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 | |
3541 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 24 points:
(2,5)(6,8)(9,10)(11,19)(12,13)(14,16)(15,18)(17,24)(20,21)(22,23);(9,11,15,14)(10,16,18,19)(12,22,17,20)(13,21,24,23);(1,2)(3,6)(4,5)(7,8)(9,12,15,17)(10,13,18,24)(11,20,14,22)(16,23,19,21);(3,7)(6,8)(9,13)(10,17)(11,21)(12,18)(14,23)(15,24)(16,20)(19,22);(1,3,4,7)(2,6,5,8)(9,14,15,11)(10,16,18,19)(12,22,17,20)(13,23,24,21);(1,2)(3,6)(4,5)(7,8)Polycyclic presentation:
2^8|b^2=g,c^2=g,e^2=gh,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.
| Fitting subgroup of | #62919⋊C3 |
| maximal subgroup of | #347079, #347103, #347127, … |
| maximal normal subgroup of | #347079, #347103, #347127, … |
| maximal quotient of | #7626598, #7626658, #7626693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55907);