Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| isoclinism | isoclinic class of D191 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C8×D191 |
| Fitting | C4×C8×C191 ⋊ C2 |
| derived, Sylow | C191 ⋊ C2×C4×C8 |
162 conjugacy classes of subgroups.
3104 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C82×D191, #322×D191, C8×#15690270, … |
| maximal normal subgroup of | C82×D191, #322×D191, C8×#15690270, … |
| maximal quotient of | C82×D191, #322×D191, C8×#15690270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 493);