Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2359296 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C8 |
| abelian | C22×C82 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C42 | C24 |
| socle, prime radical | C24 | C42 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
671 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 256 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3,4,5,6,7,8);(9,10,11,12,13,14,15,16);(17,18);(19,20)256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 10298);