Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C251 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D251 |
| commutator, socle | C2×C251 | C24×C4 |
| Fitting, prime radical | #585×C251 | C2 |
| cosocle | C4×C251 | C25 |
| hypercenter | #585 | D251 |
| hypocenter | C251 | #3573 |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C4 ◁ #585 | |
1424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
Polycyclic presentation:
2^7,251|a^2=f,f^2=g,h^a=h^250,e^b=eg,d^c=dg4318 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 19222);