Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18827 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3499 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
1080 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)(20,21,24,27)(22,26,23,25)(28,29)(30,34)(31,41)(32,44)(33,36)(35,43)(37,47)(38,54)(39,52)(40,49)(42,53)(45,50)(46,51)(48,56)(55,58)(57,59);(21,25)(22,23)(26,27)(28,30,33,40)(29,34,36,49)(31,38,42,55)(32,45,47,39)(35,48,51,59)(37,52,44,50)(41,58,53,54)(43,57,46,56);(28,31)(29,35)(30,38)(32,46)(33,42)(34,48)(36,51)(37,53)(39,57)(40,55)(41,44)(43,47)(45,56)(49,59)(50,58)(52,54);(20,22,24,23)(21,26,27,25)(29,36)(34,49)(35,51)(37,44)(41,53)(48,59)(50,52)(54,58)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11815);