Finite Group DatabasebetaFinite Group Databasebeta| order | 16940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic847 |
| unambiguous semidirect product | C7⋊(C5×Dic121) |
| derived, Hall | C7×C121 ⋊ C4×C5 |
| Hall | C5×C7×C121 ⋊ C4 |
| Hall | C5×C121 ⋊ Dic7 |
| Sylow | C121 ⋊ C5×Dic7 |
| Hall | C5×C7 ⋊ Dic121 |
| Sylow | C7 ⋊ C5×Dic121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D847 |
| commutator, hypocenter | C7×C121 | C4×C5 |
| Frattini | C2×C11 | C5×D77 |
| Fitting | C2×C5×C7×C121 | C2 |
| socle, prime radical | C2×C5×C7×C11 | D11 |
| cosocle | C2×C7×C121 | C2×C5 |
| LCS | G ▷ C7×C121 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16940 |
4250 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16940, 8);