Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18523 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C2×#120 |
| prime radical | C19×#3475 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×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)(20,21,25,28)(22,29,31,34)(23,27,24,32)(26,33,35,30)(36,37,42,46)(38,47,39,50)(40,44,41,45)(43,48,51,49);(20,22,25,31)(21,26,28,35)(23,30,24,33)(27,34,32,29)(36,38,42,39)(37,43,46,51)(40,48,41,49)(44,47,45,50);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(36,39,42,38)(37,43,46,51)(40,49,41,48)(44,47,45,50);(36,40,42,41)(37,44,46,45)(38,48,39,49)(43,47,51,50)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11511);