Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11925895⋊D13 |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C22×C5 |
| Hall | C13×#10597243 ⋊ C22 |
| Hall | D11×D143 ⋊ C5 |
| Hall | #10597243 ⋊ C2×D13 |
| Sylow | C112 ⋊ C2×C5×D13 |
| Sylow | C13 ⋊ #11925892⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C13 | C22×C5 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 286 |
A minimal faithful permutation representation — 2 generators on 35 points:
(2,6,7,5,10,3,4,11,8,9)(12,13,18,14,20)(15,22,21,16,19)(23,24,26,28,30,32,34,35,33,31,29,27,25);(1,2,5,10,4,7,11,6,9,8,3)(13,14)(15,17)(16,19)(18,22)(20,21)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)Polycyclic presentation:
2^2,5,11^2,13|e^a=e^10,f^a=f^12,d^b=d^10,d^c=d^4,e^c=e^4179 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 123);