Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#22302 |
| 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 | |
598 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)(36,37,41,44,40,43,45,38)(39,47,50,46,49,42,51,48);(20,21)(22,25)(23,24)(26,27)(28,30,32,31)(29,33,34,35)(36,38,45,43,40,44,41,37)(39,48,51,42,49,46,50,47);(21,24)(25,27)(28,31,32,30)(29,33,34,35)(36,39,40,49)(37,42,43,47)(38,46,44,48)(41,50,45,51);(20,22,23,26)(21,25,24,27)(39,49)(42,47)(46,48)(50,51)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15290);