Finite Group Databasebeta

← Prev (#48001054) Next (#48001056) →

C11⋊C5×D323 #48001055

order35530
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D323
unambiguous semidirect productC17⋊(D19×C11⋊C5)
unambiguous semidirect productC19⋊(D17×C11⋊C5)
unambiguous semidirect product(C11×D323)⋊C5

Splittings

Fitting, socle, derived, HallC11×C17×C19 ⋊ C2×C5
HallC17×C19×C11⋊C5 ⋊ C2
HallC11×D323 ⋊ C5
HallC19×C11⋊C5 ⋊ D17
HallC17×C11⋊C5 ⋊ D19
HallC17×C19 ⋊ C2×C11⋊C5
HallC11×C19 ⋊ C5×D17
HallC11×C17 ⋊ C5×D19
SylowC19 ⋊ D17×C11⋊C5
SylowC17 ⋊ D19×C11⋊C5
SylowC11 ⋊ C5×D323

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C17×C19C2×C5
LCSG ▷ C11×C17×C19
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3553

Conjugacy classes & character table

1141 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 20);