Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D4×Dic382 |
| Sylow | C191 ⋊ D4×Q8 |
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1925 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37571622, #37571626, #37571684, … |
| maximal normal subgroup of | #37571622, #37571626, #37571684, … |
| maximal quotient of | C22⋊C4×Dic382, D4×Dic191⋊C4, D4×C4⋊Dic191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1215);