Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#32851 |
| 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 ◁ C43×C19 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4864 |
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)(21,22)(25,26)(28,29,32,35)(30,36,38,33)(31,34,40,43)(37,42,39,41)(44,45,48,52)(46,54,56,50)(47,51,49,53)(55,59,57,58);(20,21,24,22)(23,25,27,26)(28,30,32,38)(29,33,35,36)(31,39,40,37)(34,42,43,41)(46,55)(47,49)(50,58)(51,53)(54,59)(56,57);(20,22,24,21)(23,25,27,26)(31,40)(34,43)(37,39)(41,42)(44,46,48,56)(45,50,52,54)(47,55,49,57)(51,58,53,59);(20,23,24,27)(21,25,22,26)(28,31,32,40)(29,34,35,43)(30,37,38,39)(33,41,36,42)(44,47,48,49)(45,51,52,53)(46,55,56,57)(50,58,54,59)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25839);