Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23525 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #394 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#394 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1332 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)(23,37)(24,29)(25,30)(26,31)(27,35)(28,40)(33,44)(34,43)(36,47)(38,42)(39,46)(41,45)(48,50)(49,51);(20,22)(21,27)(23,38)(24,34)(25,35)(26,36)(28,44)(29,32)(30,47)(31,43)(33,41)(37,51)(39,50)(40,49)(42,46)(45,48);(20,23,24,39,26,41,25,40)(21,28,30,45,31,46,29,37)(22,33,35,50,36,38,34,49)(27,42,32,48,43,44,47,51);(20,24,26,25)(21,29,31,30)(22,34,36,35)(23,39,41,40)(27,32,43,47)(28,37,46,45)(33,49,38,50)(42,48,44,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16513);