Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#21484 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#120 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C4×#120 |
| prime radical | C19×#3025 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C8×C19 ◁ G | |
1306 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)(20,21,25,24,26,29,38,37)(22,27,33,31,32,40,47,46)(23,28,36,34,35,41,49,48)(30,42,45,51,44,39,50,43);(20,22)(21,27)(23,30)(24,31)(25,33)(26,32)(28,39)(29,40)(34,43)(35,44)(36,45)(37,46)(38,47)(41,42)(48,51)(49,50);(20,23)(21,28)(22,30)(24,34)(25,36)(26,35)(27,39)(29,41)(31,43)(32,44)(33,45)(37,48)(38,49)(40,42)(46,51)(47,50);(20,24,25,29,26,37,38,21)(22,31,33,40,32,46,47,27)(23,34,36,41,35,48,49,28)(30,43,45,42,44,51,50,39)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14472);