Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | #117×D19 |
| Fitting | C19×#117 ⋊ C2 |
| Sylow | C19 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 159 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×H(3,ℤ/4), D19×#339, #14563343, … |
| maximal normal subgroup of | D19×H(3,ℤ/4), D19×#339, #14563343, … |
| maximal quotient of | D19×#376, C4×C22⋊C4×D19, C4×C4⋊C4×D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1001);