Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#20259310 |
| Fitting | C2×C42×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×#124 |
330 conjugacy classes of subgroups.
3068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570871, #37570873, C2×#27132402, … |
| maximal normal subgroup of | #37570871, #37570873, C2×#27132402, … |
| maximal quotient of | C2×#27132529, C2×#27132554, C2×#27132565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1066);