Finite Group DatabasebetaFinite Group Databasebeta| order | 34790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊(C7⋊(D71⋊C5)) |
| unambiguous semidirect product | (C71⋊C5)⋊(C7⋊D7) |
| unambiguous semidirect product | (C7⋊D497)⋊C5 |
| Fitting, socle, derived, Hall | C72×C71 ⋊ C2×C5 |
| Hall | C72×C71⋊C5 ⋊ C2 |
| Hall | C7⋊D497 ⋊ C5 |
| Hall | C71⋊C5 ⋊ C7⋊D7 |
| Sylow | C71 ⋊ C5×C7⋊D7 |
| Sylow | C72 ⋊ D71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C71 | C2×C5 |
| LCS | G ▷ C72×C71 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3479 |
A minimal faithful permutation representation — 3 generators on 85 points:
(2,3)(4,5)(6,7)(9,10)(11,12)(13,14)(16,20,21,39,43,17,18,26,28,61)(19,33,34,72,74,23,24,51,52,71)(22,46,47,48,66,30,31,68,59,70)(25,57,58,60,27,36,37,75,38,41)(29,50,32,56,67,42,45,49,44,69)(35,79,76,77,83,54,55,53,73,84)(40,78,82,62,65,63,64,85,80,81);(8,9,11,13,14,12,10)(15,16,19,25,38,43,66,83,47,69,74,45,49,30,20,27,42,26,40,65,58,72,85,55,80,28,44,54,33,37,59,46,64,76,51,73,77,34,53,78,31,48,57,24,35,56,39,62,79,82,52,75,81,63,21,29,41,18,22,32,50,71,67,68,84,70,61,60,36,23,17);(1,2,4,6,7,5,3)Polycyclic presentation:
2,5,7^2,71|c^a=c^6,d^a=d^6,e^a=e^70,e^b=e^57473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34790, 34);