Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33348 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33351 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×#99 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C2×D4 | C24×C19 |
| prime radical | C19×#3487 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×Q8×C19 ◁ C2×C19×2−1+4 ◁ G | |
1212 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)(22,32)(23,28)(24,29)(25,39,40,30)(26,31)(27,34,42,38)(33,43)(35,48,49,44)(36,45)(37,46)(41,47,51,50);(20,22,26,24)(21,27,31,42)(23,33,36,37)(25,34,40,38)(28,41,45,51)(29,30,32,39)(35,47,49,50)(43,48,46,44);(20,23,26,36)(21,28,31,45)(22,33,24,37)(25,35,40,49)(27,41,42,51)(29,46,32,43)(30,44,39,48)(34,47,38,50);(20,24,26,22)(21,29,31,32)(23,33,36,37)(25,38,40,34)(27,30,42,39)(28,43,45,46)(35,47,49,50)(41,48,51,44)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26339);