Finite Group Databasebeta

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C3×C5×C19×D19⋊C3 #44570577

order32490
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C19 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C19×D19⋊C3
unambiguous semidirect productD19⋊(C32×C5×C19)
unambiguous semidirect product(C19⋊C3)⋊(C2×C3×C5×C19)
unambiguous semidirect product(C3×D19)⋊(C3×C5×C19)
unambiguous semidirect product(C5×D19)⋊(C32×C19)
unambiguous semidirect product(C3×C5×D19)⋊(C3×C19)

Splittings

Fitting, socleC3×C5×C192 ⋊ C2×C3
derivedC19 ⋊ C2×C32×C5×C19
HallC3×C5×C19×C19⋊C3 ⋊ C2
HallC5×C19×D19 ⋊ C32
HallC3×C19×C19⋊C3 ⋊ C2×C5
HallC5×C192 ⋊ C2×C32
HallC19×D19 ⋊ C32×C5
SylowC192 ⋊ C2×C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5×C19D19⋊C3
commutator, cosocle, hypocenterC19C2×C32×C5×C19
FrattiniC1G
Fitting, socleC3×C5×C192C2×C3
LCSG ▷ C19
UCSC1 ◁ C3×C5×C19

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1710

Conjugacy classes & character table

2565 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 161);