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 |
| prime radical | #3455 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
3093 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 48 points:
(1,2,6,8)(3,9,11,4)(5,13,14,7)(10,12,16,15)(17,18,22,23)(19,27,30,24)(20,25,31,35)(21,33,34,26)(28,39,41,36)(29,37,43,40)(32,45,44,38)(42,46,48,47);(1,3,6,11)(2,4,8,9)(5,10,14,16)(7,12,13,15)(18,23)(20,31)(24,27)(26,33)(28,41)(32,44)(37,40)(42,48);(1,4)(2,3)(5,12)(6,9)(7,10)(8,11)(13,16)(14,15)(17,18)(19,27)(20,25)(21,26)(22,23)(24,30)(28,39)(29,40)(31,35)(32,38)(33,34)(36,41)(37,43)(42,47)(44,45)(46,48);(1,5,6,14)(2,7,8,13)(3,10,11,16)(4,12,9,15)(17,19,22,30)(18,24,23,27)(20,28,31,41)(21,29,34,43)(25,36,35,39)(26,37,33,40)(32,42,44,48)(38,46,45,47);(17,20,22,31)(18,25,23,35)(19,28,30,41)(21,32,34,44)(24,36,27,39)(26,38,33,45)(29,42,43,48)(37,46,40,47);(17,21)(18,26)(19,29)(20,32)(22,34)(23,33)(24,37)(25,38)(27,40)(28,42)(30,43)(31,44)(35,45)(36,46)(39,47)(41,48)Polycyclic presentation:
2^8|a^2=g,b^2=gh,d^2=g,e^2=h,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 | #347009, #347019, #347023, … |
| maximal normal subgroup of | #347009, #347019, #347023, … |
| maximal quotient of | #7626375, #7626380, #7626382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55877);