Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18929 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3506 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(20,21,25,29)(22,30,33,34)(23,27,24,28)(26,32,35,31)(36,37)(38,46)(39,44)(40,43)(41,45)(42,48)(47,50)(49,51);(20,22,25,33)(21,26,29,35)(23,31,24,32)(27,34,28,30)(36,38,41,47)(37,42,45,51)(39,49,40,48)(43,50,44,46);(20,23,25,24)(21,27,29,28)(22,31,33,32)(26,34,35,30)(37,43)(39,40)(42,50)(44,45)(46,51)(48,49);(20,23,25,24)(21,28,29,27)(22,32,33,31)(26,34,35,30)(38,47)(42,51)(46,50)(48,49)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11917);