Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#71859 |
| Sylow | C3 ⋊ C2×#2122 |
1406 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10710960, C2×D3×#2122, C2×#10710961, … |
| maximal normal subgroup of | C2×#10710960, C2×D3×#2122, C2×#10710961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322300);