Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ C8×Q8 |
102 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,g^c=g^1901940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37571319, #37571323, #37571324, … |
| maximal normal subgroup of | #37571319, #37571323, #37571324, … |
| maximal quotient of | #37572381, #37572385, #37573074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 673);