Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C19×#1979 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #121 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C23×C4×C19 ◁ G | |
1438 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57);(4,6)(7,8,12,17,13,16,11,25)(9,14,20,29,19,30,26,28)(10,21,23,31,24,35,22,15)(18,32,34,27,33,37,36,38);(3,4,5,6)(7,9,11,20,13,19,12,26)(8,14,17,28,16,30,25,29)(10,18,22,34,24,33,23,36)(15,27,21,32,31,38,35,37);(7,10,12,23,13,24,11,22)(8,15,25,35,16,31,17,21)(9,18,26,36,19,33,20,34)(14,27,29,37,30,38,28,32)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14235);