Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #103×D19 |
| Fitting | C19×#103 ⋊ C2 |
| Sylow | C19 ⋊ C2×#103 |
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 608 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#103×D19, D19×#416, D19×#419, … |
| maximal normal subgroup of | C2×#103×D19, D19×#416, D19×#419, … |
| maximal quotient of | D19×Q8⋊C8, #14562036, #14562062, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 538);