Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#21478 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#120 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C4×#120 |
| prime radical | C19×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C8×C19 ◁ G | |
1282 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)(20,21,26,31,27,32,25,38)(22,33,36,28,37,47,42,46)(23,29,39,24,30,40,43,41)(34,35,49,51,45,48,50,44);(20,22)(21,28)(23,34)(24,35)(25,42)(26,36)(27,37)(29,44)(30,45)(31,47)(32,46)(33,38)(39,49)(40,51)(41,48)(43,50);(20,23)(21,29)(22,34)(24,31)(25,43)(26,39)(27,30)(28,44)(32,40)(33,48)(35,47)(36,49)(37,45)(38,41)(42,50)(46,51);(20,24,26,40,27,41,25,29)(21,30,31,43,32,23,38,39)(22,35,36,51,37,48,42,44)(28,45,47,50,46,34,33,49)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14466);