Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23918 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#24010 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C25×C19 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C24×C4×C19 ◁ G | |
1428 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1216 |
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)(24,25)(26,29)(27,28)(30,31)(32,33,37,40)(34,38,36,44)(35,42,43,46)(39,45,47,41);(20,21)(22,23)(25,28)(29,31)(32,34,37,36)(33,38,40,44)(35,41,43,45)(39,46,47,42);(21,23)(24,26,27,30)(25,29,28,31)(32,35)(33,39)(34,41)(36,45)(37,43)(38,46)(40,47)(42,44);(25,28)(29,31)(32,34,37,36)(33,38,40,44)(35,41,43,45)(39,46,47,42)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16998);