Finite Group DatabasebetaFinite Group Databasebeta| order | 33813 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C13⋊#14579583 |
| derived, Hall | C13×C172 ⋊ C9 |
| Sylow | C172 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ #14579583 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C13⋊(C172⋊C3) |
| commutator, hypocenter | C13×C172 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C13×C172 | C3 |
| LCS | G ▷ C13×C172 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1989 |
Polycyclic presentation:
3,13,17^2,3|a^3=e,b^a=b^3,c^a=c^11d,d^a=c^3d^53765 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33813, 6);