Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63011 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C22 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
4025 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 6 generators on 16 points:
(1,2)(3,6)(4,7)(5,8)(9,10)(11,15)(12,14)(13,16);(1,2)(3,6)(4,7)(5,8)(9,10,12,14)(11,13,16,15);(1,3)(2,5)(4,8)(6,7)(9,10)(11,13)(12,14)(15,16);(9,11)(10,13)(12,16)(14,15);(1,3)(2,6)(4,8)(5,7);(1,2)(3,5)(4,7)(6,8)Polycyclic presentation:
2^8|b^2=g,b^a=bg,c^a=ch,d^a=dg,c^b=cgh,f^e=fh76 conjugacy classes — view the full character table.
| maximal subgroup of | #511853, #6350169, #6350170, … |
| maximal normal subgroup of | #511853, #6350169, #6350170, … |
| maximal quotient of | #7627211, #7627212, #7627215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 56000);