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 | |
3650 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)(9,10,14,17)(11,18,12,15)(13,21,22,16)(19,23,20,24);(9,11,14,12)(10,15,17,18)(13,19,22,20)(16,23,21,24);(1,2)(3,6)(4,5)(7,8)(9,10)(11,18)(12,15)(13,16)(14,17)(19,24)(20,23)(21,22);(3,7)(6,8)(9,10)(11,15)(12,18)(13,16)(14,17)(19,23)(20,24)(21,22);(1,3,4,7)(2,6,5,8)(9,12,14,11)(10,15,17,18)(13,20,22,19)(16,23,21,24);(1,2)(3,6)(4,5)(7,8)(9,13,14,22)(10,16,17,21)(11,19,12,20)(15,23,18,24)Polycyclic presentation:
2^8|a^2=g,b^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.
| Fitting subgroup of | #62923⋊C3 |
| maximal subgroup of | #6350829, #6350830, #6350853, … |
| maximal normal subgroup of | #6350829, #6350830, #6350853, … |
| maximal quotient of | #7626600, #7626656, #7626662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55911);