Finite Group DatabasebetaFinite Group Databasebeta| order | 31434 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C31 ⋊ C2×C3 |
| Hall | #30628406 ⋊ C2 |
| Hall | C13⋊D403 ⋊ C3 |
| Sylow | C132 ⋊ D31⋊C3 |
| Sylow | C31 ⋊ #11759815 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C31 | C2×C3 |
| LCS | G ▷ C132×C31 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 5239 |
A minimal faithful permutation representation — 3 generators on 57 points:
(2,6,7,3,4,8)(5,12,11,9,10,13)(15,19,20,16,17,21)(18,25,24,22,23,26)(28,32,33,29,30,34)(31,40,41,35,36,48)(37,50,51,43,44,56)(38,49,45,46,42,39)(47,57,54,53,52,55);(14,15,18,17,21,24,23,25,26,20,19,22,16)(27,28,31,37,45,33,32,38,47,54,41,49,40,44,52,51,56,57,50,36,42,48,55,53,46,30,34,39,43,35,29);(1,2,5,4,8,11,10,12,13,7,6,9,3)Polycyclic presentation:
2,3,13^2,31|c^a=c^12,d^a=d^12,e^a=e^30,c^b=c^3,d^b=d^3,e^b=e^25879 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31434, 57);