Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22⋊Q8×D191 |
| Fitting | C22⋊Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #328×D191, #37571038, #37571051, … |
| maximal normal subgroup of | #328×D191, #37571038, #37571051, … |
| maximal quotient of | #380×D191, #385×D191, #387×D191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1043);