Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19547 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
552 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)(20,21,25,29)(22,26,31,35)(23,28,24,33)(27,32,34,30)(36,37)(38,40)(39,47)(41,46)(42,44)(43,49)(45,50)(48,51);(20,22)(21,26)(23,32)(24,30)(25,31)(27,33)(28,34)(29,35)(36,38,40,37,42,46,41,44)(39,45,49,43,50,47,48,51);(20,22)(21,27)(23,30)(24,32)(25,31)(26,33)(28,35)(29,34)(36,39)(37,43)(38,45)(40,49)(41,48)(42,50)(44,51)(46,47);(20,23,25,24)(21,28,29,33)(22,30,31,32)(26,27,35,34)(36,40,42,41)(37,38,44,46)(39,48,50,49)(43,47,51,45)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12535);