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 | |
3657 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)(11,18)(12,15)(13,16)(14,20)(17,22)(19,23)(21,24);(9,11,15,13)(10,16,12,18)(14,19,22,21)(17,23,20,24);(1,2)(3,6)(4,5)(7,8)(9,10,15,12)(11,18,13,16)(14,17,22,20)(19,24,21,23);(3,7)(6,8)(9,12,15,10)(11,18,13,16)(14,20,22,17)(19,24,21,23);(1,3)(2,6)(4,7)(5,8)(9,13,15,11)(10,16,12,18)(14,21,22,19)(17,23,20,24);(1,2)(3,6)(4,5)(7,8)(9,14)(10,17)(11,19)(12,20)(13,21)(15,22)(16,23)(18,24)Polycyclic presentation:
2^8|b^2=g,c^2=g,d^2=g,e^2=g,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 | #62899⋊C3 |
| maximal subgroup of | #347067, #347091, #347115, … |
| maximal normal subgroup of | #347067, #347091, #347115, … |
| maximal quotient of | #7626575, #7626577, #7626671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55887);