Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #131×D19 |
| Fitting | C19×#131 ⋊ C2 |
| Sylow | C19 ⋊ C2×#131 |
266 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 304 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#350, #14565261, D19×#443, … |
| maximal normal subgroup of | D19×#350, #14565261, D19×#443, … |
| maximal quotient of | D19×#405, #131×Dic19, #14572057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1310);