Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#36609 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| prime radical | C2×C19×#127 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1938 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 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)(22,25)(23,26)(24,27)(28,29)(30,33)(31,32)(34,35)(36,37,41,39)(38,42,40,43);(20,22,23,27)(21,24,26,25)(29,32)(33,34)(36,37,41,39)(38,43,40,42);(20,21,23,26)(22,25,27,24)(28,29)(30,34)(31,32)(33,35)(36,38,41,40)(37,42,39,43);(20,21)(22,24)(23,26)(25,27)(28,30,31,35)(29,33,32,34)(36,39,41,37)(38,42,40,43);(20,22)(21,25)(23,27)(24,26)(28,29)(30,34)(31,32)(33,35)(36,40,41,38)(37,43,39,42)1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29597);