Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×D3×#123 |
| Fitting | C22×C3×#123 ⋊ C2 |
| Sylow | C3 ⋊ C23×#123 |
15150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×#525, C22×D3×#534, D3×#15412, … |
| maximal normal subgroup of | C22×D3×#525, C22×D3×#534, D3×#15412, … |
| maximal quotient of | C22×D3×#386, D3×#35713 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076213);