Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11349 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #391 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1445 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
580 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)(22,26,31,41)(23,33,35,48)(24,29)(25,28)(27,34,43,50)(30,45)(32,40,36,44)(37,38)(39,49)(42,47)(46,51);(20,22,24,36,25,31,37,32)(21,26,38,40,28,41,29,44)(23,30,34,49,35,46,50,47)(27,42,48,51,43,39,33,45);(20,23,24,34,25,35,37,50)(21,27,38,48,28,43,29,33)(22,30,36,49,31,46,32,47)(26,39,40,45,41,42,44,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4337);