Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33460 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#508 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25,30,36)(26,38,27,33)(28,37,31,34)(29,44,46,52)(32,42,49,40)(35,43,53,47)(39,50,41,51)(45,54,55,48);(24,26,30,27)(25,32,36,49)(28,39,31,41)(29,45,46,55)(33,44,38,52)(34,48,37,54)(35,51,53,50)(40,43,42,47);(20,22,23,21)(24,27,30,26)(25,33,36,38)(28,39,31,41)(29,42,46,40)(32,44,49,52)(34,51,37,50)(35,48,53,54)(43,45,47,55);(24,28,30,31)(25,34,36,37)(26,39,27,41)(29,43,46,47)(32,48,49,54)(33,50,38,51)(35,52,53,44)(40,45,42,55)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26448);