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 | |
3553 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 24 points:
(2,5)(6,8)(9,10)(11,17)(12,16)(13,14)(15,19)(18,23)(20,21)(22,24);(10,14)(15,17)(16,21)(22,23);(1,2)(3,6)(4,5)(7,8)(9,10)(11,15)(12,16)(13,14)(17,19)(18,22)(20,21)(23,24);(3,7)(6,8)(9,11,13,19)(10,15,14,17)(12,18,20,24)(16,22,21,23);(1,3)(2,6)(4,7)(5,8)(9,12,13,20)(10,16,14,21)(11,18,19,24)(15,22,17,23);(1,2)(3,6)(4,5)(7,8)Polycyclic presentation:
2^8|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 | #347066, #347090, #347114, … |
| maximal normal subgroup of | #347066, #347090, #347114, … |
| maximal quotient of | #7626574, #7626576, #7626670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55886);