Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23425 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
1938 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(28,29,34,39)(30,40,42,51)(31,45,48,52)(32,38,33,37)(35,44,50,43)(36,46,53,47)(41,55,56,49)(54,57,59,58);(21,23)(24,25)(26,27)(28,30)(29,35)(31,41)(32,44)(33,43)(34,42)(36,49)(37,51)(38,40)(39,50)(45,59)(46,58)(47,57)(48,56)(52,54)(53,55);(25,27)(28,31,34,48)(29,36,39,53)(30,41,42,56)(32,47,33,46)(35,49,50,55)(37,45,38,52)(40,54,51,59)(43,58,44,57);(30,42)(35,50)(40,51)(41,56)(43,44)(49,55)(54,59)(57,58)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16413);