Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#9588 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #121 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C22×C19 | #388 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
304 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(21,25)(22,29)(23,26)(27,35)(28,33)(30,32)(36,37,39,42,41,45,40,44)(38,46,48,51,47,50,49,43);(20,21,26,33,24,28,23,25)(22,30,34,32,29,27,31,35)(37,42,45,44)(38,47)(43,50,51,46)(48,49);(20,22,23,31,24,29,26,34)(21,27,25,32,28,30,33,35)(36,38,39,48,41,47,40,49)(37,43,44,50,45,51,42,46)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2576);