Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×C19×#2381 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C19 | C24 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
2326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49);(3,4,5,6)(8,11)(9,13)(16,20)(17,23)(22,25)(24,29);(8,11)(12,14)(15,16,19,20)(17,21,23,27)(18,25,26,22)(24,30,29,28);(7,8,10,11)(9,12,13,14)(15,17)(16,21)(18,24)(19,23)(20,27)(22,28)(25,30)(26,29);(7,9)(8,12)(10,13)(11,14)(15,18,19,26)(16,22,20,25)(17,24,23,29)(21,28,27,30)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27333);