Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊#1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D5⋊(C3⋊#168) |
| derived, Hall | C3×C52 ⋊ C2×C8 |
| Sylow | C52 ⋊ C2×C3⋊C8 |
| Sylow | C3 ⋊ D5⋊#168 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,b^2=d,c^2=d,e^a=e^2,f^a=f^2,g^a=g^4,f^c=f^4132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 751);