Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C191 ⋊ #499 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,b^2=df,c^2=e,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^1903062 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570571, #37570573, #37570580, … |
| maximal normal subgroup of | #37570571, #37570573, #37570580, … |
| maximal quotient of | #37572684, #37573248, #37573253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 951);