Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#12995 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #447 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1874 |
| prime radical | C19×#3067 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
476 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)(20,21,26,33,27,34,51,65,28,35,50,64,25,32,24,31)(22,36,40,58,41,62,38,55,42,69,48,29,39,56,76,57)(23,43,46,63,45,61,49,67,47,66,53,59,52,30,44,60)(37,70,73,81,72,80,71,82,74,83,78,79,77,68,75,54);(20,22,27,39,28,42,25,41)(21,29,34,55,35,58,32,57)(23,37,45,77,47,74,52,72)(24,48,26,38,51,40,50,76)(30,54,43,79,61,82,66,81)(31,62,33,36,65,56,64,69)(44,78,46,71,49,73,53,75)(59,83,60,80,63,70,67,68);(20,23)(21,30)(22,37)(24,49)(25,52)(26,53)(27,45)(28,47)(29,54)(31,63)(32,66)(33,67)(34,43)(35,61)(36,68)(38,75)(39,77)(40,78)(41,72)(42,74)(44,51)(46,50)(48,73)(55,79)(56,83)(57,81)(58,82)(59,65)(60,64)(62,70)(69,80)(71,76)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5983);