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×#13833 |
| 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 | |
1326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25,27,26)(29,32)(30,34)(36,37,40,39)(38,42,43,41);(24,25,27,26)(29,32)(33,35)(37,39)(41,42);(20,22,23,21)(24,26,27,25)(28,29)(30,33)(31,32)(34,35)(36,38)(37,41)(39,42)(40,43);(28,30)(29,33)(31,34)(32,35)(36,39,40,37)(38,42,43,41)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6821);