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C3×C13⋊H(5,𝔽3) #23748615

order9477
automorphism?
homologyAbelianization (H1) = C35 · Schur multiplier (H2) = C39

Aliases

direct productC3×C13⋊H(5,𝔽3)
unambiguous semidirect product(C3×C13)⋊H(5,𝔽3)

Splittings

FittingC32×C13×H(3,𝔽3) ⋊ C3
SylowC13 ⋊ C3×H(5,𝔽3)

Subgroups

subgroupG/H
centerC32C33×C13⋊C3
commutator, cosocleC3×C13C35
FrattiniC3C34×C13⋊C3
FittingC32×C13×H(3,𝔽3)C3
socleC32×C13C34
hypercenterC32×H(3,𝔽3)C13⋊C3
hypocenterC13C3×H(5,𝔽3)
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C32 ◁ C32×H(3,𝔽3)

6776 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

645 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 4024);