Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23814 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C19×#376 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 63 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,27,28)(26,29,30,31)(32,33,36,40,37,41,51,57)(34,42,45,53,44,55,49,38)(35,46,47,54,48,56,50,39)(43,52,60,63,59,62,61,58);(20,21)(22,23)(25,28)(29,31)(32,34,37,44)(33,38,41,53)(35,43,48,59)(36,49,51,45)(39,52,54,62)(40,55,57,42)(46,58,56,63)(47,61,50,60);(21,23)(32,35,37,48)(33,39,41,54)(34,43,44,59)(36,50,51,47)(38,52,53,62)(40,56,57,46)(42,58,55,63)(45,61,49,60);(24,26,27,30)(25,29,28,31)(34,44)(38,53)(42,55)(43,59)(45,49)(52,62)(58,63)(60,61)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16802);