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 | |
3663 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 24 points:
(2,4)(6,7)(9,10)(11,16)(12,14)(13,20)(15,19)(17,21)(18,22)(23,24);(1,2,5,4)(3,7,8,6)(9,11)(10,15)(12,16)(13,18)(14,19)(17,22)(20,23)(21,24);(1,3,5,8)(2,6,4,7)(9,10,14,12)(11,16,19,15)(13,17,21,20)(18,23,24,22);(1,4,5,2)(3,7,8,6)(9,12,14,10)(11,16,19,15)(13,20,21,17)(18,23,24,22);(9,11)(10,16)(12,15)(13,18)(14,19)(17,23)(20,22)(21,24);(9,13)(10,17)(11,18)(12,20)(14,21)(15,22)(16,23)(19,24)Polycyclic presentation:
2^8|b^2=gh,c^2=g,d^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 | #62905⋊C3 |
| maximal subgroup of | #346557, #346565, #346573, … |
| maximal normal subgroup of | #346557, #346565, #346573, … |
| maximal quotient of | #7626583, #7626667, #7626679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55893);