Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#8992 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C22×C19 | #386 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25,26,27)(28,29,32,35,33,30,31,34);(20,21,22,25,24,26,23,27)(28,30,33,29)(31,34,32,35);(20,22,24,23)(21,25,26,27)(28,29,33,30)(31,35,32,34)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1980);