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 | |
3293 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)(3,12)(4,10)(5,16)(6,14)(7,11)(8,15)(9,13)(18,22)(23,29)(24,30)(31,32);(1,3)(2,6)(4,5)(7,14)(8,16)(9,10)(11,12)(13,15);(1,4)(2,8)(3,13)(5,14)(6,9)(7,15)(10,11)(12,16)(17,18)(19,23)(20,24)(21,22)(25,31)(26,29)(27,32)(28,30);(1,5,7,13)(2,9,11,16)(3,4,14,15)(6,10,12,8)(17,19,21,26)(18,23,22,29)(20,27,28,25)(24,32,30,31);(1,4)(2,10)(3,5)(6,9)(7,15)(8,11)(12,16)(13,14)(17,20,21,28)(18,24,22,30)(19,25,26,27)(23,31,29,32);(1,6)(2,3)(4,9)(5,10)(7,12)(8,13)(11,14)(15,16)(17,18)(19,23)(20,24)(21,22)(25,31)(26,29)(27,32)(28,30)Polycyclic presentation:
2^8|d^2=h,e^2=gh,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 | #346804, #346828, #346852, … |
| maximal normal subgroup of | #346804, #346828, #346852, … |
| maximal quotient of | #7626617, #7626657, #7626712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55936);