Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2286 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
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)(26,30)(32,33)(34,41)(35,38)(36,44)(37,40)(39,45)(42,46)(43,47);(25,28)(29,31)(32,34,37,35)(33,38,40,41)(36,42,45,43)(39,46,44,47);(20,22,23,21)(24,25)(26,29)(27,28)(30,31)(32,35,37,34)(33,38,40,41)(36,43,45,42)(39,46,44,47);(24,26)(25,29)(27,30)(28,31)(32,33)(34,41)(35,38)(36,39)(37,40)(42,47)(43,46)(44,45);(32,36,37,45)(33,39,40,44)(34,42,35,43)(38,46,41,47)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27400);