Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18975 |
| 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 | |
810 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)(24,32)(25,28)(26,30)(31,34)(33,35)(36,37,41,43)(38,45,42,50)(39,47,48,46)(40,49,51,44);(20,22,25,31)(21,26,28,35)(23,30,24,33)(27,34,32,29)(36,38,41,42)(37,39,43,48)(40,47,51,46)(44,50,49,45);(20,21)(22,26)(23,32)(24,27)(25,28)(29,30)(31,35)(33,34)(36,39)(37,42)(38,43)(40,50)(41,48)(44,46)(45,51)(47,49);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(37,43)(39,48)(44,49)(45,50)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11963);