Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#4536 |
| Sylow | C3 ⋊ C22×AΣL(1,𝔽16) |
2774 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #72248033, C22×D3×AΣL(1,𝔽16), #72248055, … |
| maximal normal subgroup of | #72248033, C22×D3×AΣL(1,𝔽16), #72248055, … |
| maximal quotient of | #72255063, C2×#10710647 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322279);