Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24987 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#24987 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
638 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)(21,26)(22,30)(23,34)(24,36)(28,43)(29,39)(32,33)(35,47)(37,41)(40,48)(44,45)(50,51);(20,21,24,26,25,29,36,39)(22,27,30,41,33,42,32,37)(23,28,34,38,35,43,47,49)(31,40,44,50,46,51,45,48);(20,22)(21,27)(23,31)(24,32)(25,33)(26,37)(28,40)(29,42)(30,36)(34,45)(35,46)(38,48)(39,41)(43,51)(44,47)(49,50);(20,23,24,34,25,35,36,47)(21,28,26,38,29,43,39,49)(22,31,32,45,33,46,30,44)(27,40,37,48,42,51,41,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17975);