Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#32697 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×#41×C19 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
528 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)(20,21,26,30,25,31,43,51)(22,27,35,47,34,46,44,49)(23,36,39,40,38,28,48,33)(24,29,42,32,41,37,45,50);(20,22)(21,27)(23,37)(24,40)(25,34)(26,44)(28,45)(29,38)(30,49)(31,46)(32,39)(33,41)(35,43)(36,42)(47,51)(48,50);(20,23,25,38)(21,28)(22,32)(24,27,41,46)(26,39,43,48)(29,44)(30,33)(31,36)(34,50)(35,37)(40,51)(42,47,45,49);(20,24,25,41)(21,29,31,37)(22,33,34,40)(23,27,38,46)(26,45,43,42)(28,44,36,35)(30,50,51,32)(39,49,48,47)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25685);