Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#24809 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
830 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)(20,21,24,29,25,30,38,28)(22,31,34,26,36,32,35,42)(23,37,39,27,40,43,51,44)(33,47,48,45,50,41,49,46);(20,22,24,34,25,36,38,35)(21,26,28,31,30,42,29,32)(23,33,39,48,40,50,51,49)(27,41,37,45,44,47,43,46);(20,21)(22,32)(23,27)(24,28)(25,30)(26,34)(29,38)(31,36)(33,46)(35,42)(37,39)(40,44)(41,48)(43,51)(45,50)(47,49);(20,23,38,51,25,40,24,39)(21,27,29,43,30,44,28,37)(22,33,35,49,36,50,34,48)(26,41,32,46,42,47,31,45)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17797);