Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×ΓL(1,𝔽8)×C7⋊#595 |
| Fitting, socle | C3×C72×C17 ⋊ C3×C4 |
| derived, Hall | C72×C17 ⋊ C32×C4 |
| Hall | C3×C7×C17×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C7×C7⋊#595 ⋊ C32 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ #595 |
| Sylow | C72 ⋊ C32×#595 |
| Sylow | C17 ⋊ C3×ΓL(1,𝔽8)×Dic7 |
152 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 152 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) = 2142 |
570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 389);