Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×Q8×D15 |
| Fitting | C3×C52×Q8 ⋊ C2 |
| Hall | C3×C52 ⋊ C2×Q8 |
| Sylow | C52 ⋊ D3×Q8 |
| Sylow | C3 ⋊ C5×Q8×D5 |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 921);