Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ #500 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,b^2=d,c^2=ef,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^1901352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37574655, #37574656, #37574660, … |
| maximal normal subgroup of | #37574655, #37574656, #37574660, … |
| maximal quotient of | #37572678, #37573251, #37573252, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 953);