Finite Group Databasebeta

← Prev (#34089415) Next (#34089417) →

D3×C13×C23⋊C11 #34089416

order19734
automorphism?
homologyAbelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productD3×C13×C23⋊C11
unambiguous semidirect productC3⋊(C2×C13×C23⋊C11)
unambiguous semidirect product(D3×C23)⋊(C11×C13)
unambiguous semidirect product(D3×C13×C23)⋊C11

Splittings

Fitting, socle, HallC3×C13×C23 ⋊ C2×C11
derived, HallC3×C23 ⋊ C2×C11×C13
HallC3×C13×C23⋊C11 ⋊ C2
HallD3×C13×C23 ⋊ C11
HallC3×C23⋊C11 ⋊ C2×C13
HallC13×C23 ⋊ D3×C11
HallD3×C23 ⋊ C11×C13
HallC3×C13 ⋊ C2×C23⋊C11
SylowC23 ⋊ D3×C11×C13
SylowC3 ⋊ C2×C13×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC13D3×C23⋊C11
commutator, cosocle, hypocenterC3×C23C2×C11×C13
FrattiniC1G
Fitting, socleC3×C13×C23C2×C11
LCSG ▷ C3×C23
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 897

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 23);