Finite Group DatabasebetaFinite Group Databasebeta| order | 33524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C29×C289 ⋊ C4 |
| Sylow | C289 ⋊ Dic29 |
| Sylow | C29 ⋊ #11923876 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C29×C289 | C4 |
| Frattini | C17 | #14520309 |
| socle | C17×C29 | #595 |
| prime radical, cosocle | C29×D289 | C2 |
| LCS | G ▷ C29×C289 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8381 |
Polycyclic presentation:
2^2,17,29,17|a^2=b,c^17=e^11,c^a=c^13e,d^a=d^28,e^a=e^13,c^b=c^16e^6,e^b=e^162120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33524, 10);