Finite Group DatabasebetaFinite Group Databasebeta| order | 32272 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C2017 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2017 | C16 |
| prime radical | D2017 | C8 |
| cosocle | #30633241 | C2 |
| LCS | G ▷ C2017 | |
| UCS | C1 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2017 |
Polycyclic presentation:
2^4,2017|a^2=b,b^2=c,c^2=d,e^a=e^1909,e^b=e^1579,e^c=e^229,e^d=e^2016142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32272, 54);