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 | |
3305 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 32 points:
(1,2)(3,7)(4,11)(5,6)(8,12)(9,13)(10,16)(14,15)(17,18,23,25)(19,22,20,24)(21,26,30,32)(27,29,28,31);(3,9)(7,13)(10,15)(14,16)(17,19,23,20)(18,24,25,22)(21,28,30,27)(26,29,32,31);(2,6)(7,13)(8,11)(14,16)(18,25)(19,20)(26,32)(27,28);(1,2)(3,7)(4,8)(5,6)(9,13)(10,14)(11,12)(15,16)(17,20,23,19)(18,22,25,24)(21,28,30,27)(26,29,32,31);(1,3,5,9)(2,7,6,13)(4,10,12,15)(8,14,11,16)(17,21,23,30)(18,26,25,32)(19,27,20,28)(22,29,24,31);(1,4)(2,8)(3,10)(5,12)(6,11)(7,14)(9,15)(13,16)(17,22)(18,19)(20,25)(21,29)(23,24)(26,27)(28,32)(30,31)Polycyclic presentation:
2^8|a^2=g,b^2=g,d^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 | #347003, #347011, #347015, … |
| maximal normal subgroup of | #347003, #347011, #347015, … |
| maximal quotient of | #7626370, #7626380, #7626382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55869);