Finite Group DatabasebetaFinite Group Databasebeta| order | 31350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C11⋊#15668133 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C11×C19 | C2×C3 |
| LCS | G ▷ C52×C11×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3135 |
A minimal faithful permutation representation — 2 generators on 45 points:
(1,2,4)(3,13,9,6,7,15)(5,10,14,11,12,8)(17,18)(19,20)(21,22)(23,24)(25,26)(28,32,33,29,30,34)(31,40,37,35,36,42)(38,43,45,44,41,39);(1,3,8,14,6)(2,5,7,13,11)(4,9,10,12,15)(16,17,19,21,23,25,26,24,22,20,18)(27,28,31,37,43,40,44,30,34,39,45,33,32,38,36,41,42,35,29)Polycyclic presentation:
2,3,5^2,11,19|c^a=c^4,d^a=d^4,e^a=e^10,f^a=f^18,c^b=cd,d^b=c^2d^3,f^b=f^7890 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31350, 76);