Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#22055 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
1024 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25)(26,30)(27,29)(28,31)(32,33)(34,44)(35,39)(36,43)(37,42)(38,41)(40,46)(45,47);(20,22,23,21)(24,26)(25,28)(27,31)(29,30)(32,34)(33,39)(35,37)(36,46)(38,45)(40,41)(42,44)(43,47);(26,31)(28,30)(32,35,37,34)(33,40,42,47)(36,46,38,45)(39,43,44,41);(25,29)(28,30)(32,36,37,38)(33,41,42,43)(34,45,35,46)(39,47,44,40)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15043);