Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ #504 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,d^2=e,e^2=f,g^a=g^190,c^b=cf1940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37574354, #37574357, #37574359, … |
| maximal normal subgroup of | #37574354, #37574357, #37574359, … |
| maximal quotient of | #37574117, #37574134, #37574279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 966);