Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24802 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#24804 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
858 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)(24,25,31,35,30,37,29,36)(26,34,28,46,40,48,39,32)(27,41,43,33,45,51,44,50)(38,52,53,49,54,47,42,55);(20,21)(22,23)(24,26,29,39,30,40,31,28)(25,32,35,34,37,46,36,48)(27,38,43,53,45,54,44,42)(33,47,41,49,50,52,51,55);(21,23)(24,27)(25,33)(26,38)(28,42)(29,43)(30,45)(31,44)(32,47)(34,49)(35,41)(36,51)(37,50)(39,53)(40,54)(46,52)(48,55);(24,28,31,40,30,39,29,26)(25,34,36,32,37,48,35,46)(27,42,44,54,45,53,43,38)(33,49,51,47,50,55,41,52)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17792);