Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C191⋊#338 |
| Sylow | C191 ⋊ #338 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,e^a=ef,d^b=df,g^b=g^1901922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570511, #37570512, #37570514, … |
| maximal normal subgroup of | #37570511, #37570512, #37570514, … |
| maximal quotient of | #37570350, #37570351, #37570391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 307);