Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #356×D131 |
| Fitting | #356×C131 ⋊ C2 |
| Sylow | C131 ⋊ C2×#356 |
240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2096 |
871 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 6189);