Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#21476 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| 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 ◁ C2×C42×C19 ◁ G | |
1322 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)(24,25,29,33)(26,34,37,48)(27,31,38,46)(28,40,43,32)(30,41,45,36)(35,51,52,50)(39,49,42,47)(44,54,55,53);(24,26)(25,30)(27,35)(28,41)(29,37)(31,44)(32,48)(33,45)(34,40)(36,43)(38,52)(39,54)(42,53)(46,55)(47,50)(49,51);(24,27,29,38)(25,31,33,46)(26,35,37,52)(28,42,43,39)(30,44,45,55)(32,49,40,47)(34,50,48,51)(36,54,41,53);(20,22,23,21)(27,38)(31,46)(35,52)(39,42)(44,55)(47,49)(50,51)(53,54)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14464);