Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13201 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #390 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1955 |
| prime radical | C19×#525 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C8×C19 ◁ G | |
420 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)(20,21,25,31,26,30,45,49,27,32,46,35,24,29,34,40)(22,33,37,51,36,43,48,50,38,41,28,47,44,23,39,42);(20,22,34,48,24,44,46,37,27,38,45,39,26,36,25,28)(21,23,40,51,29,41,35,42,32,43,49,47,30,33,31,50);(20,23,24,41,27,43,26,33)(21,28,30,39,32,37,29,48)(22,35,36,40,38,31,44,49)(25,42,34,47,46,50,45,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6189);