Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#23756143 |
| derived, Hall | C72×C17 ⋊ C32×C4 |
| Hall | C3×C17×#3861 ⋊ C4 |
| Hall | C7⋊Dic119 ⋊ C32 |
| Hall | C3×#3861 ⋊ Dic17 |
| Sylow | C72 ⋊ C32×Dic17 |
| Sylow | C17 ⋊ C3×#10596874 |
360 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9996 |
996 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 288);