Finite Group DatabasebetaFinite Group Databasebeta| order | 5740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(#4223⋊C5) |
| unambiguous semidirect product | (C7⋊#4223)⋊C5 |
| Fitting, socle, derived, Hall | C7×C41 ⋊ C4×C5 |
| Hall | C7×C41⋊C5 ⋊ C4 |
| Hall | C7⋊#4223 ⋊ C5 |
| Hall | C41⋊C5 ⋊ Dic7 |
| Sylow | C41 ⋊ C5×Dic7 |
| Sylow | C7 ⋊ #4223⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C41 | C4×C5 |
| LCS | G ▷ C7×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,7,41|a^2=c,d^a=d^6,e^a=e^32,e^b=e^10,e^c=e^4064 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5740, 15);