Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#29551 |
| 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 ◁ C19×#376 ◁ G | |
650 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)(20,21)(22,26)(23,25)(24,27)(36,37,42,46)(38,43,39,48)(40,45,41,50)(44,47,51,49);(20,22,23,27)(21,24,25,26)(28,29,31,32)(30,33,34,35)(36,38,42,39)(37,43,46,48)(40,49,41,47)(44,50,51,45);(29,32)(33,35)(36,39,42,38)(37,44,46,51)(40,49,41,47)(43,50,48,45);(21,25)(24,26)(28,30,31,34)(29,33,32,35)(36,40,42,41)(37,45,46,50)(38,47,39,49)(43,51,48,44)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 22539);