Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C19×#21250 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1434 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)(21,23)(24,25,29,34,30,33,28,42)(26,31,37,46,36,47,43,45)(27,38,41,48,39,52,40,32)(35,49,51,44,50,55,53,54);(20,21,22,23)(24,26,28,37,30,36,29,43)(25,31,34,45,33,47,42,46)(27,35,40,51,39,50,41,53)(32,44,38,49,48,54,52,55);(24,27,28,40,30,39,29,41)(25,32,34,38,33,48,42,52)(26,35,37,51,36,50,43,53)(31,44,45,49,47,54,46,55);(27,39)(32,48)(35,50)(38,52)(40,41)(44,54)(49,55)(51,53)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14238);