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 | |
3546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 24 points:
(2,5)(6,8)(9,10,14,15)(11,12,17,20)(13,16,21,22)(18,19,23,24);(10,15)(11,17)(16,22)(18,23);(1,2)(3,6)(4,5)(7,8)(9,11)(10,12)(13,18)(14,17)(15,20)(16,19)(21,23)(22,24);(3,7)(6,8)(9,12)(10,11)(13,19)(14,20)(15,17)(16,18)(21,24)(22,23);(1,3,4,7)(2,6,5,8);(1,2)(3,6)(4,5)(7,8)(9,13,14,21)(10,16,15,22)(11,18,17,23)(12,19,20,24)Polycyclic presentation:
2^8|a^2=g,e^2=h,f^2=g,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 | #6350879, #6350880, #6350903, … |
| maximal normal subgroup of | #6350879, #6350880, #6350903, … |
| maximal quotient of | #7626599, #7626655, #7626661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55909);