Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62892 |
| 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 | |
3662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 24 points:
(1,2)(3,7)(4,5)(6,8)(9,10)(11,18)(12,22)(13,16)(14,23)(15,17)(19,24)(20,21);(2,5)(6,7)(9,11,15,13)(10,16,17,18)(12,20,23,19)(14,21,22,24);(1,2)(3,6)(4,5)(7,8)(9,12)(10,14)(11,19)(13,20)(15,23)(16,24)(17,22)(18,21);(1,3,4,8)(2,6,5,7)(9,12)(10,14)(11,20)(13,19)(15,23)(16,21)(17,22)(18,24);(9,13,15,11)(10,16,17,18)(12,20,23,19)(14,24,22,21);(9,14)(10,12)(11,21)(13,24)(15,22)(16,20)(17,23)(18,19)Polycyclic presentation:
2^8|b^2=h,d^2=gh,e^2=h,b^a=bg,c^a=ch,d^a=dg,f^a=fh,c^b=cg,e^d=eh73 conjugacy classes — view the full character table.
| maximal subgroup of | #6352957, #6352987, #6353017, … |
| maximal normal subgroup of | #6352957, #6352987, #6353017, … |
| maximal quotient of | #7626624, #7626633, #7626709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55945);