Finite Group DatabasebetaFinite Group Databasebeta| order | 16884 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C3⋊((C67⋊C3)⋊C4) |
| unambiguous semidirect product | C3⋊(C7×(C67⋊C3)⋊C4) |
| unambiguous semidirect product | (C67⋊C3)⋊(C7×Dic3) |
| unambiguous semidirect product | Dic201⋊(C3×C7) |
| derived | C3×C67 ⋊ C3×C4×C7 |
| Hall | C3×C7×C67⋊C3 ⋊ C4 |
| Hall | C3×C67⋊C3 ⋊ C4×C7 |
| Hall | C7×C67 ⋊ C3×Dic3 |
| Sylow | C67 ⋊ C3×C7×Dic3 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5628 |
588 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16884, 82);