Finite Group DatabasebetaFinite Group Databasebeta| order | 21987 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×C7×C349⋊C3 |
| unambiguous semidirect product | C349⋊(C32×C7) |
| unambiguous semidirect product | (C3×C349)⋊(C3×C7) |
| Fitting, socle | C3×C7×C349 ⋊ C3 |
| derived, Sylow | C349 ⋊ C32×C7 |
| Hall | C7×C349 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C349⋊C3 |
| commutator, cosocle, hypocenter | C349 | C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C349 | C3 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C3×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7329 |
2499 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21987, 8);