Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19817 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C19 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
554 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 4864 |
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)(21,25)(23,31)(26,34)(27,32)(28,35)(29,33)(36,37,40,43)(38,44,46,51)(39,47,49,42)(41,48,50,45);(20,21,24,27)(22,28,30,34)(23,32,31,25)(26,33,35,29);(36,38,40,46)(37,41,43,50)(39,48,49,45)(42,51,47,44);(20,22,24,30)(21,26,27,35)(23,33,31,29)(25,34,32,28)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12805);