Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#10941 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #386 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1437 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
904 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,29,25,28,36,42)(22,26,32,39,31,38,35,43)(23,27,34,40,33,41,47,51)(30,44,46,50,45,37,48,49);(20,22)(21,26,28,38)(23,30)(24,35)(25,31)(27,37,41,44)(29,43,42,39)(32,36)(33,45)(34,48)(40,50,51,49)(46,47);(20,23,24,34,25,33,36,47)(21,27,29,40,28,41,42,51)(22,30,35,48,31,45,32,46)(26,37,43,50,38,44,39,49)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3929);