Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18132 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18154 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#392 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
960 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)(21,26)(22,30)(23,33)(27,39)(28,37)(29,34)(32,44)(35,46)(38,41)(40,49)(42,47)(48,50);(20,21,24,29)(22,27,30,41)(23,34,33,26)(25,28,36,42)(31,39,43,38)(32,40,44,50)(35,47,46,37)(45,49,51,48);(23,35)(26,37)(31,45)(33,46)(34,47)(38,48)(39,49)(43,51);(20,22,25,32)(21,27,28,40)(23,31,35,45)(24,30,36,44)(26,38,37,48)(29,41,42,50)(33,43,46,51)(34,39,47,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11142);