Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C19 · Schur multiplier (H2) = C2×C42 |
| direct product | C19×#7843 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C19 | C23 |
| commutator | C22 | C43×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle, prime radical | C23×C19 | C2×C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C19 ◁ G | |
526 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(25,28)(29,31)(32,33,35,38,36,39,42,45)(34,37,41,44,40,43,46,47);(24,25,26,29,27,28,30,31)(32,34)(33,37)(35,41)(36,40)(38,44)(39,43)(42,46)(45,47);(20,21,22,23)(34,40)(37,43)(41,46)(44,47)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 831);