Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33458 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C23×C19 | C2×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 87 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25)(26,36)(27,32)(28,44)(29,49)(30,33)(31,38)(34,47)(35,46)(37,61)(39,68)(40,62)(41,56)(42,71)(43,74)(45,59)(48,60)(50,58)(51,64)(52,67)(53,76)(54,73)(55,70)(57,66)(63,83)(65,86)(69,82)(72,81)(75,79)(77,87)(78,84)(80,85);(24,26,30,40)(25,31,33,52)(27,37,41,63)(28,45,48,76)(29,50,46,39)(32,51,56,78)(34,58,57,68)(35,59,49,53)(36,60,62,44)(38,66,67,47)(42,72,69,87)(43,75,70,65)(54,79,80,86)(55,81,74,77)(61,82,83,71)(64,85,84,73);(20,22,23,21)(24,27,30,41)(25,32,33,56)(26,37,40,63)(28,42,48,69)(29,43,46,70)(31,51,52,78)(34,54,57,80)(35,55,49,74)(36,61,62,83)(38,64,67,84)(39,65,50,75)(44,71,60,82)(45,72,76,87)(47,73,66,85)(53,77,59,81)(58,79,68,86);(25,33)(27,41)(31,52)(34,57)(35,49)(36,62)(37,63)(42,69)(43,70)(44,60)(53,59)(58,68)(64,84)(65,75)(72,87)(73,85)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26446);