Finite Group DatabasebetaFinite Group Databasebeta| order | 33813 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C13⋊#14579585 |
| Fitting, socle, derived, Hall | C13×C172 ⋊ C9 |
| Sylow | C172 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ #14579585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C172 | C9 |
| prime radical, cosocle | C13×C172⋊C3 | C3 |
| LCS | G ▷ C13×C172 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1989 |
Polycyclic presentation:
3^2,13,17^2|a^3=b,c^a=c^3,d^a=d^6e^6,e^a=d^5e^8,d^b=e^14,e^b=d^6e^16437 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33813, 12);