Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q16×C191 ⋊ C2 |
| Sylow | C191 ⋊ #510 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^190,d^b=de,e^b=ef1346 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37574409, #37574414, #37574469, … |
| maximal normal subgroup of | #37574409, #37574414, #37574469, … |
| maximal quotient of | #37574230, #37574240, #37574306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 990);