Finite Group DatabasebetaFinite Group Databasebeta| order | 37060 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D85⋊D109 |
| unambiguous semidirect product | D545⋊D17 |
| unambiguous semidirect product | D1853⋊D5 |
| Fitting, socle, derived, Hall | C5×C17×C109 ⋊ C22 |
| Hall | C17×C109 ⋊ C2×D5 |
| Hall | C5×C109 ⋊ C2×D17 |
| Sylow | C109 ⋊ D5×D17 |
| Hall | C5×C17 ⋊ C2×D109 |
| Sylow | C17 ⋊ D5×D109 |
| Sylow | C5 ⋊ D17×D109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C17×C109 | C22 |
| LCS | G ▷ C5×C17×C109 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9265 |
Polycyclic presentation:
2^2,5,17,109|d^a=d^16,e^a=e^108,c^b=c^4,d^b=d^162416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37060, 44);