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) = C2 |
| direct product | C19×#13108 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #387 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1917 |
| prime radical | C23×C19 | #131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C8×C19 ◁ G | |
246 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)(20,21,25,32,26,30,44,49,27,31,45,33,24,40,42,36)(22,23,29,39,34,28,46,47,35,38,48,43,41,37,51,50);(20,22,25,29,26,34,44,46,27,35,45,48,24,41,42,51)(21,28,32,47,30,38,49,43,31,37,33,50,40,23,36,39);(20,23,24,37,27,38,26,28)(21,29,30,46,31,48,40,51)(22,33,34,36,35,32,41,49)(25,43,42,47,45,39,44,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6096);