Finite Group DatabasebetaFinite Group Databasebeta| order | 21996 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C47⋊(Dic13⋊C3) |
| unambiguous semidirect product | C47⋊(C3×Dic13⋊C3) |
| unambiguous semidirect product | Dic611⋊C32 |
| unambiguous semidirect product | (C3×Dic611)⋊C3 |
| derived, Hall | C13×C47 ⋊ C32×C4 |
| Hall | C3×C13⋊C3×C47 ⋊ C4 |
| Hall | Dic611 ⋊ C32 |
| Hall | C3×C13⋊C3 ⋊ Dic47 |
| Sylow | C47 ⋊ C3×Dic13⋊C3 |
| Sylow | C13 ⋊ C32×Dic47 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7332 |
1014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21996, 43);