊(C73⋊C3)C3
hypercenterC3×3−1+2C73⋊C3
hypocenterC73C3×#731
LCSG ▷ C32×C73 ▷ C3×C73 ▷ C73
UCSC1 ◁ C32 ◁ C33 ◁ C3×3−1+2

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5913

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17739, 250);