Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C232 · Schur multiplier (H2) = C2×C23 |
| direct product | C232×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C232 | A5 |
| commutator, hypocenter | A5 | C232 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C232 | |
234 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2645 |
A minimal faithful permutation representation — 2 generators on 51 points:
(1,4,5,2,3)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,32,35,39,38,42,46,49,51,50,34,37,41,45,48,47,31,33,36,40,44,43);(1,2,3,4,5)(29,31,34,38,43,47,50,39,44,48,51,35,40,45,49,32,36,41,46,30,33,37,42)2645 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 117);