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 | |
3239 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 32 points:
(1,2,6,10)(3,11,14,7)(4,15,13,8)(5,9,12,16)(18,22)(23,29)(24,30)(31,32);(1,3)(2,7)(4,12)(5,13)(6,14)(8,16)(9,15)(10,11);(1,4)(2,8)(3,5)(6,13)(7,9)(10,15)(11,16)(12,14)(17,18)(19,23)(20,24)(21,22)(25,31)(26,29)(27,32)(28,30);(1,4)(2,8)(3,12)(5,14)(6,13)(7,16)(9,11)(10,15)(17,19,21,26)(18,23,22,29)(20,27,28,25)(24,32,30,31);(1,5,6,12)(2,9,10,16)(3,13,14,4)(7,15,11,8)(17,20,21,28)(18,24,22,30)(19,25,26,27)(23,31,29,32);(1,2)(3,7)(4,8)(5,9)(6,10)(11,14)(12,16)(13,15)(17,18)(19,23)(20,24)(21,22)(25,31)(26,29)(27,32)(28,30)Polycyclic presentation:
2^8|a^2=g,d^2=gh,e^2=h,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 | #346792, #346816, #346840, … |
| maximal normal subgroup of | #346792, #346816, #346840, … |
| maximal quotient of | #7626615, #7626653, #7626709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55933);