Finite Group DatabasebetaFinite Group Databasebeta| order | 35972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C529 · Schur multiplier (H2) = C1 |
| direct product | #595×C529 |
| Fitting, Hall | C17×C529 ⋊ C4 |
| derived, Sylow | C17 ⋊ C4×C529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C529 | #595 |
| commutator, hypocenter | C17 | C4×C529 |
| Frattini | C23 | C23×#595 |
| Fitting | C17×C529 | C4 |
| socle | C17×C23 | C4×C23 |
| prime radical, cosocle | C23×D17 | C2×C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C529 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8993 |
4232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35972, 6);