Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#10587139 |
| Hall | C32×C11 ⋊ M16 |
| Sylow | C11 ⋊ C3×ΓL(1,𝔽25) |
| Sylow | C32 ⋊ #4318 |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 528 |
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 172);