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 | |
3295 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 32 points:
(2,7)(3,8)(5,13)(12,16)(19,26)(23,30)(27,31)(28,32);(1,2)(3,10)(4,8)(5,9)(6,7)(11,16)(12,15)(13,14)(17,18,22,25)(19,23,26,30)(20,21,24,29)(27,28,31,32);(1,3,6,8)(2,4,7,10)(5,11,13,15)(9,12,14,16)(17,19)(18,23)(20,27)(21,28)(22,26)(24,31)(25,30)(29,32);(1,2)(3,4)(5,9)(6,7)(8,10)(11,12)(13,14)(15,16)(17,20)(18,21)(19,27)(22,24)(23,28)(25,29)(26,31)(30,32);(1,4)(2,8)(3,7)(5,12)(6,10)(9,15)(11,14)(13,16)(17,21)(18,24)(19,28)(20,25)(22,29)(23,31)(26,32)(27,30);(1,5)(2,9)(3,11)(4,12)(6,13)(7,14)(8,15)(10,16)(17,19)(18,23)(20,27)(21,28)(22,26)(24,31)(25,30)(29,32)Polycyclic presentation:
2^8|b^2=gh,c^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 | #346556, #346564, #346572, … |
| maximal normal subgroup of | #346556, #346564, #346572, … |
| maximal quotient of | #7626580, #7626583, #7626664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55890);