Finite Group DatabasebetaFinite Group Databasebeta| order | 20512 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C641 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C641 | C32 |
| prime radical | D641 | C16 |
| cosocle | #23779671 | C2 |
| LCS | G ▷ C641 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 641 |
Polycyclic presentation:
2^5,641|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^160,f^b=f^601,f^c=f^318,f^d=f^487,f^e=f^64052 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20512, 247);