Finite Group DatabasebetaFinite Group Databasebeta| order | 3104 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#11715906 |
| unambiguous semidirect product | (C2×#11715906)⋊C2 |
| Fitting | C22×C97 ⋊ C8 |
| Sylow | C97 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 388 |
Polycyclic presentation:
2^5,97|a^2=d,d^2=e,b^a=bc,f^a=f^64,f^d=f^22,f^e=f^9668 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3104, 238);