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 | |
3339 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 32 points:
(1,2)(3,10)(4,7)(5,8)(6,12)(9,14)(11,15)(13,16)(19,25)(23,26)(27,31)(30,32);(1,3,7,5)(2,8,4,10)(6,11,14,13)(9,15,12,16)(17,18,22,20)(19,23,25,26)(21,24,29,28)(27,30,31,32);(1,2,7,4)(3,10,5,8)(6,9,14,12)(11,16,13,15)(17,19)(18,23)(20,26)(21,27)(22,25)(24,30)(28,32)(29,31);(1,4,7,2)(3,10,5,8)(6,12,14,9)(11,16,13,15)(17,20,22,18)(19,26,25,23)(21,24,29,28)(27,30,31,32);(1,5,7,3)(2,8,4,10)(6,13,14,11)(9,15,12,16)(17,21,22,29)(18,24,20,28)(19,27,25,31)(23,30,26,32);(1,6,7,14)(2,9,4,12)(3,11,5,13)(8,15,10,16)(17,19)(18,23)(20,26)(21,27)(22,25)(24,30)(28,32)(29,31)Polycyclic presentation:
2^8|b^2=h,c^2=g,d^2=h,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 | #10580714, #10580715, #10580722, … |
| maximal normal subgroup of | #10580714, #10580715, #10580722, … |
| maximal quotient of | #7626632, #7626639, #7626645, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55958);