Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
| direct product | C2×D3×#343 |
| Fitting | C2×C3×#343 ⋊ C2 |
| Sylow | C3 ⋊ C22×#343 |
2494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#20943, D3×#10755, D3×#11016 |
| maximal normal subgroup of | D3×#20943, D3×#10755, D3×#11016 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 167008);