Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| 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 | |
3423 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 40 points:
(2,5)(6,8)(10,15)(13,25)(16,19)(17,26)(21,35)(24,36)(28,31)(34,40);(1,2)(3,6)(4,5)(7,8)(12,23)(17,26)(20,33)(24,36)(28,31)(30,37)(34,40)(38,39);(9,10,14,15)(11,19,22,16)(12,17,23,26)(13,18,25,27)(20,31,33,28)(21,32,35,29)(24,30,36,37)(34,39,40,38);(9,11,14,22)(10,16,15,19)(12,20,23,33)(13,21,25,35)(17,28,26,31)(18,29,27,32)(24,34,36,40)(30,38,37,39);(1,3,4,7)(2,6,5,8)(9,12)(10,17)(11,20)(13,24)(14,23)(15,26)(16,28)(18,30)(19,31)(21,34)(22,33)(25,36)(27,37)(29,38)(32,39)(35,40);(9,13)(10,18)(11,21)(12,24)(14,25)(15,27)(16,29)(17,30)(19,32)(20,34)(22,35)(23,36)(26,37)(28,38)(31,39)(33,40)Polycyclic presentation:
2^8|c^2=h,d^2=h,e^2=g,b^a=bg,c^a=ch,f^a=fh,e^b=eh,d^c=dh82 conjugacy classes — view the full character table.
| Fitting subgroup of | #62850⋊C3 |
| maximal subgroup of | #346958, #346974, #346981, … |
| maximal normal subgroup of | #346958, #346974, #346981, … |
| maximal quotient of | #7625689, #7625691, #7625712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55838);