Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C191 ⋊ #350 |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^190,c^b=cf,d^b=df1928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #350×D191, C2×#27132447, #37574146, … |
| maximal normal subgroup of | #350×D191, C2×#27132447, #37574146, … |
| maximal quotient of | #37570446, #37570462, #37570475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 333);