Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12952 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12954 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1864 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C23×C19 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
380 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)(20,21,25,30,26,32,50,31)(22,33,37,65,38,53,48,60)(23,39,41,61,42,77,49,76)(24,43,46,29,47,62,71,63)(27,51,54,35,56,44,55,36)(28,45,57,40,59,78,58,79)(34,66,69,83,70,52,74,82)(64,73,81,68,75,72,80,67);(20,22,26,38)(21,27)(23,34,42,70)(24,44,47,51)(25,48,50,37)(28,52)(29,60)(30,55)(31,54)(32,56)(33,43)(35,71,36,46)(39,75)(40,73,79,72)(41,74,49,69)(45,68,78,67)(53,62)(57,83)(58,82)(59,66)(61,81)(63,65)(64,77)(76,80);(20,23,26,42)(21,28,32,59)(22,34,38,70)(24,45,47,78)(25,49,50,41)(27,52,56,66)(29,61,63,76)(30,58,31,57)(33,64,53,75)(35,72,36,73)(37,74,48,69)(39,43,77,62)(40,46,79,71)(44,68,51,67)(54,83,55,82)(60,81,65,80)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5942);