Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#29495 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C43×C19 ◁ G | |
728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,25)(24,27)(36,37,40,43)(38,44,47,51)(39,48,45,42)(41,49,50,46);(20,22,23,27)(21,24,25,26)(28,29)(30,33)(31,32)(34,35);(29,32)(33,35)(36,38,45,49,40,47,39,46)(37,41,48,51,43,50,42,44);(21,25)(24,26)(28,30,31,34)(29,33,32,35)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 22483);