Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C5 |
| direct product | C8×C3⋊(C5⋊D5) |
| Fitting | C3×C52×C8 ⋊ C2 |
| derived, Hall | C3×C52 ⋊ C2×C8 |
| Sylow | C52 ⋊ D3×C8 |
| Sylow | C3 ⋊ C8×C5⋊D5 |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 449);