Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| 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 | |
3691 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 6 generators on 24 points:
(2,5)(6,8)(9,10)(11,17)(12,18)(13,16)(14,15)(19,23)(20,24)(21,22);(3,7)(6,8)(10,15)(11,18)(13,21)(20,23);(1,2)(3,6)(4,5)(7,8)(9,11)(10,12)(13,19)(14,18)(15,17)(16,20)(21,24)(22,23);(9,12)(10,11)(13,20)(14,17)(15,18)(16,19)(21,23)(22,24);(1,3)(2,6)(4,7)(5,8)(9,13,14,21)(10,16,15,22)(11,19,18,24)(12,20,17,23);(1,2)(3,6)(4,5)(7,8)(9,12)(10,11)(13,20)(14,17)(15,18)(16,19)(21,23)(22,24)Polycyclic presentation:
2^8|e^2=g,b^a=bg,c^a=ch,d^a=dg,f^a=fh,c^b=cg,e^b=eh76 conjugacy classes — view the full character table.
| maximal subgroup of | #185267, #185273, #185279, … |
| maximal normal subgroup of | #185267, #185273, #185279, … |
| maximal quotient of | #7626206, #7626209, #7626243, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55808);