Finite Group DatabasebetaFinite Group Databasebeta| order | 21204 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#20296620 |
| derived, Hall | C19×C31 ⋊ C32×C4 |
| Hall | C3×#13183714 ⋊ C4 |
| Hall | Dic589 ⋊ C32 |
| Sylow | C31 ⋊ C3×(C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ C3×(C31⋊C3)⋊C4 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7068 |
624 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21204, 84);