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 | |
3229 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 32 points:
(3,10)(7,14)(11,15)(12,16)(18,20)(23,25)(24,28)(30,31);(1,2,6,9)(3,7,10,14)(4,5,8,13)(11,12,15,16)(17,18,22,20)(19,25,27,23)(21,24,29,28)(26,31,32,30);(1,3)(2,7)(4,11)(5,12)(6,10)(8,15)(9,14)(13,16)(17,19,22,27)(18,23,20,25)(21,26,29,32)(24,30,28,31);(1,4)(2,5)(3,11)(6,8)(7,12)(9,13)(10,15)(14,16)(17,20,22,18)(19,25,27,23)(21,28,29,24)(26,31,32,30);(1,5)(2,8)(3,12)(4,9)(6,13)(7,15)(10,16)(11,14)(17,21,22,29)(18,24,20,28)(19,26,27,32)(23,30,25,31);(1,3)(2,7)(4,11)(5,12)(6,10)(8,15)(9,14)(13,16)Polycyclic presentation:
2^8|b^2=gh,c^2=g,d^2=g,e^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 | #347069, #347093, #347117, … |
| maximal normal subgroup of | #347069, #347093, #347117, … |
| maximal quotient of | #7626589, #7626591, #7626671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55899);