Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#4475 |
| Fitting | C22×C3×#100 ⋊ C2 |
| Sylow | C3 ⋊ C22×AΣL(1,𝔽16) |
2774 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 2774 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #72248021, #72248026, C22×D3×AΣL(1,𝔽16), … |
| maximal normal subgroup of | #72248021, #72248026, C22×D3×AΣL(1,𝔽16), … |
| maximal quotient of | #72249310, C2×#10710648 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322280);