Finite Group DatabasebetaFinite Group Databasebeta| order | 34790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C5⋊(C7⋊D497) |
| unambiguous semidirect product | C7⋊D2485 |
| unambiguous semidirect product | C71⋊(C5⋊(C7⋊D7)) |
| Fitting, socle, derived, Hall | C5×C72×C71 ⋊ C2 |
| Hall | C72×C71 ⋊ D5 |
| Hall | C5×C71 ⋊ C7⋊D7 |
| Hall | C5×C72 ⋊ D71 |
| Sylow | C71 ⋊ C5⋊(C7⋊D7) |
| Sylow | C72 ⋊ D355 |
| Sylow | C5 ⋊ C7⋊D497 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C71 | C2 |
| LCS | G ▷ C5×C72×C71 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17395 |
Polycyclic presentation:
2,5,7^2,71|b^a=b^4,c^a=c^6,d^a=d^6,e^a=e^708699 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34790, 48);