Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
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 | |
5611 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 20 points:
(2,4)(5,6)(7,11)(8,15)(9,10)(12,16)(13,17)(14,20)(18,19);(1,2,3,4)(7,13)(11,17)(14,19)(18,20);(6,10)(11,17)(12,15)(18,20);(5,6)(7,11)(8,12)(9,10)(13,17)(14,18)(15,16)(19,20);(5,7,9,13)(6,11,10,17)(8,14,16,19)(12,18,15,20);(5,8)(6,12)(7,14)(9,16)(10,15)(11,18)(13,19)(17,20)Polycyclic presentation:
2^8|b^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.
| Fitting subgroup of | #62853⋊C3 |
| maximal subgroup of | #346960, #346976, #346982, … |
| maximal normal subgroup of | #346960, #346976, #346982, … |
| maximal quotient of | #7625693, #7625700, #7625716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55841);