Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#71650 |
| Fitting | C2×C3×#518 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1887 |
2526 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#1887, C2×#10826821, C2×#10826822 |
| maximal normal subgroup of | C2×D3×#1887, C2×#10826821, C2×#10826822 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171126);