Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13033 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13034 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1879 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,30,26,32,51,63,27,33,24,31,47,62,48,66)(22,34,37,55,38,60,49,56,39,70,36,67,52,64,45,28)(23,40,42,68,43,61,46,29,44,57,41,58,53,65,50,59)(35,54,72,78,73,79,75,82,74,80,71,83,77,81,76,69);(20,22)(21,28,33,56)(23,35)(24,45)(25,49)(26,52)(27,39)(29,54,59,80)(30,60,31,64)(32,67,62,55)(34,66,70,63)(36,48)(37,51)(38,47)(40,69,57,82)(41,76)(42,75)(43,77)(44,74)(46,72)(50,71)(53,73)(58,81,68,79)(61,83,65,78);(20,23,27,44)(21,29,33,59)(22,35,39,74)(24,46,25,50)(26,53,47,43)(28,54,56,80)(30,61,31,65)(32,68,62,58)(34,69,70,82)(36,75,37,76)(38,77,52,73)(40,66,57,63)(41,48,42,51)(45,72,49,71)(55,81,67,79)(60,83,64,78)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6022);