Finite Group Databasebeta

← Prev (#37551598) Next (#37551600) →

C9×C47×C11⋊C5 #37551599

order23265
automorphism?
homologyAbelianization (H1) = C5×C9×C47 · Schur multiplier (H2) = C1

Aliases

direct productC9×C47×C11⋊C5
unambiguous semidirect productC11⋊(C5×C9×C47)
unambiguous semidirect product(C9×C11)⋊(C5×C47)
unambiguous semidirect product(C11×C47)⋊(C5×C9)
unambiguous semidirect product(C9×C11×C47)⋊C5

Splittings

Fitting, HallC9×C11×C47 ⋊ C5
derived, SylowC11 ⋊ C5×C9×C47
HallC11×C47 ⋊ C5×C9
HallC9×C11 ⋊ C5×C47

Subgroups

subgroupG/H
center, hypercenterC9×C47C11⋊C5
commutator, hypocenterC11C5×C9×C47
FrattiniC3C3×C47×C11⋊C5
FittingC9×C11×C47C5
socleC3×C11×C47C3×C5
prime radicalC3×C47×C11⋊C5C3
cosocleC3×C11C3×C5×C47
LCSG ▷ C11
UCSC1 ◁ C9×C47

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4653

Conjugacy classes & character table

2961 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23265, 2);