Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18445 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#538 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
848 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(22,29)(23,27)(24,32)(25,28)(26,30)(31,34)(33,35)(36,37,40,42)(38,44,46,51)(39,47,49,43)(41,48,50,45);(20,22,25,31)(21,26,28,35)(23,30,24,33)(27,34,32,29)(36,38,40,46)(37,41,42,50)(39,48,49,45)(43,51,47,44);(20,21)(22,26)(23,32)(24,27)(25,28)(29,30)(31,35)(33,34)(36,37)(38,41)(39,47)(40,42)(43,49)(44,48)(45,51)(46,50);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(37,42)(41,50)(43,47)(44,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11433);