Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23542 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
1362 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(28,29,34,39)(30,40,44,51)(31,45,47,55)(32,38,33,37)(35,43,52,42)(36,49,54,48)(41,57,58,50)(46,53,59,56);(24,25)(26,27)(28,30,34,44)(29,35,39,52)(31,46,47,59)(32,43,33,42)(36,53,54,56)(37,51,38,40)(41,48,58,49)(45,57,55,50);(21,23)(25,27)(28,31,32,48,34,47,33,49)(29,36,37,45,39,54,38,55)(30,41,42,59,44,58,43,46)(35,50,40,56,52,57,51,53);(31,47)(36,54)(41,58)(45,55)(46,59)(48,49)(50,57)(53,56)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16530);