Finite Group DatabasebetaFinite Group Databasebeta| order | 4384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#11764049 |
| unambiguous semidirect product | (C2×#11764049)⋊C2 |
| Fitting | C22×C137 ⋊ C8 |
| Sylow | C137 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 548 |
Polycyclic presentation:
2^5,137|a^2=d,d^2=e,b^a=bc,f^a=f^127,f^d=f^100,f^e=f^13688 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4384, 238);