Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×Dic191 |
| Sylow | C191 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 215 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×Dic191, #100×Dic191, #102×Dic191, … |
| maximal normal subgroup of | #99×Dic191, #100×Dic191, #102×Dic191, … |
| maximal quotient of | C2×C22⋊C4×Dic191, C2×C4⋊C4×Dic191, C4×D4×Dic191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1010);