Finite Group Databasebeta

← Prev (#30660208) Next (#30660210) →

C3×C11×C13×C13⋊C3 #30660209

order16731
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C32×C11×C13 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×C13×C13⋊C3
unambiguous semidirect productC13⋊(C32×C11×C13)
unambiguous semidirect product(C3×C13)⋊(C3×C11×C13)
unambiguous semidirect product(C11×C13)⋊(C32×C13)
unambiguous semidirect product(C3×C11×C13)⋊(C3×C13)

Splittings

Fitting, socleC3×C11×C132 ⋊ C3
derivedC13 ⋊ C32×C11×C13
HallC11×C132 ⋊ C32
SylowC132 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11×C13C13⋊C3
commutator, cosocle, hypocenterC13C32×C11×C13
FrattiniC1G
Fitting, socleC3×C11×C132C3
LCSG ▷ C13
UCSC1 ◁ C3×C11×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1287

Conjugacy classes & character table

3003 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×C13×D13⋊C3, C3×C11×(C13⋊C3)⋊D13, C3×C11×D13×C13⋊C3, …
maximal normal subgroup ofC3×C11×C13×D13⋊C3, C3×C11×(C13⋊C3)⋊D13, C3×C11×D13×C13⋊C3, …
maximal quotient ofC2×C3×C11×C13×C13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16731, 12);