Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| direct product | C3×#20300038 |
| Fitting, socle | C3×C5×C112 ⋊ Dic3 |
| derived | C5×C112⋊C3 ⋊ C3×C4 |
| Hall | C3×C5×C112⋊C3 ⋊ C4 |
| Hall | C3×C112⋊C3 ⋊ AGL(1,𝔽5) |
| Hall | C5×C112 ⋊ C3×Dic3 |
| Sylow | C112 ⋊ C3×ΓL(1,𝔽16) |
| Sylow | C5 ⋊ C3×#13089721 |
72 conjugacy classes of subgroups.
177 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 530);