Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#15690277 |
| Sylow | C191 ⋊ C22×Q16 |
258 conjugacy classes of subgroups.
1928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37572858, #37572859, #37572861, … |
| maximal normal subgroup of | #37572858, #37572859, #37572861, … |
| maximal quotient of | C22×#20259245, C22×#20259246, C22×#20259255, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1325);