Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#85453 |
| Fitting | C2×#568 ⋊ D3 |
1365 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1365 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11715001, #72226336, #72228334, … |
| maximal normal subgroup of | C2×#11715001, #72226336, #72228334, … |
| maximal quotient of | #72228334, D3×#85453 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1089039);