Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| 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 | |
3950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 16 points:
(2,5)(6,8)(9,10)(11,15)(12,13)(14,16);(3,7)(6,8)(10,13)(14,15);(1,2)(3,6)(4,5)(7,8)(9,10)(11,14)(12,13)(15,16);(9,11,12,16)(10,14,13,15);(1,3,4,7)(2,6,5,8);(1,2)(3,6)(4,5)(7,8)Polycyclic presentation:
2^8|d^2=g,e^2=h,b^a=bg,c^a=ch,d^a=dg,f^a=fh,c^b=cg,e^b=eh76 conjugacy classes — view the full character table.
| maximal subgroup of | #185424, #185430, #185436, … |
| maximal normal subgroup of | #185424, #185430, #185436, … |
| maximal quotient of | #7626232, #7626240, #7626266, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55822);