Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#20710 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #381 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| socle | C2×C19 | C2×#381 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1276 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)(22,30,33,26)(23,34)(24,28)(25,29)(27,36)(31,38,45,42)(32,43,46,39)(35,47)(37,41)(40,48)(44,49,51,50);(20,22)(21,26)(23,31)(24,32)(25,33)(27,38)(28,39)(29,30)(34,42)(35,44)(36,45)(37,46)(40,49)(41,43)(47,50)(48,51);(20,23)(21,27,29,34)(22,31)(24,35)(25,36)(26,38,30,42)(28,40,41,47)(32,44)(33,45)(37,48)(39,49,43,50)(46,51);(20,24,25,37)(21,28,29,41)(22,32,33,46)(23,35,36,48)(26,39,30,43)(27,40,34,47)(31,44,45,51)(38,49,42,50)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13698);