Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18924 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C23×C19 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
878 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)(21,25)(22,23)(26,27)(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);(20,21,24,27)(22,25,23,26)(28,30,34,42)(29,35,39,50)(31,41,48,56)(32,44,33,43)(36,49,53,55)(37,51,38,40)(45,59,52,54)(46,58,47,57);(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);(20,22,24,23)(21,26,27,25)(30,42)(35,50)(40,51)(41,56)(43,44)(49,55)(54,59)(57,58)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11912);