Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43 |
| direct product | C42×ΓL(1,𝔽25) |
| Fitting | C3×C42×C8 ⋊ C2 |
| Sylow | C3 ⋊ C42×M16 |
1734 conjugacy classes of subgroups; only the 915 normal subgroups are shown.
This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 915 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 166897);