Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#22304 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle, prime radical | C23×C19 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
578 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 4864 |
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)(21,24)(22,26)(28,29)(30,33)(31,35)(32,34)(36,37,42,38,41,45,40,44)(39,43,47,46,48,50,49,51);(20,21)(22,25)(23,24)(26,27)(28,30,32,31)(29,33,34,35)(36,38,42,45,41,44,40,37)(39,46,47,50,48,51,49,43);(21,24)(25,27)(28,31,32,30)(29,33,34,35)(36,39)(37,43)(38,46)(40,49)(41,48)(42,47)(44,51)(45,50);(20,22,23,26)(21,25,24,27)(36,40,41,42)(37,44,45,38)(39,47,48,49)(43,46,50,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15292);