Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | D3×#2199 |
| Fitting | C3×#2199 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2199 |
1392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1392 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#85559, D3×#85557, D3×#73027, … |
| maximal normal subgroup of | D3×#33551, D3×#33550, D3×#33555, … |
| maximal quotient of | D3×#13343, D3×#13348, D3×#13050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323594);