Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C191 ⋊ #349 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^190,d^b=df1922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570455, #37570456, #37570457, … |
| maximal normal subgroup of | #37570455, #37570456, #37570457, … |
| maximal quotient of | #37570444, #37570460, #37570478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 331);