Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34371 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C24×C19 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25,28,26)(27,30,31,29)(33,38)(34,35)(36,44)(46,47);(25,26)(29,30)(32,33,37,38)(34,40,35,39)(36,41,44,45)(42,47,43,46);(32,34,37,35)(33,39,38,40)(36,42,44,43)(41,46,45,47);(24,26,28,25)(27,30,31,29)(32,35,37,34)(33,40,38,39)(36,43,44,42)(41,47,45,46);(24,27)(25,29)(26,30)(28,31)(32,36)(33,41)(34,42)(35,43)(37,44)(38,45)(39,46)(40,47)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27359);