Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34491 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1956 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(25,28)(26,27)(33,37)(35,43)(38,40)(41,47);(24,25,29,28)(26,31,27,30)(32,33)(34,40)(35,39)(36,37)(38,42)(41,46)(43,44)(45,47);(24,26,29,27)(25,30,28,31);(20,22,23,21)(24,27,29,26)(25,31,28,30)(32,34,36,42)(33,38,37,40)(35,41,43,47)(39,45,44,46);(24,28,29,25)(26,31,27,30)(32,35,36,43)(33,39,37,44)(34,41,42,47)(38,45,40,46)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27479);