Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of #67448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#67448 |
| Fitting | C2×C3×#323 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1343 |
1164 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 79736);