Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#11744762 |
| unambiguous semidirect product | (C2×#11744762)⋊C2 |
| Fitting | C22×C113 ⋊ C8 |
| Sylow | C113 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 452 |
Polycyclic presentation:
2^5,113|a^2=d,d^2=e,b^a=bc,f^a=f^18,f^d=f^98,f^e=f^11276 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 238);