Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10786 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 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)(24,25,29,35,30,33,28,34)(26,31,38,45,37,46,43,49)(27,39,41,32,42,48,40,47)(36,50,52,54,51,55,53,44);(21,23)(24,26)(25,31,33,46)(27,36)(28,38)(29,43)(30,37)(32,44,47,54)(34,45,35,49)(39,50,48,55)(40,52)(41,53)(42,51);(24,27,30,42)(25,32,33,47)(26,36,37,51)(28,41,29,40)(31,44,46,54)(34,48,35,39)(38,53,43,52)(45,55,49,50)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3774);