Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33388 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33393 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×#102 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#578 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
1102 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)(20,21,25,30,26,32,46,31)(22,33,36,55,37,60,45,59)(23,28,40,53,38,51,67,54)(24,41,43,29,44,56,72,57)(27,42,48,35,50,64,49,65)(34,58,63,77,61,79,71,80)(39,68,70,52,66,78,83,76)(47,69,74,62,73,82,75,81);(20,22,26,37)(21,27,32,50)(23,34,38,61)(24,42,44,64)(25,45,46,36)(28,47,51,73)(29,55,57,59)(30,49,31,48)(33,41,60,56)(35,43,65,72)(39,69,66,82)(40,71,67,63)(52,77,76,80)(53,75,54,74)(58,68,79,78)(62,70,81,83);(20,23)(21,28)(22,34)(24,39)(25,40)(26,38)(27,47)(29,52)(30,53)(31,54)(32,51)(33,58)(35,62)(36,63)(37,61)(41,68)(42,69)(43,70)(44,66)(45,71)(46,67)(48,74)(49,75)(50,73)(55,77)(56,78)(57,76)(59,80)(60,79)(64,82)(65,81)(72,83);(23,38)(28,51)(34,61)(39,66)(40,67)(47,73)(52,76)(53,54)(58,79)(62,81)(63,71)(68,78)(69,82)(70,83)(74,75)(77,80)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26381);