Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #87856⋊C3 |
| Hall | #87856 ⋊ C3 |
| Hall | C52⋊C3 ⋊ M16 |
| Sylow | C52 ⋊ C3×M16 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^2,3,2^2,5^2|a^2=d,b^2=e,d^2=e,b^a=be,f^a=f^3,g^a=g^3,f^c=fg,g^c=f^2g^3,f^d=f^4,g^d=g^438 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 500);