Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ #460 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|b^2=d,c^2=f,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 | #37571579, #37571581, #37571585, … |
| maximal normal subgroup of | #37571579, #37571581, #37571585, … |
| maximal quotient of | #37571868, #37571880, #37571890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 749);