Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19079 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3545 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
906 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)(22,30)(23,31)(24,29)(25,28)(26,27)(32,35)(33,34)(36,37,40,42)(38,44,46,51)(39,47,49,43)(41,48,50,45);(20,22)(21,23)(24,34)(25,31)(26,32)(27,33)(28,35)(29,30)(36,38)(37,41)(39,48)(40,46)(42,50)(43,51)(44,47)(45,49);(20,23)(21,22)(24,30)(25,35)(26,33)(27,32)(28,31)(29,34)(36,37)(38,41)(39,47)(40,42)(43,49)(44,48)(45,51)(46,50);(21,27)(23,33)(28,29)(30,35)(37,42)(41,50)(43,47)(44,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12067);