Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#32853 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C43×C19 ◁ G | |
568 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)(21,22)(25,26)(28,29,31,32)(30,34,35,33)(36,37,40,43)(38,44,46,41)(39,42,48,51)(45,50,47,49);(20,21,24,22)(23,25,27,26)(28,30,31,35)(29,33,32,34)(36,38,40,46)(37,41,43,44)(39,47,48,45)(42,50,51,49);(20,22,24,21)(23,25,27,26)(29,32)(30,34)(33,35)(39,48)(42,51)(45,47)(49,50);(20,23,24,27)(21,25,22,26)(28,29,31,32)(30,33,35,34)(36,39,40,48)(37,42,43,51)(38,45,46,47)(41,49,44,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25841);