Finite Group Databasebeta

← Prev (#26015198) Next (#26015200) →

C5×C29⋊(D13⋊C3) #26015199

order11310
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29⋊(D13⋊C3)
unambiguous semidirect productC29⋊(C5×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C5×D29)
unambiguous semidirect productD377⋊(C3×C5)
unambiguous semidirect product(C5×D377)⋊C3

Splittings

Fitting, socle, HallC5×C13×C29 ⋊ C2×C3
derived, HallC13×C29 ⋊ C2×C3×C5
HallC5×C29×C13⋊C3 ⋊ C2
HallC5×D377 ⋊ C3
HallC29×C13⋊C3 ⋊ C2×C5
HallD377 ⋊ C3×C5
HallC5×C13⋊C3 ⋊ D29
HallC5×C29 ⋊ D13⋊C3
HallC5×C13 ⋊ C3×D29
HallC13⋊C3 ⋊ C5×D29
SylowC29 ⋊ C5×D13⋊C3
SylowC13 ⋊ C3×C5×D29

Subgroups

subgroupG/H
center, hypercenterC5C29⋊(D13⋊C3)
commutator, cosocle, hypocenterC13×C29C2×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C29C2×C3
LCSG ▷ C13×C29
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

530 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#13094087⋊C3, C5×#13094088⋊C3, C5×D29×D13⋊C3, …
maximal normal subgroup ofC5×#13094087⋊C3, C5×#13094088⋊C3, C5×D29×D13⋊C3, …
maximal quotient ofC5×Dic377⋊C3, C2×C5×C29⋊(D13⋊C3), C5×C29⋊(D13⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11310, 20);