Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C3⋊(C7⋊#595) |
| unambiguous semidirect product | C3⋊(C3×C7×C7⋊#595) |
| Fitting, socle, Hall | C32×C72×C17 ⋊ C4 |
| derived | C3×C7×C17 ⋊ C3×C4×C7 |
| Hall | C72×C17 ⋊ C3×Dic3 |
| Hall | C32×C72 ⋊ #595 |
| Hall | C32×C17 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ C3×C3⋊#595 |
| Sylow | C17 ⋊ C3×C7×Dic21 |
| Sylow | C32 ⋊ C7×C7⋊#595 |
184 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 714 |
2268 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 576);