Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C2×C19×#2370 |
| 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 | |
2510 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(3,4,6,5)(7,8,11,10)(9,13,14,12)(15,16)(17,21)(18,22)(19,20);(3,5,6,4)(8,10)(12,13)(16,20)(18,21);(7,9)(8,12)(10,13)(11,14)(15,17,19,22)(16,21,20,18);(7,10,11,8)(9,13,14,12)(15,18,19,21)(16,22,20,17)1900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27132);