Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13229 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#13229 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1964 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×#41 | C23×C19 |
| prime radical | C19×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×C19×#131 ◁ G | |
452 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)(22,32,36,47)(23,37)(24,40,33,29)(25,43)(26,31)(27,28)(30,44)(34,48,49,42)(35,38,50,46)(39,51)(41,45);(20,22,33,28,26,36,24,41)(21,27,40,47,31,45,29,32)(23,34,46,30,39,49,38,43)(25,35,48,37,44,50,42,51);(20,23,25,27,26,39,44,45)(21,28,30,37,31,41,43,51)(22,34,35,40,36,49,50,29)(24,38,42,32,33,46,48,47)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6217);