Finite Group DatabasebetaFinite Group Databasebeta| order | 32708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D221⋊D37 |
| unambiguous semidirect product | D481⋊D17 |
| unambiguous semidirect product | D629⋊D13 |
| Fitting, socle, derived, Hall | C13×C17×C37 ⋊ C22 |
| Hall | C17×C37 ⋊ C2×D13 |
| Hall | C13×C37 ⋊ C2×D17 |
| Hall | C13×C17 ⋊ C2×D37 |
| Sylow | C37 ⋊ D13×D17 |
| Sylow | C17 ⋊ D13×D37 |
| Sylow | C13 ⋊ D17×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C17×C37 | C22 |
| LCS | G ▷ C13×C17×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8177 |
Polycyclic presentation:
2^2,13,17,37|d^a=d^16,e^a=e^36,c^b=c^12,d^b=d^162096 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32708, 44);