Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10792 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C4×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | C22⋊#95 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C2×C19×#117 ◁ G | |
1204 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 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)(22,26,31,42)(23,33)(24,36)(25,28)(27,35)(29,39)(30,46,48,50)(32,44,37,41)(34,45)(38,43)(40,49,51,47);(20,22)(21,26,28,42)(23,30)(24,37)(25,31)(27,40,43,51)(29,44,36,41)(32,39)(33,50,45,46)(34,48)(35,49)(38,47);(20,23)(21,27)(22,30)(24,38)(25,34)(26,40)(28,43)(29,45)(31,48)(32,49)(33,36)(35,39)(37,47)(41,50)(42,51)(44,46)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3780);