Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| 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 | |
3621 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 6 generators on 24 points:
(2,5)(6,8)(9,10)(11,17)(12,14)(13,20)(15,19)(16,21)(18,22)(23,24);(3,7)(6,8)(9,11,14,19)(10,15,12,17)(13,18,21,24)(16,22,20,23);(1,2)(3,6)(4,5)(7,8)(9,12,14,10)(11,15,19,17)(13,20,21,16)(18,22,24,23);(9,13)(10,16)(11,18)(12,20)(14,21)(15,22)(17,23)(19,24);(1,3)(2,6)(4,7)(5,8)(9,11)(10,17)(12,15)(13,18)(14,19)(16,23)(20,22)(21,24);(1,2)(3,6)(4,5)(7,8)(9,13)(10,16)(11,18)(12,20)(14,21)(15,22)(17,23)(19,24)Polycyclic presentation:
2^8|b^2=g,c^2=g,b^a=bg,c^a=ch,d^a=dg,f^a=fh,c^b=cg,e^b=eh76 conjugacy classes — view the full character table.
| maximal subgroup of | #185271, #185277, #185283, … |
| maximal normal subgroup of | #185271, #185277, #185283, … |
| maximal quotient of | #7626204, #7626205, #7626244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55807);