Finite Group Databasebeta

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C3×C5×C41×C19⋊C3 #46856323

order35055
automorphism?
homologyAbelianization (H1) = C32×C5×C41 · Schur multiplier (H2) = C3

Aliases

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

Splittings

Fitting, socleC3×C5×C19×C41 ⋊ C3
derived, SylowC19 ⋊ C32×C5×C41
HallC5×C19×C41 ⋊ C32
HallC19×C41 ⋊ C32×C5
HallC5×C19 ⋊ C32×C41

Subgroups

subgroupG/H
center, hypercenterC3×C5×C41C19⋊C3
commutator, cosocle, hypocenterC19C32×C5×C41
FrattiniC1G
Fitting, socleC3×C5×C19×C41C3
LCSG ▷ C19
UCSC1 ◁ C3×C5×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11685

Conjugacy classes & character table

5535 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35055, 10);