Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C191 ⋊ C2 |
| Sylow | C191 ⋊ #578 |
248 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^190,e^b=ef,g^b=g^190,d^c=df1922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37574482, #37574486, #37574496, … |
| maximal normal subgroup of | #37574482, #37574486, #37574496, … |
| maximal quotient of | #37581054, #37581120, #37581365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1366);