Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D193⋊#100 |
| Sylow | C193 ⋊ C2×#100 |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,193|a^2=e,e^2=f,b^a=bd,d^a=df,g^a=g^112,e^b=ef,g^c=g^192,g^e=g^192502 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 1532);