Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C191 ⋊ C2 |
| Sylow | C191 ⋊ #568 |
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,191|a^2=e,e^2=f,d^a=df,c^b=cf,g^d=g^1901934 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37581425, #37581428, #37581432, … |
| maximal normal subgroup of | #37581425, #37581428, #37581432, … |
| maximal quotient of | #37580936, #37580946, #37580947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1314);