Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ #461 |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^190,e^c=ef1919 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37571699, #37571701, #37571720, … |
| maximal normal subgroup of | #37571699, #37571701, #37571720, … |
| maximal quotient of | #37571895, #37571909, #37571919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 754);