Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#26848 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,27)(23,25)(24,26)(28,29)(30,41)(31,46)(32,50)(33,52)(34,39)(35,40)(36,44)(37,48)(38,51)(42,58)(43,57)(45,54)(47,59)(49,56)(53,55);(20,22,24,23)(21,25,26,27)(28,30,33,44,35,45,34,53)(29,36,39,41,40,55,52,54)(31,47,48,42,49,32,43,51)(37,50,46,58,57,59,56,38);(20,23,24,22)(21,25,26,27)(28,31,33,48,35,49,34,43)(29,37,39,46,40,57,52,56)(30,42,44,32,45,51,53,47)(36,38,41,50,55,58,54,59);(21,26)(25,27)(28,32,33,51,35,47,34,42)(29,38,39,50,40,58,52,59)(30,43,44,31,45,48,53,49)(36,37,41,46,55,57,54,56)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19836);