Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11319 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #401 |
| commutator | C24 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1443 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
532 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)(20,21,24,29,25,28,37,44)(22,26,32,40,31,39,36,45)(23,33,35,48,34,27,41,43)(30,38,47,50,46,42,49,51);(20,22)(21,26,28,39)(23,30,34,46)(24,36)(25,31)(27,42)(29,45,44,40)(32,37)(33,38)(35,49,41,47)(43,50)(48,51);(20,23)(21,27,28,33)(22,30,31,46)(24,35)(25,34)(26,38)(29,43,44,48)(32,47,36,49)(37,41)(39,42)(40,50)(45,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4307);