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 | |
3459 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)(3,7)(4,5)(6,8)(10,15)(11,19)(13,26)(17,23)(21,31)(24,37)(29,34)(38,40);(2,5)(6,7)(9,10,14,15)(11,16,19,20)(12,23,25,17)(13,18,26,27)(21,33,31,28)(22,29,32,34)(24,36,37,30)(35,40,39,38);(1,2)(3,6)(4,5)(7,8)(9,10)(11,20)(12,17)(13,18)(14,15)(16,19)(21,33)(22,34)(23,25)(24,30)(26,27)(28,31)(29,32)(35,40)(36,37)(38,39);(1,3)(2,6)(4,8)(5,7)(9,11)(10,16)(12,21)(13,22)(14,19)(15,20)(17,28)(18,29)(23,33)(24,35)(25,31)(26,32)(27,34)(30,38)(36,40)(37,39);(9,12,14,25)(10,17,15,23)(11,21,19,31)(13,24,26,37)(16,28,20,33)(18,30,27,36)(22,35,32,39)(29,38,34,40);(9,13)(10,18)(11,22)(12,24)(14,26)(15,27)(16,29)(17,30)(19,32)(20,34)(21,35)(23,36)(25,37)(28,38)(31,39)(33,40)Polycyclic presentation:
2^8|b^2=h,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 | #347158, #347168, #347179, … |
| maximal normal subgroup of | #347158, #347168, #347179, … |
| maximal quotient of | #7626373, #7626378, #7626415, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55874);