Finite Group Databasebeta

← Prev (#47977666) Next (#47977668) →

D19⋊C3×D155 #47977667

order35340
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD19⋊C3×D155
unambiguous semidirect productD19⋊(C3×D155)
unambiguous semidirect product(C5×D19⋊C3)⋊D31
unambiguous semidirect product(C31×D19⋊C3)⋊D5

Splittings

Fitting, socle, derived, HallC5×C19×C31 ⋊ C22×C3
HallD19×D155 ⋊ C3
HallC5×C31×C19⋊C3 ⋊ C22
HallC31×C19⋊C3 ⋊ C2×D5
HallC19×C31 ⋊ C2×C3×D5
HallC5×C19⋊C3 ⋊ C2×D31
HallC5×C31 ⋊ C2×D19⋊C3
HallC5×C19 ⋊ C2×C3×D31
HallC19⋊C3 ⋊ C2×D155
SylowC31 ⋊ D5×D19⋊C3
SylowC19 ⋊ C2×C3×D155
SylowC5 ⋊ D31×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C19×C31C22×C3
LCSG ▷ C5×C19×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2945

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 139);