Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#22553498 |
| Fitting | C2×#120×C131 ⋊ C2 |
| Sylow | C131 ⋊ C2×B(4,𝔽2) |
1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2096 |
1852 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 13893);