Finite Group DatabasebetaFinite Group Databasebeta| order | 34790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊AGL(1,𝔽71) |
| unambiguous semidirect product | ((C71⋊C5)⋊C7)⋊D7 |
| unambiguous semidirect product | (C7⋊(D71⋊C5))⋊C7 |
| unambiguous semidirect product | (C7⋊(D71⋊C7))⋊C5 |
| Fitting, socle, derived | C7×C71 ⋊ C2×C5×C7 |
| Hall | C7×(C71⋊C5)⋊C7 ⋊ C2 |
| Hall | C7⋊(D71⋊C7) ⋊ C5 |
| Hall | C7×C71⋊C7 ⋊ C2×C5 |
| Hall | C71⋊C5 ⋊ C7×D7 |
| Sylow | C71 ⋊ C5×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C71 | C2×C5×C7 |
| LCS | G ▷ C7×C71 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 497 |
Polycyclic presentation:
2,5,7^2,71|d^a=d^6,e^a=e^70,e^b=e^57,e^c=e^45182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34790, 21);