Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#15690274 |
| Fitting | C22×Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ C22×SD16 |
298 conjugacy classes of subgroups.
1928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37572851, #37572857, #37572873, … |
| maximal normal subgroup of | #37572851, #37572857, #37572873, … |
| maximal quotient of | C22×#20259242, C22×#20259246, C22×#20259253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1321);