Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×D8×C191 ⋊ C2 |
| Sylow | C191 ⋊ #493 |
162 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|b^2=df,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^c=g^1901352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37574553, #37574554, #37574558, … |
| maximal normal subgroup of | #37574553, #37574554, #37574558, … |
| maximal quotient of | #37572109, #37572111, #37572113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 924);