Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D25⋊(C3⋊C8) |
| derived, Hall | C3×C25 ⋊ C2×C8 |
| Sylow | C25 ⋊ C2×C3⋊C8 |
| Sylow | C3 ⋊ D25⋊C8 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,b^2=d,c^2=d,f^5=g,e^a=e^2,f^a=f^2g,g^a=g^2,f^c=f^4g^4,g^c=g^496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 112);