Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24986 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#24986 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | #2420 |
| prime radical | C19×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ G | |
642 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)(22,33)(23,37)(24,28)(25,42)(26,31)(27,32)(29,40)(30,36)(34,43)(35,44)(38,45)(39,47)(41,46)(48,49)(50,51);(20,22,25,24,27,36,26,35)(21,28,31,33,32,44,42,30)(23,38,40,34,41,49,39,50)(29,45,37,51,47,48,46,43);(20,23)(21,29)(22,34)(24,38)(25,39)(26,40)(27,41)(28,43)(30,45)(31,46)(32,47)(33,48)(35,49)(36,50)(37,42)(44,51);(20,24,25,36,27,35,26,22)(21,30,31,28,32,33,42,44)(23,38,39,50,41,49,40,34)(29,45,46,43,47,48,37,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17974);