Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21080 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#121 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#388 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1000 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)(20,21,25,29,26,30,24,40)(22,31,35,42,33,45,34,27)(23,36,39,51,38,28,37,43)(32,46,49,41,47,44,48,50);(20,22)(21,27,30,42)(23,32)(24,34)(25,35)(26,33)(28,41,36,50)(29,31,40,45)(37,48)(38,47)(39,49)(43,44,51,46);(20,23,24,37,26,38,25,39)(21,28,29,43,30,36,40,51)(22,32,34,48,33,47,35,49)(27,41,31,44,42,50,45,46);(22,33)(27,42)(31,45)(32,47)(34,35)(41,50)(44,46)(48,49)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14068);