Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#22892 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×2−1+4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
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)(24,25,31,37)(26,38,27,41)(28,34,46,52)(29,36,30,35)(32,43,33,40)(39,54,42,50)(44,49,55,48)(45,53,47,51);(20,22,23,21)(24,26,31,27)(25,32,37,33)(28,44,46,55)(29,43,30,40)(34,50,52,54)(35,41,36,38)(39,47,42,45)(48,53,49,51);(24,27,31,26)(25,33,37,32)(28,42,46,39)(29,43,30,40)(34,49,52,48)(35,41,36,38)(44,45,55,47)(50,51,54,53);(24,28)(25,34)(26,39)(27,42)(29,47)(30,45)(31,46)(32,48)(33,49)(35,53)(36,51)(37,52)(38,54)(40,55)(41,50)(43,44)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15880);