Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18933 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3544 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
858 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)(22,28)(23,31)(24,26)(25,30)(27,32)(29,35)(33,34)(36,37,41,43)(38,45,42,50)(39,47,48,46)(40,49,51,44);(23,32)(27,31)(28,35)(30,33)(36,38,41,42)(37,39,43,48)(40,47,51,46)(44,50,49,45);(20,22)(21,25)(23,33)(24,29)(26,34)(27,35)(28,31)(30,32)(36,39)(37,42)(38,43)(40,50)(41,48)(44,46)(45,51)(47,49);(21,26)(25,34)(27,31)(28,35)(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, 11921);