Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23474 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #393 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| socle | C2×C19 | C2×#393 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1164 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)(22,26)(23,33,36,27)(24,28)(25,29)(30,43,34,38)(31,39)(32,40)(35,46,48,41)(37,42)(44,51,47,49)(45,50);(20,22)(21,26)(23,34,36,30)(24,31)(25,32)(27,38,33,43)(28,39)(29,40)(35,47,48,44)(37,45)(41,49,46,51)(42,50);(20,23)(21,27)(22,30)(24,35)(25,36)(26,38)(28,41)(29,33)(31,44)(32,34)(37,48)(39,49)(40,43)(42,46)(45,47)(50,51);(20,24,25,37)(21,28,29,42)(22,31,32,45)(23,35,36,48)(26,39,40,50)(27,41,33,46)(30,44,34,47)(38,49,43,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16462);