Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10035 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C22×C19 | #392 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
498 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 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)(24,27)(25,30)(26,33)(29,35)(32,34)(36,37,41,45)(38,46,49,50)(39,44,40,43)(42,48,51,47);(25,34)(28,35)(36,38,41,49)(37,42,45,51)(39,48,40,47)(43,50,44,46);(20,22)(21,25)(23,32)(24,29)(26,35)(27,34)(28,31)(30,33)(38,47)(39,40)(42,46)(43,44)(48,49)(50,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3023);