Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#13825 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C19 | C24 |
| commutator | C22 | C22×C42×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
1630 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 4864 |
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)(24,25,27,26)(29,31)(32,33,36,37)(34,38,39,35);(20,21,23,22)(33,37)(35,38);(24,25,27,26)(28,29)(30,31)(32,34)(33,35)(36,39)(37,38);(20,22,23,21)(24,26,27,25)(32,35)(33,34)(36,38)(37,39)1900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6813);