Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C19×#21244 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#121 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#390 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1460 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26,31,40)(23,33)(24,36)(25,28)(27,35)(29,37)(30,42,43,51)(32,46,45,39)(34,47)(38,49,50,44)(41,48);(20,22)(21,26,28,40)(23,30)(24,32)(25,31)(27,38,41,50)(29,39,36,46)(33,42,47,51)(34,43)(35,44)(37,45)(48,49);(20,23,24,35,25,34,37,48)(21,27,29,33,28,41,36,47)(22,30,32,44,31,43,45,49)(26,38,39,42,40,50,46,51);(23,34)(27,41)(30,43)(33,47)(35,48)(38,50)(42,51)(44,49)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14232);