Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33435 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C24 |
| commutator | C22 | C23×C8×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C22×C19 | C23×C8 |
| prime radical | C19×#532 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ 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)(22,23)(24,25,28,34,29,35,43,51,30,33,44,49,45,50,46,55)(26,31,37,47,38,27,39,40,36,41,52,54,53,42,32,48);(21,23)(24,26)(25,31)(27,35)(28,37)(29,38)(30,36)(32,46)(33,41)(34,47)(39,43)(40,51)(42,50)(44,52)(45,53)(48,55)(49,54);(24,27,28,40,29,41,43,54,30,42,44,48,45,31,46,47)(25,32,34,26,35,37,51,38,33,39,49,36,50,52,55,53);(25,33)(26,36)(32,39)(34,49)(35,50)(37,52)(38,53)(51,55)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26423);