Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#32897 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×2−1+6 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
3512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,27,33)(22,34,38,55)(23,39,42,57)(24,30,44,54)(25,32,26,31)(28,45,50,37)(29,47,52,41)(35,48,63,74)(36,64,67,59)(40,69,72,76)(43,56,46,53)(49,66,75,65)(51,70,77,71)(58,61,68,62)(60,79,81,73)(78,80,83,82);(20,22)(21,28)(23,35)(24,36)(25,45)(26,37)(27,38)(29,48)(30,49)(31,55)(32,34)(33,50)(39,68)(40,60)(41,62)(42,63)(43,66)(44,67)(46,65)(47,61)(51,73)(52,74)(53,59)(54,75)(56,64)(57,58)(69,83)(70,82)(71,80)(72,81)(76,78)(77,79);(20,23,27,42)(21,29,33,52)(22,35,38,63)(24,40,44,72)(25,41,26,47)(28,48,50,74)(30,51,54,77)(31,39,32,57)(34,58,55,68)(36,60,67,81)(37,61,45,62)(43,70,46,71)(49,73,75,79)(53,76,56,69)(59,78,64,83)(65,80,66,82);(20,24)(21,30)(22,36)(23,40)(25,46)(26,43)(27,44)(28,49)(29,51)(31,56)(32,53)(33,54)(34,59)(35,60)(37,66)(38,67)(39,69)(41,71)(42,72)(45,65)(47,70)(48,73)(50,75)(52,77)(55,64)(57,76)(58,78)(61,82)(62,80)(63,81)(68,83)(74,79)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25885);