Finite Group Databasebeta

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C3×C19⋊C3×C41⋊C5 #46856320

order35055
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C19⋊C3×C41⋊C5
unambiguous semidirect productC19⋊(C32×C41⋊C5)
unambiguous semidirect productC41⋊(C3×C5×C19⋊C3)
unambiguous semidirect product(C3×C19)⋊(C3×C41⋊C5)
unambiguous semidirect product(C3×C41)⋊(C5×C19⋊C3)
unambiguous semidirect product(C41×C19⋊C3)⋊(C3×C5)
unambiguous semidirect product(C19×C41⋊C5)⋊C32
unambiguous semidirect product(C3×C41×C19⋊C3)⋊C5
unambiguous semidirect product(C3×C19×C41⋊C5)⋊C3

Splittings

Fitting, socleC3×C19×C41 ⋊ C3×C5
derived, HallC19×C41 ⋊ C32×C5
HallC3×C41×C19⋊C3 ⋊ C5
HallC19×C41⋊C5 ⋊ C32
SylowC41 ⋊ C3×C5×C19⋊C3
SylowC19 ⋊ C32×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C19⋊C3×C41⋊C5
commutator, cosocle, hypocenterC19×C41C32×C5
FrattiniC1G
Fitting, socleC3×C19×C41C3×C5
LCSG ▷ C19×C41
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2337

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35055, 7);