Finite Group Databasebeta

← Prev (#35204358) Next (#35204360) →

C9×C41×C11⋊C5 #35204359

order20295
automorphism?
homologyAbelianization (H1) = C5×C9×C41 · Schur multiplier (H2) = C1

Aliases

direct productC9×C41×C11⋊C5
unambiguous semidirect productC11⋊(C5×C9×C41)
unambiguous semidirect product(C9×C11)⋊(C5×C41)

Splittings

Fitting, HallC9×C11×C41 ⋊ C5
derived, SylowC11 ⋊ C5×C9×C41
HallC11×C41 ⋊ C5×C9
HallC9×C11 ⋊ C5×C41

Subgroups

subgroupG/H
center, hypercenterC9×C41C11⋊C5
commutator, hypocenterC11C5×C9×C41
FrattiniC3C3×C41×C11⋊C5
FittingC9×C11×C41C5
socleC3×C11×C41C3×C5
prime radicalC3×C41×C11⋊C5C3
cosocleC3×C11C3×C5×C41
LCSG ▷ C11
UCSC1 ◁ C9×C41

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4059

Conjugacy classes & character table

2583 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20295, 3);