Finite Group DatabasebetaFinite Group Databasebeta| order | 35972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C23⋊#595 |
| unambiguous semidirect product | C23⋊(C23×#595) |
| Fitting, socle, Hall | C17×C232 ⋊ C4 |
| derived | C17×C23 ⋊ C4×C23 |
| Sylow | C232 ⋊ #595 |
| Sylow | C17 ⋊ C23×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C23⋊#595 |
| commutator, hypocenter | C17×C23 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C17×C232 | C4 |
| prime radical | C232×D17 | C2 |
| cosocle | C23×D17 | C2×C23 |
| LCS | G ▷ C17×C23 | |
| UCS | C1 ◁ C23 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 782 |
2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35972, 23);