Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62892 |
| 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 | |
3659 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 24 points:
(1,2,5,3)(4,7,8,6)(9,10,16,19)(11,20,14,17)(12,15,13,18)(21,22,23,24);(2,3)(6,7)(9,11,16,14)(10,17,19,20)(12,23,13,21)(15,22,18,24);(1,3,5,2)(4,7,8,6)(9,12,16,13)(10,18,19,15)(11,21,14,23)(17,22,20,24);(1,4,5,8)(2,6,3,7)(9,13,16,12)(10,15,19,18)(11,21,14,23)(17,22,20,24);(9,14,16,11)(10,17,19,20)(12,23,13,21)(15,24,18,22);(9,15)(10,12)(11,22)(13,19)(14,24)(16,18)(17,23)(20,21)Polycyclic presentation:
2^8|a^2=g,b^2=h,c^2=g,d^2=g,e^2=h,b^a=bg,c^a=ch,d^a=dg,f^a=fh,c^b=cg,e^d=eh73 conjugacy classes — view the full character table.
| maximal subgroup of | #347072, #347096, #347120, … |
| maximal normal subgroup of | #347072, #347096, #347120, … |
| maximal quotient of | #7626605, #7626634, #7626691, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55918);