Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C8 |
| direct product | D3×#1709 |
| Fitting | C3×#1709 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1709 |
982 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 199 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12519, D3×#19603 |
| maximal normal subgroup of | D3×#12519, D3×#19603 |
| maximal quotient of | D3×#12509 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 157233);