Finite Group Databasebeta

← Prev (#35204357) Next (#35204359) →

C9×C11×C41⋊C5 #35204358

order20295
automorphism?
homologyAbelianization (H1) = C5×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×C41⋊C5
unambiguous semidirect productC41⋊(C5×C9×C11)
unambiguous semidirect product(C9×C41)⋊(C5×C11)

Splittings

Fitting, HallC9×C11×C41 ⋊ C5
derived, SylowC41 ⋊ C5×C9×C11
HallC11×C41 ⋊ C5×C9
HallC9×C41 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC9×C11C41⋊C5
commutator, hypocenterC41C5×C9×C11
FrattiniC3C3×C11×C41⋊C5
FittingC9×C11×C41C5
socleC3×C11×C41C3×C5
prime radicalC3×C11×C41⋊C5C3
cosocleC3×C41C3×C5×C11
LCSG ▷ C41
UCSC1 ◁ C9×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4059

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20295, 2);