Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#1629 |
| Fitting | C3×#1629 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1629 |
1722 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#18524, #72219782 |
| maximal normal subgroup of | D3×#18524 |
| maximal quotient of | D3×#12364, D3×#12366, #72219782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 145175);