Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13215 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#13215 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1961 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
466 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)(22,33)(23,38,42,47)(24,36)(25,30)(26,32)(27,31)(28,41,46,44)(29,34)(35,40,45,50)(37,43)(39,48,51,49);(20,22,34,32,25,37,43,30,26,29,33,21,27,36,24,31)(23,39,48,47,41,45,40,46,42,51,49,38,44,35,50,28);(20,23,26,42)(21,28)(22,35)(24,40,43,50)(25,41,27,44)(29,45)(30,38)(31,47)(32,46)(33,48,34,49)(36,51)(37,39)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6203);