Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23649 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#397 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
892 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(22,30,33,43)(23,27)(24,28)(25,29)(26,32,40,37)(31,46,34,45)(35,41)(36,42)(38,44)(39,48,50,47)(49,51);(20,22)(21,26)(23,34)(24,37)(25,33)(27,39)(28,43)(29,40)(30,44)(31,35)(32,38)(36,47)(41,50)(42,46)(45,51)(48,49);(20,23,24,36,25,35,38,49)(21,27,28,42,29,41,44,51)(22,31,32,47,33,34,37,48)(26,39,30,45,40,50,43,46);(23,35)(27,41)(31,34)(36,49)(39,50)(42,51)(45,46)(47,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16637);