Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9034 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C22×C19 | #386 |
| prime radical | C24×C19 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
482 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(20,21,24,28,25,29,23,27)(22,30,31,26,33,34,32,35)(36,37)(38,46,48,50)(39,49,42,43)(40,44)(41,45)(47,51);(20,22)(21,26)(23,31)(24,32)(25,33)(27,34)(28,30)(29,35)(36,38,40,49,41,48,51,43)(37,42,44,50,45,39,47,46);(20,23,25,24)(21,27,29,28)(22,31,33,32)(26,34,35,30)(36,39,41,42)(37,43,45,49)(38,47,48,44)(40,46,51,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2022);