Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19441 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C23×C19 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(20,21,24,27)(22,28,30,35)(23,32,29,26)(25,33,34,31)(37,41)(38,45)(39,42)(44,50)(47,48)(49,51);(20,22,29,33,24,30,23,31)(21,25,32,35,27,34,26,28)(36,37,42,50,40,44,39,41)(38,46,45,49,48,43,47,51);(22,30)(25,34)(28,35)(31,33)(36,38,40,48)(37,43,44,46)(39,47,42,45)(41,49,50,51);(37,44)(41,50)(43,46)(49,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12429);