Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×D3×#496 |
| Fitting | C2×C3×#496 ⋊ C2 |
| Sylow | C3 ⋊ C22×#496 |
4038 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3151, D32×#496 |
| maximal normal subgroup of | C2×D3×#3151 |
| maximal quotient of | D32×#496, C2×D3×#1721, C2×D3×#1715 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1038990);