Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214×C4 |
| direct product | C23×#127 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C23 |
| commutator, Frattini, cosocle | C22 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
12015 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 6 generators on 14 points:
(3,4);(5,6);(1,2)(3,4)(5,6);(8,10)(12,13);(11,12,14,13);(7,8,9,10)(11,13,14,12)112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55652);