Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D5×#66526 |
| unambiguous semidirect product | C5⋊(C22×C5×#66526) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C5×#66526) |
| Fitting, socle | C2×C52×C37 ⋊ C2×C9 |
| derived | C5×C37 ⋊ C22×C5×C9 |
| Hall | C52×#66526 ⋊ C22 |
| Hall | C2×C5×D5×C37 ⋊ C9 |
| Hall | C52×C37 ⋊ C22×C9 |
| Sylow | C37 ⋊ C2×C5×C9×D5 |
| Sylow | C52 ⋊ C22×#66526 |
144 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 740 |
520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 468);