Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #15257 |
| automorphism | Aut(G) order 65536 |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, prime radical, cosocle | C24 | C24 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
517 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 256 |
A minimal faithful permutation representation — 4 generators on 32 points:
(3,7)(6,8)(10,13)(11,15)(17,18,21,19)(20,23,24,22)(25,26)(27,28)(29,31)(30,32);(2,5)(6,8)(10,13)(14,16)(18,19)(20,24)(25,27,29,32)(26,28,31,30);(1,2,4,5)(3,6,7,8)(9,10)(11,14)(12,13)(15,16)(17,19,21,18)(20,23,24,22)(25,27)(26,30)(28,31)(29,32);(1,3)(2,6)(4,7)(5,8)(9,11,12,15)(10,14,13,16)(17,20)(18,22)(19,23)(21,24)(25,28,29,30)(26,27,31,32)Polycyclic presentation:
2^8|a^2=e,b^2=gh,c^2=fg,d^2=f,b^a=be,c^a=cf,d^a=dh,c^b=cg,d^b=de58 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#16213, #610385, #610390, … |
| maximal normal subgroup of | C2×#16213, #610385, #610390, … |
| maximal quotient of | #154893, #154896, #154898, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 9201);