Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#25198 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3020 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(20,21,24,29,25,30,40,28)(22,31,34,42,35,44,33,26)(23,36,38,43,39,45,37,27)(32,41,47,50,48,51,49,46);(20,22,24,34,25,35,40,33)(21,26,29,31,30,42,28,44)(23,32,38,47,39,48,37,49)(27,41,36,50,43,51,45,46);(20,23,25,39)(21,27,30,43)(22,32,35,48)(24,37,40,38)(26,41,42,51)(28,36,29,45)(31,46,44,50)(33,47,34,49);(20,21)(22,26)(23,27)(24,29)(25,30)(28,40)(31,34)(32,41)(33,44)(35,42)(36,38)(37,45)(39,43)(46,49)(47,50)(48,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18186);