Finite Group Databasebeta

← Prev (#19104156) Next (#19104158) →

C11×C22⋊(C13⋊C9) #19104157

order5148
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×C22⋊(C13⋊C9)
unambiguous semidirect productC22⋊(C11×C13⋊C9)
unambiguous semidirect productC13⋊(C11×C22⋊C9)
unambiguous semidirect product(C22×C11)⋊(C13⋊C9)
unambiguous semidirect product(C11×C13)⋊(C22⋊C9)

Splittings

derived, HallC22×C13 ⋊ C9×C11
HallC22×C11×C13 ⋊ C9
HallC11×C13 ⋊ C22⋊C9
HallC22×C11 ⋊ C13⋊C9
SylowC13 ⋊ C11×C22⋊C9
SylowC22 ⋊ C11×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C11C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C9×C11
FrattiniC3C11×C22⋊(C13⋊C3)
Fitting, socleC22×C3×C11×C13C3
LCSG ▷ C22×C13
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×C22⋊(C13⋊C9), C5×C11×C22⋊(C13⋊C9), C11×C22⋊#11717941, …
maximal normal subgroup ofC11⋊C5×C22⋊(C13⋊C9), C5×C11×C22⋊(C13⋊C9), C7×C11×C22⋊(C13⋊C9)
maximal quotient ofC5×C11×C22⋊(C13⋊C9), C11×C22⋊#11717941, C11×C22⋊#11717942, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 33);