Finite Group DatabasebetaFinite Group Databasebeta| order | 19734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(C23⋊(D13⋊C3)) |
| unambiguous semidirect product | C23⋊(C11⋊(D13⋊C3)) |
| unambiguous semidirect product | (C13⋊C3)⋊D253 |
| unambiguous semidirect product | D3289⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C13×C23 | C2×C3 |
| LCS | G ▷ C11×C13×C23 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3289 |
Polycyclic presentation:
2,3,11,13,23|c^a=c^10,d^a=d^12,e^a=e^22,d^b=d^3890 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19734, 33);