Finite Group Databasebeta

← Prev (#34084332) Next (#34084334) →

C2×C5×C17×D19⋊C3 #34084333

order19380
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C17×D19⋊C3
unambiguous semidirect productD19⋊(C2×C3×C5×C17)
unambiguous semidirect product(C19⋊C3)⋊(C22×C5×C17)
unambiguous semidirect product(C2×D19)⋊(C3×C5×C17)
unambiguous semidirect product(C2×C19⋊C3)⋊(C2×C5×C17)
unambiguous semidirect product(C2×C5×D19)⋊(C3×C17)
unambiguous semidirect product(C2×C17×D19)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C17×D19)⋊C3

Splittings

Fitting, socleC2×C5×C17×C19 ⋊ C2×C3
derived, SylowC19 ⋊ C22×C3×C5×C17
HallC2×C5×C17×D19 ⋊ C3
HallC5×C17×C19⋊C3 ⋊ C22
HallC5×C17×C19 ⋊ C22×C3
HallC2×C17×D19 ⋊ C3×C5
HallC17×C19⋊C3 ⋊ C22×C5
HallC2×C5×D19 ⋊ C3×C17
HallC17×C19 ⋊ C22×C3×C5
HallC5×C19⋊C3 ⋊ C22×C17
HallC5×C19 ⋊ C22×C3×C17
HallC2×D19 ⋊ C3×C5×C17
HallC19⋊C3 ⋊ C22×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17D19⋊C3
commutator, cosocle, hypocenterC19C22×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C5×C17×C19C2×C3
LCSG ▷ C19
UCSC1 ◁ C2×C5×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3230

Conjugacy classes & character table

1530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 45);