Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23622 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#396 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
960 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)(20,21,26,30,25,31,24,29)(22,32,40,43,35,42,34,27)(23,28,37,44,39,45,38,46)(33,47,48,41,36,50,49,51);(20,22,24,34,25,35,26,40)(21,27,30,32,31,43,29,42)(23,36,38,48,39,33,37,49)(28,41,44,50,45,51,46,47);(20,23)(21,28)(22,33)(24,37)(25,39)(26,38)(27,41)(29,44)(30,46)(31,45)(32,47)(34,48)(35,36)(40,49)(42,50)(43,51);(20,24,25,26)(21,29,31,30)(22,34,35,40)(23,37,39,38)(27,42,43,32)(28,44,45,46)(33,48,36,49)(41,50,51,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16610);