Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#22308 |
| 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 | |
650 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)(22,25)(23,27)(24,26)(28,29)(30,32)(31,34)(33,35)(36,37,41,44,40,43,45,38)(39,47,49,46,48,42,50,51);(20,22,24,23)(21,25,26,27)(28,30,32,29)(31,34,35,33)(36,38,45,43,40,44,41,37)(39,46,50,47,48,51,49,42);(20,23,24,22)(21,25,26,27)(29,30)(33,34)(36,39,40,48)(37,42,43,47)(38,46,44,51)(41,49,45,50);(28,31,32,35)(29,33,30,34)(39,48)(42,47)(46,51)(49,50)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15296);