Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
562 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,29)(23,27)(24,33)(25,28)(26,31)(30,34)(32,35)(36,37,42,45)(38,40,44,41)(39,46,49,50)(43,47,51,48);(20,22,24,31,25,32,23,30)(21,26,27,29,28,34,33,35)(36,38,41,37,42,44,40,45)(39,46,47,43,49,50,48,51);(20,21)(22,26)(23,33)(24,27)(25,28)(29,31)(30,35)(32,34)(36,39,42,49)(37,43,45,51)(38,46,44,50)(40,48,41,47);(20,23,25,24)(21,27,28,33)(22,30,32,31)(26,29,34,35)(36,40,42,41)(37,44,45,38)(39,47,49,48)(43,46,51,50)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12520);