Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#17398 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C25×C19 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C42×C19 ◁ G | |
1034 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)(20,21,23,29,25,28,35,42)(22,27,32,41,30,40,43,51)(24,26,34,38,31,37,45,49)(33,36,47,48,44,39,46,50);(21,26)(22,30)(23,34)(27,39)(28,37)(32,46)(33,44)(35,45)(36,40)(41,51)(43,47)(48,50);(20,22,31,44)(21,27,37,39)(23,32,45,46)(24,33,25,30)(26,36,28,40)(29,41,49,50)(34,47,35,43)(38,48,42,51);(21,28)(26,37)(27,40)(29,42)(36,39)(38,49)(41,51)(48,50)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10386);