Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C191 ⋊ #544 |
206 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=f,b^2=e,c^2=f,b^a=be,c^a=cf,d^a=de,g^a=g^190,c^b=ce1922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37571459, #37571462, #37571493, … |
| maximal normal subgroup of | #37571459, #37571462, #37571493, … |
| maximal quotient of | #37575138, #37575144, #37575253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1180);