Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11248 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #387 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1441 |
| prime radical | C24×C19 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
604 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(20,21,25,29,26,31,24,30)(22,32,35,44,36,43,34,27)(23,37,39,47,41,46,40,28)(33,42,38,45,49,51,50,48);(20,22,24,34,26,36,25,35)(21,27,29,32,31,44,30,43)(23,38,39,49,41,50,40,33)(28,45,46,42,47,48,37,51);(20,23,24,39,26,41,25,40)(21,28,29,46,31,47,30,37)(22,33,34,38,36,49,35,50)(27,42,32,48,44,51,43,45)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4236);