Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#25191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3012 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
1010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,29,36,31,37,30,35)(26,38,42,52,43,51,41,32)(27,44,47,34,28,48,46,33)(39,49,40,50,55,54,45,53);(20,21)(22,23)(24,26,29,42,31,43,30,41)(25,32,36,38,37,52,35,51)(27,45,47,39,28,40,46,55)(33,53,44,49,34,50,48,54);(21,23)(24,27,31,28)(25,33,37,34)(26,39,43,55)(29,46,30,47)(32,49,52,54)(35,44,36,48)(38,53,51,50)(40,42,45,41);(24,28,31,27)(25,34,37,33)(26,40,43,45)(29,46,30,47)(32,50,52,53)(35,44,36,48)(38,54,51,49)(39,42,55,41)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18179);