Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C191 ⋊ #543 |
242 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=f,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^c=g^1901922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37571442, #37571445, #37571476, … |
| maximal normal subgroup of | #37571442, #37571445, #37571476, … |
| maximal quotient of | #37575132, #37575134, #37575248, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1175);