Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of #4466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#67512 |
| Sylow | C3 ⋊ C2×#1313 |
302 conjugacy classes of subgroups.
| transitive degree | μt(G) = 768 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#1313, C2×#10707069, C2×#11771325, … |
| maximal normal subgroup of | C2×D3×#1313, C2×#10707069, C2×#10707075 |
| maximal quotient of | C2×#10682524, C2×#11771325 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 78566);