Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62892 |
| 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 | |
3336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 32 points:
(2,7)(3,9)(5,13)(12,15)(19,25)(23,27)(26,31)(30,32);(1,2)(3,8)(4,9)(5,10)(6,7)(11,15)(12,16)(13,14)(17,18,22,21)(19,23,25,27)(20,24,28,29)(26,30,31,32);(1,3)(2,4)(5,11)(6,9)(7,8)(10,12)(13,16)(14,15)(17,19)(18,23)(20,26)(21,27)(22,25)(24,30)(28,31)(29,32);(1,3)(2,8)(4,7)(5,11)(6,9)(10,15)(12,14)(13,16)(17,20)(18,24)(19,26)(21,29)(22,28)(23,30)(25,31)(27,32);(1,4,6,8)(2,9,7,3)(5,12,13,15)(10,16,14,11)(17,21,22,18)(19,27,25,23)(20,24,28,29)(26,30,31,32);(1,5,6,13)(2,10,7,14)(3,11,9,16)(4,12,8,15)(17,19)(18,23)(20,26)(21,27)(22,25)(24,30)(28,31)(29,32)Polycyclic presentation:
2^8|b^2=gh,e^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dg,f^a=fh,c^b=cg,e^d=eh73 conjugacy classes — view the full character table.
| maximal subgroup of | #6350739, #6350740, #6350763, … |
| maximal normal subgroup of | #6350739, #6350740, #6350763, … |
| maximal quotient of | #7626611, #7626641, #7626646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55926);