Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
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 | |
5885 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 6 generators on 20 points:
(2,4)(5,6)(7,11)(8,15)(9,10)(12,16)(13,17)(14,20)(18,19);(1,2)(3,4)(7,13)(11,17)(14,19)(18,20);(6,10)(11,17)(12,15)(18,20);(5,6)(7,11)(8,12)(9,10)(13,17)(14,18)(15,16)(19,20);(5,7)(6,11)(8,14)(9,13)(10,17)(12,18)(15,20)(16,19);(5,8)(6,12)(7,14)(9,16)(10,15)(11,18)(13,19)(17,20)Polycyclic presentation:
2^8|b^a=bg,c^a=ch,f^a=fh,e^b=eh,d^c=dh82 conjugacy classes — view the full character table.
| maximal subgroup of | #346950, #346964, #346988, … |
| maximal normal subgroup of | #346950, #346964, #346988, … |
| maximal quotient of | #7625680, #7625681, #7625704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55830);