Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23740 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#399 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
988 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)(20,21,24,29,25,30,26,40)(22,31,33,43,35,47,34,27)(23,36,39,46,38,28,41,45)(32,48,37,51,49,44,50,42);(20,22,26,33,25,35,24,34)(21,27,40,31,30,43,29,47)(23,37,41,49,38,50,39,32)(28,44,46,42,36,48,45,51);(20,23)(21,28)(22,32)(24,39)(25,38)(26,41)(27,42)(29,45)(30,36)(31,48)(33,37)(34,50)(35,49)(40,46)(43,51)(44,47);(23,38)(28,36)(32,49)(37,50)(39,41)(42,51)(44,48)(45,46)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16728);