Finite Group Databasebeta

← Prev (#36373262) Next (#36373264) →

C13×C11⋊(Dic13⋊C3) #36373263

order22308
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C11⋊(Dic13⋊C3)
unambiguous semidirect productC11⋊(C13×Dic13⋊C3)
unambiguous semidirect productDic143⋊(C3×C13)

Splittings

derivedC11×C13 ⋊ C3×C4×C13
HallC13×Dic143 ⋊ C3
HallC11×C13×C13⋊C3 ⋊ C4
HallC11×C132 ⋊ C3×C4
HallC13×C13⋊C3 ⋊ Dic11
SylowC132 ⋊ C3×Dic11
SylowC11 ⋊ C13×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C13C11⋊(D13⋊C3)
commutator, hypocenterC11×C13C3×C4×C13
FrattiniC2C13×C11⋊(D13⋊C3)
Fitting, socleC2×C11×C132C2×C3
prime radicalC2×C11×C13×C13⋊C3C2
cosocleC2×C11×C13C2×C3×C13
LCSG ▷ C11×C13
UCSC1 ◁ C2×C13

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1716

Conjugacy classes & character table

1118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22308, 50);