Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#12902 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | #127 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1843 |
| prime radical | C23×C19 | #131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C22×C8×C19 ◁ G | |
278 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)(20,21,24,29,25,30,40,51,26,31,41,52,42,53,66,77)(22,27,34,45,35,46,59,71,33,44,57,69,58,70,79,82)(23,28,38,49,39,50,65,76,37,48,63,74,64,75,81,83)(32,54,56,78,36,60,62,80,55,43,67,68,61,47,72,73);(20,22)(21,27)(23,36,37,61)(24,34)(25,35)(26,33)(28,47,48,60)(29,45)(30,46)(31,44)(32,39,55,64)(38,62,63,72)(40,59)(41,57)(42,58)(43,50,54,75)(49,73,74,80)(51,71)(52,69)(53,70)(56,65,67,81)(66,79)(68,76,78,83)(77,82);(20,23)(21,28)(22,32,33,55)(24,38)(25,39)(26,37)(27,43,44,54)(29,49)(30,50)(31,48)(34,56,57,67)(35,36,58,61)(40,65)(41,63)(42,64)(45,68,69,78)(46,47,70,60)(51,76)(52,74)(53,75)(59,62,79,72)(66,81)(71,73,82,80)(77,83)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5890);