Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22284 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#22284 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2328 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3154 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
796 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)(20,21)(22,24)(23,36,40,46)(25,31)(26,32)(27,34)(28,39,47,50)(29,41)(30,43)(33,48,49,44)(35,42)(37,38,45,51);(20,22,25,34,26,35,43,29)(21,27,30,24,32,41,31,42)(23,37,50,33,40,45,39,49)(28,38,36,44,47,51,46,48);(20,23,26,40)(21,28)(22,33)(24,38,42,51)(25,39,43,50)(27,44,41,48)(29,45)(30,46)(31,36)(32,47)(34,37)(35,49);(20,24,25,41,26,42,43,27)(21,29,30,22,32,34,31,35)(23,38,39,48,40,51,50,44)(28,45,46,33,47,37,36,49)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15272);