Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C22×C42 |
| direct product | C19×#20470 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C22 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C23×C4 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
958 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)(26,29)(27,28)(30,31)(32,33)(34,38)(35,36)(37,40)(39,44)(41,42)(43,46)(45,47);(25,28)(29,31)(32,34,36,42,37,43,39,45)(33,38,35,41,40,46,44,47);(20,22,23,21)(32,35)(33,39)(34,41)(36,40)(37,44)(38,45)(42,46)(43,47);(24,26,27,30)(25,29,28,31)(33,40)(35,44)(38,46)(41,47)1900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13458);