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 | |
3452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 40 points:
(1,2)(3,7)(4,5)(6,8)(10,15)(16,26)(17,27)(18,28)(29,37)(30,38)(31,32)(39,40);(2,5)(6,7)(10,15)(11,19)(17,27)(18,28)(20,33)(21,34)(31,32)(35,36);(1,2)(3,6)(4,5)(7,8)(9,10)(11,16)(12,17)(13,18)(14,15)(19,26)(20,29)(21,30)(22,31)(23,27)(24,32)(25,28)(33,37)(34,38)(35,39)(36,40);(1,3)(2,6)(4,8)(5,7)(9,11)(10,16)(12,20)(13,21)(14,19)(15,26)(17,29)(18,30)(22,35)(23,33)(24,36)(25,34)(27,37)(28,38)(31,39)(32,40);(9,12,14,23)(10,17,15,27)(11,20,19,33)(13,24,25,22)(16,29,26,37)(18,32,28,31)(21,36,34,35)(30,40,38,39);(9,13,14,25)(10,18,15,28)(11,21,19,34)(12,22,23,24)(16,30,26,38)(17,31,27,32)(20,35,33,36)(29,39,37,40)Polycyclic presentation:
2^8|e^2=h,f^2=h,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 | #63044⋊C3 |
| maximal subgroup of | #493650, #511828, #7622890, … |
| maximal normal subgroup of | #493650, #511828, #7622890, … |
| maximal quotient of | #7627403, #7627427, #7627432, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 56032);