Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C64×C251 ⋊ C2 |
| Sylow | C251 ⋊ M128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C2×D251 |
| commutator, socle | C2×C251 | C2×C32 |
| Fitting | C64×C251 | C2 |
| prime radical | C2×D251 | C32 |
| cosocle | C32×C251 | C22 |
| hypercenter | C64 | D251 |
| hypocenter | C251 | M128 |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C32 ◁ C64 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16064 |
Polycyclic presentation:
2^7,251|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^2508080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 2720);