Finite Group DatabasebetaFinite Group Databasebeta| order | 35972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C529⋊#595 |
| Fitting, derived, Hall | C17×C529 ⋊ C4 |
| Sylow | C529 ⋊ #595 |
| Sylow | C17 ⋊ Dic529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C17×C529 | C4 |
| Frattini | C23 | C23⋊#595 |
| socle | C17×C23 | Dic23 |
| prime radical | C23×D17 | D23 |
| cosocle | D17×C529 | C2 |
| LCS | G ▷ C17×C529 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8993 |
Polycyclic presentation:
2^2,17,23^2|a^2=b,d^23=e^22,c^a=c^13,d^a=d^22e,e^a=e^22,c^b=c^162648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35972, 7);