Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11131 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #392 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1439 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
852 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)(20,21,25,29,26,31,24,30)(22,32,36,42,35,43,34,27)(23,28,38,46,39,47,40,45)(33,48,37,41,49,44,50,51);(20,22,24,34,26,35,25,36)(21,27,29,32,31,42,30,43)(23,37,38,49,39,50,40,33)(28,44,45,41,47,48,46,51);(20,23)(21,28)(22,33)(24,40)(25,38)(26,39)(27,41)(29,46)(30,45)(31,47)(32,44)(34,50)(35,49)(36,37)(42,51)(43,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4119);