Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D3×#3169 |
| Fitting | C3×#3169 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3169 |
2566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#19603, D3×#33748 |
| maximal normal subgroup of | D3×#19603, D3×#33748 |
| maximal quotient of | D3×#33748 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1039298);