Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19037 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
812 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)(36,37,41,38)(39,46,47,51)(40,45,50,43)(42,49,44,48);(20,22)(21,26)(23,31)(24,30)(25,32)(27,35)(28,34)(29,33)(36,38,41,37)(39,44,47,42)(40,43,50,45)(46,49,51,48);(20,21)(22,26)(23,27)(24,33)(25,28)(29,30)(31,35)(32,34)(36,39)(37,42)(38,44)(40,49)(41,47)(43,51)(45,46)(48,50);(20,23,25,24)(21,27,28,33)(22,30,32,31)(26,29,34,35)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12025);