Finite Group DatabasebetaFinite Group Databasebeta| order | 32708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D17×D37 |
| unambiguous semidirect product | (D17×C37)⋊(C2×C13) |
| unambiguous semidirect product | (C17×D37)⋊(C2×C13) |
| unambiguous semidirect product | D629⋊(C2×C13) |
| Fitting, socle, Hall | C13×C17×C37 ⋊ C22 |
| derived, Hall | C17×C37 ⋊ C22×C13 |
| Hall | C13×C37 ⋊ C2×D17 |
| Hall | C13×C17 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×C13×D17 |
| Sylow | C17 ⋊ C2×C13×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D17×D37 |
| commutator, cosocle, hypocenter | C17×C37 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C37 | C22 |
| LCS | G ▷ C17×C37 | |
| UCS | C1 ◁ C13 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8177 |
2600 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32708, 16);