Finite Group Databasebeta

← Prev (#26044575) Next (#26044577) →

C2×C9×C131⋊C5 #26044576

order11790
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C9×C131⋊C5
unambiguous semidirect product(C2×C131)⋊(C5×C9)
unambiguous semidirect product(C2×C9×C131)⋊C5

Splittings

Fitting, HallC2×C9×C131 ⋊ C5
derived, SylowC131 ⋊ C2×C5×C9
HallC9×C131 ⋊ C2×C5
HallC2×C131 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9C131⋊C5
commutator, hypocenterC131C2×C5×C9
FrattiniC3C2×C3×C131⋊C5
FittingC2×C9×C131C5
socleC2×C3×C131C3×C5
prime radicalC2×C3×C131⋊C5C3
cosocleC3×C131C2×C3×C5
LCSG ▷ C131
UCSC1 ◁ C2×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

558 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C9×C131⋊C5, C9×Dic131⋊C5, Dic9×C131⋊C5, …
maximal normal subgroup ofC4×C9×C131⋊C5, C9×Dic131⋊C5, Dic9×C131⋊C5, …
maximal quotient ofC4×C9×C131⋊C5, C22×C9×C131⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11790, 2);