Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24404 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24407 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C19×#3485 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25)(26,34,37,30)(27,36)(28,35,39,32)(29,33)(31,38);(20,21)(22,23)(24,26,29,37)(25,30,33,34)(27,35,38,32)(28,36,39,31);(21,23)(24,27)(25,31)(26,35)(28,30)(29,38)(32,37)(33,36)(34,39);(24,28)(25,32)(26,36)(27,30)(29,39)(31,37)(33,35)(34,38)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17395);