Finite Group Databasebeta

← Prev (#49114454) Next (#49114456) →

C7×C9×C11⋊#261 #49114455

order36036
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×C11⋊#261
unambiguous semidirect productC11⋊(C7×C9×#261)

Splittings

Fitting, HallC7×C9×C11×C13 ⋊ C4
derived, HallC11×C13 ⋊ C4×C7×C9
HallC9×C11×C13 ⋊ C4×C7
HallC7×C11×C13 ⋊ C4×C9
HallC7×C9×C13 ⋊ Dic11
HallC7×C9×C11 ⋊ #261
HallC9×C13 ⋊ C7×Dic11
HallC9×C11 ⋊ C7×#261
HallC7×C13 ⋊ C9×Dic11
HallC7×C11 ⋊ C9×#261
SylowC13 ⋊ C7×C9×Dic11
SylowC11 ⋊ C7×C9×#261

Subgroups

subgroupG/H
center, hypercenterC7×C9C11⋊#261
commutator, hypocenterC11×C13C4×C7×C9
FrattiniC3C3×C7×C11⋊#261
FittingC7×C9×C11×C13C4
socleC3×C7×C11×C13C3×C4
prime radicalC3×C7×C11×D13C2×C3
cosocleC3×C11×D13C2×C3×C7
LCSG ▷ C11×C13
UCSC1 ◁ C7×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

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(36036, 123);