Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11029 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #121 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C23×C4×C19 ◁ G | |
1242 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(28,29,33,39,34,37,32,38)(30,40,43,51,44,35,42,52)(31,45,48,54,49,36,47,55)(41,50,57,59,58,56,46,53);(21,23)(24,25)(26,27)(28,30,34,44)(29,35,37,40)(31,46,49,57)(32,43,33,42)(36,53,45,59)(38,52,39,51)(41,48,58,47)(50,55,56,54);(25,27)(28,31,34,49)(29,36,37,45)(30,41,44,58)(32,48,33,47)(35,50,40,56)(38,55,39,54)(42,57,43,46)(51,59,52,53)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4017);