Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#13244 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #466 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C23×C19 | #135 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,30,37,32,38,31,56)(26,39,43,59,44,67,55,70)(27,45,48,77,50,78,49,64)(28,36,29,54,53,68,52,35)(33,57,60,41,62,42,61,51)(34,63,65,80,66,46,76,47)(40,58,73,83,74,85,81,84)(69,79,75,82,86,71,87,72);(20,21,22,23)(24,26,28,51,31,43,52,57,32,44,53,41,30,55,29,42)(25,33,54,39,37,61,68,70,38,62,35,67,56,60,36,59)(27,40,46,79,49,73,80,82,50,74,63,71,48,81,47,72)(34,58,77,69,65,84,78,87,66,85,64,86,76,83,45,75);(24,27,28,46,31,49,52,80,32,50,53,63,30,48,29,47)(25,34,54,77,37,65,68,78,38,66,35,64,56,76,36,45)(26,40,51,79,43,73,57,82,44,74,41,71,55,81,42,72)(33,58,39,69,61,84,70,87,62,85,67,86,60,83,59,75)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6232);