Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C8 |
| direct product | C19×#19724 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3184 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
712 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,30)(23,27)(24,28)(25,35)(26,29)(31,33)(32,34)(36,37)(38,44)(39,49)(40,45)(41,50)(42,46)(43,47)(48,51);(20,22,25,27,26,32,24,31)(21,23,28,30,29,33,35,34)(36,38,41,47,42,48,40,39)(37,43,45,44,46,49,50,51);(20,23,26,33)(21,27,29,31)(22,28,32,35)(24,34,25,30)(36,39,40,48,42,47,41,38)(37,44,50,43,46,51,45,49);(20,24,26,25)(21,28,29,35)(22,31,32,27)(23,30,33,34)(36,40,42,41)(37,45,46,50)(38,47,48,39)(43,51,49,44)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12712);