Finite Group DatabasebetaFinite Group Databasebeta| order | 33865 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C521⋊C5)⋊C13 |
| unambiguous semidirect product | (C521⋊C13)⋊C5 |
| Fitting, socle, derived, Sylow | C521 ⋊ C5×C13 |
| Hall | C521⋊C13 ⋊ C5 |
| Hall | C521⋊C5 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C521 | C5×C13 |
| LCS | G ▷ C521 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 521 |
Polycyclic presentation:
5,13,521|c^a=c^25,c^b=c^42273 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33865, 1);