Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2238 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13008 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #481 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1874 |
| prime radical | C19×#3054 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C22×M16×C19 ◁ G | |
516 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,29,25,30,41,47,26,28,23,36,38,45,39,49)(22,31,34,44,35,46,40,43,33,50,32,48,42,51,37,27);(20,22)(21,27,28,43)(23,37)(24,40)(25,42)(26,33)(29,46,36,51)(30,48,45,44)(31,49,50,47)(32,39)(34,41)(35,38);(21,28)(23,24)(27,43)(30,45)(32,34)(37,40)(39,41)(44,48)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5996);