Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | SD16×Dic19 |
| Sylow | C19 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 59 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 | C4×SD16×D19, C2×SD16×Dic19, C4×#10597362, … |
| maximal normal subgroup of | C4×SD16×D19, C2×SD16×Dic19, C4×#10597362, … |
| maximal quotient of | SD16×C19⋊C8, #14562472, #14562479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 638);