Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#21559 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#121 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C4×#121 |
| prime radical | C19×#3067 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C8×C19 ◁ G | |
868 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)(20,21,25,31,27,32,26,30)(22,33,24,28,36,43,35,44)(23,37,39,29,40,45,41,46)(34,48,38,47,49,42,50,51);(20,22,25,24,27,36,26,35)(21,28,30,33,32,44,31,43)(23,34,39,38,40,49,41,50)(29,42,37,47,46,48,45,51);(20,23)(21,29)(22,34)(24,38)(25,39)(26,41)(27,40)(28,42)(30,37)(31,45)(32,46)(33,47)(35,50)(36,49)(43,51)(44,48);(20,24,25,36,27,35,26,22)(21,28,31,43,32,44,30,33)(23,38,39,49,40,50,41,34)(29,42,45,51,46,48,37,47)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14547);