Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#33697 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C22×C19 | C22×D8 |
| prime radical | C19×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
598 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)(22,25)(23,24)(26,27)(28,29)(30,37)(31,36)(32,38)(33,40)(34,39)(35,42)(41,49)(43,55)(44,51)(45,56)(46,52)(47,54)(48,57)(50,58)(53,59);(21,24)(25,27)(28,30,34,44,32,43,48,47,35,45,50,59,49,46,33,31)(29,36,40,52,41,53,58,56,42,54,57,55,38,51,39,37);(20,22,23,26)(21,25,24,27)(28,31,33,46,49,59,50,45,35,47,48,43,32,44,34,30)(29,37,39,51,38,55,57,54,42,56,58,53,41,52,40,36);(28,32,35,49)(29,38,42,41)(30,43,45,46)(31,44,47,59)(33,34,48,50)(36,51,54,53)(37,55,56,52)(39,57,58,40)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26685);