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×#13035 |
| 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 | |
456 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)(20,21,25,32,50,53,49,30,27,34,48,64,26,33,24,31)(22,35,39,28,51,55,37,65,41,68,75,57,40,62,38,56)(23,42,44,61,52,63,43,60,46,58,47,29,45,59,77,66)(36,54,71,79,76,82,70,78,73,81,74,67,72,80,69,83);(20,22,26,51,27,41,50,40)(21,28,53,56,34,57,33,65)(23,36,52,72,46,73,45,76)(24,39,48,37,49,75,25,38)(29,54,60,82,61,81,66,80)(30,62,64,68,31,55,32,35)(42,67,59,83,58,79,63,78)(43,74,47,70,77,71,44,69);(20,23)(21,29)(22,36)(24,47)(25,43)(26,52)(27,46)(28,54)(30,59)(31,63)(32,42)(33,66)(34,61)(35,67)(37,71)(38,74)(39,70)(40,76)(41,73)(44,49)(45,50)(48,77)(51,72)(53,60)(55,78)(56,82)(57,81)(58,64)(62,83)(65,80)(68,79)(69,75)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6023);