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 | |
3360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 6 generators on 32 points:
(1,2)(3,11)(4,10)(5,9)(6,8)(7,12)(13,25)(14,18)(15,22)(16,21)(17,23)(19,26)(20,27)(24,29)(28,30)(31,32);(1,3,6,14)(2,7,8,20)(4,13,15,28)(5,12,16,27)(9,11,21,18)(10,19,22,31)(17,26,29,32)(23,25,24,30);(2,8)(3,12)(7,18)(9,21)(10,22)(11,20)(13,26)(14,27)(19,30)(23,24)(25,31)(28,32);(2,9)(4,15)(7,11)(8,21)(10,24)(13,28)(17,29)(18,20)(19,30)(22,23)(25,31)(26,32);(1,4,16,29)(2,10,21,24)(3,13,27,32)(5,17,6,15)(7,19,18,30)(8,22,9,23)(11,25,20,31)(12,26,14,28);(2,8)(7,20)(9,21)(10,22)(11,18)(19,31)(23,24)(25,30)Polycyclic presentation:
2^8|b^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 | #6352608, #6352638, #6352668, … |
| maximal normal subgroup of | #6352608, #6352638, #6352668, … |
| maximal quotient of | #7626607, #7626642, #7626692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55921);