Finite Group DatabasebetaFinite Group Databasebeta| order | 35090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C29⋊#11925893 |
| Fitting, socle, derived, Hall | C112×C29 ⋊ C2×C5 |
| Hall | C29×#10597245 ⋊ C2 |
| Hall | C11⋊D319 ⋊ C5 |
| Hall | #10597245 ⋊ D29 |
| Sylow | C112 ⋊ C5×D29 |
| Sylow | C29 ⋊ #11925893 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C29 | C2×C5 |
| LCS | G ▷ C112×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1595 |
A minimal faithful permutation representation — 2 generators on 51 points:
(2,6,7,5,10,3,4,11,8,9)(13,17,18,20,19,14,15,16,21,22)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51);(1,2,5,10,4,7,11,6,9,8,3)(12,13,16,15,19,21,20,22,17,18,14)(23,24,26,28,30,32,34,36,38,40,42,44,46,48,50,51,49,47,45,43,41,39,37,35,33,31,29,27,25)Polycyclic presentation:
2,5,11^2,29|c^a=c^10,d^a=d^10,e^a=e^28,c^b=c^4,d^b=d^3428 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35090, 39);