Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| 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 | |
3455 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 40 points:
(1,2)(3,4)(5,6)(7,8)(9,10)(11,16)(12,22)(13,17)(14,28)(15,19)(18,29)(20,30)(21,24)(23,25)(26,38)(27,33)(31,35)(32,39)(34,36)(37,40);(2,6)(3,7)(9,11,15,22)(10,16,19,12)(13,25,27,20)(14,21,29,35)(17,23,33,30)(18,31,28,24)(26,37,39,34)(32,36,38,40);(1,3,5,7)(2,4,6,8)(9,12)(10,11)(13,23)(14,24)(15,16)(17,20)(18,21)(19,22)(25,33)(26,36)(27,30)(28,35)(29,31)(32,34)(37,38)(39,40);(1,4)(2,7)(3,6)(5,8)(9,10)(11,16)(12,22)(13,17)(14,18)(15,19)(20,30)(21,31)(23,25)(24,35)(26,32)(27,33)(28,29)(34,40)(36,37)(38,39);(9,13,15,27)(10,17,19,33)(11,20,22,25)(12,23,16,30)(14,26,29,39)(18,32,28,38)(21,34,35,37)(24,36,31,40);(9,14)(10,18)(11,21)(12,24)(13,26)(15,29)(16,31)(17,32)(19,28)(20,34)(22,35)(23,36)(25,37)(27,39)(30,40)(33,38)Polycyclic presentation:
2^8|b^2=h,c^2=g,e^2=h,b^a=bg,c^a=ch,d^a=dg,f^a=fh,c^b=cg,e^b=eh,d^c=dh70 conjugacy classes — view the full character table.
| maximal subgroup of | #346486, #346496, #346508, … |
| maximal normal subgroup of | #346486, #346496, #346508, … |
| maximal quotient of | #7626374, #7626381, #7626415, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55875);