Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#15690569 |
| unambiguous semidirect product | (C2×#15690569)⋊C2 |
| Fitting | C22×C193 ⋊ C16 |
| Sylow | C193 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,193|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^64,g^d=g^43,g^e=g^112,g^f=g^19288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 1675);