Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #62283 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #525 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
890 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 5 generators on 40 points:
(1,2)(3,7)(4,6)(5,8)(9,10,14,18)(11,15,20,29)(12,22,24,39)(13,26,27,17)(16,31,33,25)(19,34,23,38)(21,37,36,30)(28,40,32,35);(1,3)(2,5)(4,8)(6,7)(9,11,14,20)(10,15,18,29)(12,23,24,19)(13,21,27,36)(16,32,33,28)(17,30,26,37)(22,38,39,34)(25,40,31,35);(9,12,13,25,14,24,27,31)(10,16,17,22,18,33,26,39)(11,19,21,35,20,23,36,40)(15,28,30,34,29,32,37,38);(3,8)(5,7)(12,24)(16,33)(19,23)(22,39)(25,31)(28,32)(34,38)(35,40);(2,6)(5,7)(11,20)(15,29)(19,23)(21,36)(28,32)(30,37)(34,38)(35,40)Polycyclic presentation:
2^8|a^2=h,b^2=h,c^2=g,g^2=h,b^a=bf,c^a=cg,e^a=ef,g^a=gh,c^b=ch,d^b=df,e^b=eh,d^c=dh46 conjugacy classes — view the full character table.
| maximal subgroup of | #486083, C2×#62291, #10577596, … |
| maximal normal subgroup of | #486083, C2×#62291, #10577596, … |
| maximal quotient of | #6386758, #6389151, #6389188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55279);