Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13308 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#3061 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,30,36)(26,37,40,53)(27,41,45,52)(28,35,29,34)(31,47,50,38)(32,46,51,39)(33,43,48,44)(42,54,55,49);(20,21)(22,23)(24,26)(25,31)(27,42)(28,39)(29,46)(30,40)(32,48)(33,51)(34,49)(35,54)(36,50)(37,41)(38,44)(43,47)(45,55)(52,53);(21,23)(24,26)(25,32)(27,38)(28,46)(29,39)(30,40)(31,48)(33,50)(34,53)(35,37)(36,51)(41,54)(42,44)(43,55)(45,47)(49,52)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6296);