Finite Group DatabasebetaFinite Group Databasebeta| order | 19740 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C47 · Schur multiplier (H2) = C2 |
| direct product | C7×C47×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C7×C47 | A5 |
| commutator, hypocenter | A5 | C7×C47 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C7×C47 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1645 |
A minimal faithful permutation representation — 2 generators on 59 points:
(55,56,59,57,58);(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54)(55,56,57,58,59)1645 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19740, 105);