Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#67791 |
| Sylow | C3 ⋊ C2×#1357 |
494 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 131 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.
| maximal subgroup of | C2×#10708580, #72226166 |
| maximal normal subgroup of | C2×#10708580, #72226166 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 80772);