Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23391 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#23785 |
| 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 | |
680 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)(22,25)(23,24)(26,27)(28,29,31,33)(30,34,35,32)(36,37,40,44)(38,46,49,42)(39,43,41,45)(47,51,48,50);(21,24)(25,27)(36,38,40,49)(37,42,44,46)(39,48,41,47)(43,51,45,50);(28,30,31,35)(29,32,33,34)(38,47)(39,41)(42,50)(43,45)(46,51)(48,49);(20,22,23,26)(21,25,24,27)(36,39,40,41)(37,43,44,45)(38,48,49,47)(42,51,46,50)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16773);