Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C22 | C26 |
| prime radical | #3449 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
3433 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 40 points:
(2,5)(6,8)(10,11)(14,27)(16,19)(17,20)(23,36)(25,37)(28,31)(34,40);(1,2)(3,6)(4,5)(7,8)(9,10,15,11)(12,16,24,19)(13,20,26,17)(14,18,27,21)(22,31,35,28)(23,29,36,32)(25,33,37,30)(34,39,40,38);(1,3,4,7)(2,6,5,8)(9,11,15,10)(12,16,24,19)(13,20,26,17)(14,21,27,18)(22,28,35,31)(23,29,36,32)(25,33,37,30)(34,38,40,39);(9,12)(10,16)(11,19)(13,22)(14,23)(15,24)(17,28)(18,29)(20,31)(21,32)(25,34)(26,35)(27,36)(30,38)(33,39)(37,40);(9,13,15,26)(10,17,11,20)(12,22,24,35)(14,25,27,37)(16,28,19,31)(18,30,21,33)(23,34,36,40)(29,38,32,39);(9,14)(10,18)(11,21)(12,23)(13,25)(15,27)(16,29)(17,30)(19,32)(20,33)(22,34)(24,36)(26,37)(28,38)(31,39)(35,40)Polycyclic presentation:
2^8|b^2=h,c^2=g,e^2=h,b^a=bg,c^a=ch,f^a=fh,e^b=eh,d^c=dh82 conjugacy classes — view the full character table.
| maximal subgroup of | #346962, #346978, #346979, … |
| maximal normal subgroup of | #346962, #346978, #346979, … |
| maximal quotient of | #7625698, #7625702, #7625722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55848);