Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#26012433 |
| unambiguous semidirect product | D173⋊#380 |
| Fitting | C23×C4×C173 ⋊ C4 |
| Sylow | C173 ⋊ C2×#380 |
1232 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5536 |
1432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20952);