Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C17 · Schur multiplier (H2) = C2 |
| direct product | C2×C17×#11725075 |
| derived, Sylow | C72 ⋊ C22×C9×C17 |
| Hall | C17×#89205 ⋊ C22 |
| Hall | C2×C7×D7×C17 ⋊ C9 |
| Hall | C72×C17 ⋊ C22×C9 |
| Hall | #89205 ⋊ C22×C17 |
| Hall | C2×C7×D7 ⋊ C9×C17 |
128 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4284 |
1734 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 212);