Finite Group Databasebeta

← Prev (#26015200) Next (#26015202) →

C13⋊C3×D145 #26015201

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

Aliases

direct productC13⋊C3×D145
unambiguous semidirect productC5⋊(C13⋊C3×D29)
unambiguous semidirect productC29⋊(D5×C13⋊C3)
unambiguous semidirect product(C13×D145)⋊C3

Splittings

Fitting, socle, derived, HallC5×C13×C29 ⋊ C2×C3
HallC5×C29×C13⋊C3 ⋊ C2
HallC13×D145 ⋊ C3
HallC29×C13⋊C3 ⋊ D5
HallC13×C29 ⋊ C3×D5
HallC5×C13⋊C3 ⋊ D29
HallC5×C29 ⋊ C2×C13⋊C3
HallC5×C13 ⋊ C3×D29
SylowC29 ⋊ D5×C13⋊C3
SylowC13 ⋊ C3×D145
SylowC5 ⋊ C13⋊C3×D29

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13×C29C2×C3
LCSG ▷ C5×C13×C29
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

518 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#21419478⋊C3, #21419479⋊C3, C13⋊C3×#10596814, …
maximal normal subgroup of#21419478⋊C3, #21419479⋊C3, C13⋊C3×#10596814, …
maximal quotient ofC13⋊C3×Dic145, C2×C13⋊C3×D145, C13⋊C9×D145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11310, 22);