Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33434 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C19 | C23 |
| 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×C16×C19 ◁ G | |
690 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)(24,25,29,34,30,35,44,51,28,33,42,49,43,50,46,55)(26,36,38,52,39,40,48,54,37,31,45,47,53,27,32,41);(21,23)(24,26)(25,31)(27,35)(28,37)(29,38)(30,39)(32,46)(33,36)(34,47)(40,50)(41,51)(42,45)(43,53)(44,48)(49,52)(54,55);(24,27,29,41,30,36,44,52,28,40,42,54,43,31,46,47)(25,32,34,26,35,38,51,39,33,48,49,37,50,45,55,53);(25,33)(26,37)(32,48)(34,49)(35,50)(38,45)(39,53)(51,55)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26422);