Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8346 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#8349 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #379 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#3493 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
720 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24,25,26)(28,29,32,37,33,36,45,50)(30,38,41,51,40,34,44,47)(31,35,43,48,42,49,55,59)(39,46,54,57,53,52,56,58);(20,21)(22,26)(23,25)(24,27)(28,30)(29,34)(31,39)(32,44)(33,40)(35,46)(36,38)(37,51)(41,45)(42,53)(43,56)(47,50)(48,58)(49,52)(54,55)(57,59);(28,31,33,42)(29,35,36,49)(30,39,40,53)(32,43,45,55)(34,46,38,52)(37,48,50,59)(41,54,44,56)(47,57,51,58)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1337);