Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19535 |
| 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)(20,21,25,28)(22,29,32,35)(23,27,24,33)(26,30,34,31)(36,37)(38,40)(39,46)(41,44)(42,47)(43,45)(48,51)(49,50);(20,22,23,30,25,32,24,31)(21,26,33,35,28,34,27,29)(36,38,45,44,41,43,40,37)(39,46,47,51,49,50,48,42);(20,21)(22,26)(23,33)(24,27)(25,28)(29,31)(30,35)(32,34)(36,39,41,49)(37,42,44,51)(38,46,43,50)(40,48,45,47);(20,23,25,24)(21,27,28,33)(22,30,32,31)(26,29,34,35)(36,40,41,45)(37,38,44,43)(39,47,49,48)(42,50,51,46)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12523);