Finite Group DatabasebetaFinite Group Databasebeta| order | 33810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23×C49 · Schur multiplier (H2) = C1 |
| direct product | C3×D5×C23×C49 |
| unambiguous semidirect product | C5⋊(C2×C3×C23×C49) |
| Fitting, Hall | C3×C5×C23×C49 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C3×C23×C49 |
| Hall | C5×C23×C49 ⋊ C2×C3 |
| Hall | C3×C5×C49 ⋊ C2×C23 |
| Hall | C3×C5×C23 ⋊ C2×C49 |
| Hall | C5×C49 ⋊ C2×C3×C23 |
| Hall | C5×C23 ⋊ C2×C3×C49 |
| Hall | C3×C5 ⋊ C2×C23×C49 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16905 |
13524 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33810, 6);