Finite Group DatabasebetaFinite Group Databasebeta| order | 31020 |
| automorphism | ? |
| homology | Abelianization (H1) = C47 · Schur multiplier (H2) = C2 |
| direct product | C47×PSL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C47 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C47 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C47 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 517 |
A minimal faithful permutation representation — 2 generators on 58 points:
(1,5,4,7,11)(2,10,9,6,8);(1,3,6)(2,4,8)(7,9,10)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58)376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31020, 102);