Finite Group DatabasebetaFinite Group Databasebeta| order | 21204 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#4296⋊C4 |
| unambiguous semidirect product | #4296⋊(C4×C31) |
| derived, Sylow | C19 ⋊ C4×C9×C31 |
| Hall | C31×#4296 ⋊ C4 |
| Hall | C31×Dic19 ⋊ C9 |
| Hall | C19×C31 ⋊ C4×C9 |
| Hall | #4296 ⋊ C4×C31 |
| Hall | Dic19 ⋊ C9×C31 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2356 |
1178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21204, 66);