Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | #99×D19 |
| Fitting | C19×#99 ⋊ C2 |
| Sylow | C19 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 152 |
121 conjugacy classes — view the full character table.
| maximal subgroup of | D19×AΣL(1,𝔽16), D19×#352, #14565278, … |
| maximal normal subgroup of | D19×AΣL(1,𝔽16), D19×#352, #14565278, … |
| maximal quotient of | D19×#323, D19×#324, #14561950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 518);