Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#20259330 |
| Fitting | C2×M16×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×#131 |
266 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 151 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 | #37572319, #37572354, #37572356, … |
| maximal normal subgroup of | #37572319, #37572354, #37572356, … |
| maximal quotient of | C2×#27132620, C2×#27132621, C4×#20259330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1313);