Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#23847 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #401 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| socle | C2×C19 | C2×#401 |
| prime radical | C24×C19 | C24 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
604 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(22,30,33,26)(23,27,36,42)(24,28)(25,29)(31,40)(32,44,46,39)(34,38)(35,41,48,51)(37,43)(45,50)(47,49);(20,22)(21,26)(23,34,36,31)(24,32)(25,33)(27,40,42,38)(28,39)(29,30)(35,47,48,45)(37,46)(41,50,51,49)(43,44);(20,23)(21,27,29,42)(22,31)(24,35)(25,36)(26,38,30,40)(28,41,43,51)(32,45)(33,34)(37,48)(39,49,44,50)(46,47);(20,24,25,37)(21,28,29,43)(22,32,33,46)(23,35,36,48)(26,39,30,44)(27,41,42,51)(31,45,34,47)(38,49,40,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16835);