Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C4×Dic19 |
| Sylow | C19 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 608 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #14563422, #99×Dic19, #14564469, … |
| maximal normal subgroup of | #14563422, #99×Dic19, #14564469, … |
| maximal quotient of | #95×Dic19, #14561857, #14561860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 399);