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 | |
3395 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 6 generators on 32 points:
(1,2,6,10)(3,12,14,8)(4,15,18,25)(5,9,20,24)(7,11,21,16)(13,26,28,22)(17,27,30,32)(19,23,31,29);(1,3,6,14)(2,8,10,12)(4,16,18,11)(5,13,20,28)(7,15,21,25)(9,22,24,26)(17,29,30,23)(19,27,31,32);(1,4)(2,3)(5,17)(6,18)(7,8)(9,13)(10,14)(11,15)(12,21)(16,25)(19,22)(20,30)(23,27)(24,28)(26,31)(29,32);(1,2)(3,4)(5,9)(6,10)(7,11)(8,15)(12,25)(13,17)(14,18)(16,21)(19,23)(20,24)(22,27)(26,32)(28,30)(29,31);(1,5,6,20)(2,9,10,24)(3,13,14,28)(4,17,18,30)(7,19,21,31)(8,22,12,26)(11,23,16,29)(15,27,25,32);(5,19)(9,23)(13,27)(17,22)(20,31)(24,29)(26,30)(28,32)Polycyclic presentation:
2^8|a^2=g,b^2=g,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.
| Fitting subgroup of | #63046⋊C3 |
| maximal subgroup of | #511856, #511859, #6351945, … |
| maximal normal subgroup of | #511856, #511859, #6351945, … |
| maximal quotient of | #7627404, #7627405, #7627425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 56034);