Finite Group DatabasebetaFinite Group Databasebeta| order | 21204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C31 · Schur multiplier (H2) = C2 |
| direct product | C2×C31×#4294⋊C2 |
| unambiguous semidirect product | #4294⋊(C22×C31) |
| unambiguous semidirect product | (C2×#4294)⋊(C2×C31) |
| derived, Sylow | C19 ⋊ C22×C9×C31 |
| Hall | C31×#4294 ⋊ C22 |
| Hall | C2×C31×D19 ⋊ C9 |
| Hall | C19×C31 ⋊ C22×C9 |
| Hall | #4294 ⋊ C22×C31 |
| Hall | C2×D19 ⋊ C9×C31 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10602 |
1674 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21204, 31);