Finite Group DatabasebetaFinite Group Databasebeta| order | 24352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#20259013 |
| unambiguous semidirect product | (C2×#20259013)⋊C2 |
| Fitting | C22×C761 ⋊ C8 |
| Sylow | C761 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3044 |
Polycyclic presentation:
2^5,761|a^2=d,d^2=e,b^a=bc,f^a=f^62,f^d=f^39,f^e=f^760400 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24352, 238);