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×#26851 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
720 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)(30,42)(31,48)(32,52)(33,40)(34,39)(35,41)(36,45)(37,50)(38,43)(44,58)(46,55)(47,54)(49,56)(51,57)(53,59);(20,22,24,23)(21,25,26,27)(28,30,34,46,35,47,33,45)(29,36,40,54,41,55,39,42)(31,49,50,43,51,32,44,53)(37,56,48,59,58,52,57,38);(20,23,24,22)(21,25,26,27)(28,31,33,44,35,51,34,50)(29,37,39,57,41,58,40,48)(30,43,45,49,47,53,46,32)(36,38,42,52,55,59,54,56);(21,26)(25,27)(28,32,33,43,35,49,34,53)(29,38,39,52,41,59,40,56)(30,44,45,51,47,50,46,31)(36,37,42,57,55,58,54,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19839);