Finite Group DatabasebetaFinite Group Databasebeta| order | 35620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D65⋊D137 |
| unambiguous semidirect product | D685⋊D13 |
| unambiguous semidirect product | D1781⋊D5 |
| Fitting, socle, derived, Hall | C5×C13×C137 ⋊ C22 |
| Hall | C13×C137 ⋊ C2×D5 |
| Hall | C5×C137 ⋊ C2×D13 |
| Sylow | C137 ⋊ D5×D13 |
| Hall | C5×C13 ⋊ C2×D137 |
| Sylow | C13 ⋊ D5×D137 |
| Sylow | C5 ⋊ D13×D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C13×C137 | C22 |
| LCS | G ▷ C5×C13×C137 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8905 |
Polycyclic presentation:
2^2,5,13,137|d^a=d^12,e^a=e^136,c^b=c^4,d^b=d^122344 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35620, 44);