Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×#14559053 |
| derived, Sylow | C112 ⋊ C32×C4×C5 |
| Hall | C32×#10597244 ⋊ C4 |
| Hall | C32×C11⋊Dic11 ⋊ C5 |
| Hall | C32×C112 ⋊ C4×C5 |
| Hall | #10597244 ⋊ C32×C4 |
| Hall | C11⋊Dic11 ⋊ C32×C5 |
180 conjugacy classes of subgroups.
396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 322);