Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| 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 | |
3379 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 6 generators on 32 points:
(1,2)(3,11)(4,9)(5,7)(6,10)(8,13)(12,21)(14,25)(15,24)(16,19)(17,20)(18,26)(22,28)(23,30)(27,32)(29,31);(2,7)(3,12)(4,15)(9,23)(10,20)(13,26)(14,29)(16,30)(19,24)(22,25)(27,28)(31,32);(1,3)(2,8)(4,14)(5,12)(6,13)(7,18)(9,22)(10,11)(15,28)(16,27)(17,26)(19,31)(20,21)(23,32)(24,25)(29,30);(2,7)(3,13)(8,21)(9,19)(10,20)(11,18)(12,26)(14,28)(22,32)(23,24)(25,31)(27,29);(1,4,5,16)(2,9,7,19)(3,14,12,27)(6,15,17,30)(8,22,18,31)(10,24,20,23)(11,25,21,32)(13,28,26,29);(2,10)(7,20)(8,11)(9,24)(18,21)(19,23)(22,25)(31,32)Polycyclic presentation:
2^8|e^2=g,b^a=bg,c^a=ch,d^a=dg,f^a=fh,c^b=cg,e^b=eh,d^c=dh70 conjugacy classes — view the full character table.
| maximal subgroup of | #6352350, #6352351, #6352382, … |
| maximal normal subgroup of | #6352350, #6352351, #6352382, … |
| maximal quotient of | #7626351, #7626353, #7626360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55855);