Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13229 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#13230 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1964 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×#41 | C23×C19 |
| prime radical | C2×#41×C19 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×C19×#131 ◁ G | |
436 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,32,37,55)(23,38)(24,43,33,29)(25,46)(26,31)(27,35)(28,41)(30,39)(34,58,62,81)(36,64,59,54)(40,69,56,66)(42,67)(44,49)(45,52,57,73)(47,76)(48,74)(50,71,72,80)(51,68)(53,78,79,61)(60,65)(63,75)(70,82)(77,83);(20,22,33,35,26,37,24,44)(21,27,43,55,31,49,29,32)(23,34,56,60,42,62,40,70)(25,36,57,63,39,59,45,74)(28,47,72,79,51,77,50,53)(30,48,73,64,46,75,52,54)(38,65,69,81,67,82,66,58)(41,61,80,76,68,78,71,83);(20,23,39,68,26,42,25,41)(21,28,46,67,31,51,30,38)(22,34,59,78,37,62,36,61)(24,40,57,80,33,56,45,71)(27,47,75,82,49,77,48,65)(29,50,73,69,43,72,52,66)(32,53,64,81,55,79,54,58)(35,60,74,83,44,70,63,76)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6218);