Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4 |
| direct product | C22×D3×#117 |
| Fitting | C22×C3×#117 ⋊ C2 |
| Sylow | C3 ⋊ C23×#117 |
14334 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×#418, C22×D3×#525, D3×#20983, … |
| maximal normal subgroup of | C22×D3×#418, C22×D3×#525, D3×#20983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076124);