Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63041 |
| 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)(4,10)(5,9)(6,8)(7,15)(12,21)(13,19)(14,25)(16,23)(17,24)(18,22)(20,28)(26,31)(27,30)(29,32);(1,3)(2,7)(4,14)(5,15)(6,13)(8,21)(9,11)(10,20)(12,18)(16,27)(17,28)(19,22)(23,31)(24,25)(26,29)(30,32);(2,8)(3,12)(7,11)(9,22)(10,23)(13,15)(14,26)(19,21)(20,25)(24,32)(27,28)(30,31);(2,9)(3,13)(7,19)(8,22)(10,24)(11,21)(12,15)(14,27)(20,30)(23,32)(25,31)(26,28);(1,4,5,17)(2,10,9,24)(3,14,15,28)(6,16,18,29)(7,20,11,25)(8,23,22,32)(12,26,13,27)(19,30,21,31);(4,16)(10,23)(14,27)(17,29)(20,31)(24,32)(25,30)(26,28)Polycyclic presentation:
2^8|e^2=g,b^a=bg,c^a=ch,d^a=dg,c^b=cgh,d^b=dh,f^e=fh70 conjugacy classes — view the full character table.
| maximal subgroup of | #511857, C2×#63042, #10586381, … |
| maximal normal subgroup of | #511857, C2×#63042, #10586381, … |
| maximal quotient of | #7627401, #7627402, #7627425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 56030);