Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13314 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
536 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
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)(20,21)(22,23)(24,25,30,36)(26,37,41,50)(27,31,44,47)(28,35,29,34)(32,38,51,40)(33,43,46,42)(39,49,54,48)(45,53,52,55);(25,31)(26,38)(27,42)(28,29)(32,48)(33,34)(35,46)(36,47)(37,52)(39,54)(40,41)(43,44)(45,50)(49,51);(21,23)(24,26)(25,32)(27,39)(28,38)(29,40)(30,41)(31,45)(33,49)(34,50)(35,37)(36,51)(42,53)(43,55)(44,54)(46,48)(47,52)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6302);