Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#20259311 |
| Fitting | C22×Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×#124 |
330 conjugacy classes of subgroups.
1928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37572905, #37572921, #37572923, … |
| maximal normal subgroup of | #37572905, #37572921, #37572923, … |
| maximal quotient of | C2×#27132528, C2×#27132553, C2×#27132564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1067);