Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#74298 |
| Fitting | C2×C3×#383 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2380 |
3798 conjugacy classes of subgroups; only the 923 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 923 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11427642, C2×#11427644, #72255141, … |
| maximal normal subgroup of | C2×#11427642, C2×#11427644, #72255141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 332197);