Finite Group Databasebeta

← Prev (#34062035) Next (#34062037) →

C5×(C13⋊C3)⋊D49 #34062036

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C13⋊C3)⋊D49
unambiguous semidirect product(C13⋊C3)⋊(C5×D49)

Splittings

Fitting, HallC5×C13×C49 ⋊ C2×C3
derived, HallC13×C49 ⋊ C2×C3×C5
HallC5×C13⋊C3×C49 ⋊ C2
HallC5×D637 ⋊ C3
HallC13⋊C3×C49 ⋊ C2×C5
HallD637 ⋊ C3×C5
HallC5×C49 ⋊ D13⋊C3
HallC5×C13⋊C3 ⋊ D49
HallC5×C13 ⋊ C3×D49
SylowC49 ⋊ C5×D13⋊C3
HallC13⋊C3 ⋊ C5×D49
SylowC13 ⋊ C3×C5×D49

Subgroups

subgroupG/H
center, hypercenterC5(C13⋊C3)⋊D49
commutator, cosocle, hypocenterC13×C49C2×C3×C5
FrattiniC7C5×(C13⋊C3)⋊D7
FittingC5×C13×C49C2×C3
socleC5×C7×C13C3×D7
LCSG ▷ C13×C49
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D13⋊C3×D49, D5×(C13⋊C3)⋊D49, (C5⋊(D13⋊C3))⋊D49, …
maximal normal subgroup ofC5×D13⋊C3×D49, D5×(C13⋊C3)⋊D49, (C5⋊(D13⋊C3))⋊D49, …
maximal quotient ofC5×#21439435, C2×C5×(C13⋊C3)⋊D49

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 29);