Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C256 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C83⋊C256 |
| derived, Sylow | C83 ⋊ C256 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C128 | D83 |
| commutator, hypocenter | C83 | C256 |
| Fitting, cosocle | C83×C128 | C2 |
| socle, prime radical | C2×C83 | C128 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C128 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21248 |
Polycyclic presentation:
2^8,83|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,i^a=i^825504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 56093);