Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#21678 |
| 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 | |
638 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)(20,21)(22,26)(23,27)(24,25)(28,29)(30,32)(31,33)(34,35)(36,37,42,45,41,44,39,40)(38,46,47,51,49,43,50,48);(21,25)(26,27)(28,30,31,34)(29,32,33,35)(36,38)(37,43)(39,50)(40,51)(41,49)(42,47)(44,46)(45,48);(20,22,24,23)(21,26,25,27)(29,33)(32,35)(36,39,41,42)(37,40,44,45)(38,47,49,50)(43,48,46,51);(20,23,24,22)(21,27,25,26)(36,40,39,44,41,45,42,37)(38,48,50,43,49,51,47,46)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14666);