Finite Group DatabasebetaFinite Group Databasebeta| order | 10730 |
| automorphism | Aut(G) order 21631680 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5365 |
| unambiguous semidirect product | C5⋊D1073 |
| unambiguous semidirect product | C29⋊D185 |
| unambiguous semidirect product | C37⋊D145 |
| Fitting, socle, derived, Hall | C5×C29×C37 ⋊ C2 |
| Hall | C29×C37 ⋊ D5 |
| Hall | C5×C37 ⋊ D29 |
| Hall | C5×C29 ⋊ D37 |
| Sylow | C37 ⋊ D145 |
| Sylow | C29 ⋊ D185 |
| Sylow | C5 ⋊ D1073 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C29×C37 | C2 |
| LCS | G ▷ C5×C29×C37 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,29,37|b^a=b^4,c^a=c^28,d^a=d^362684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36339836, #36339837, #36339840, … |
| maximal normal subgroup of | #36339836, #36339837, #36339840, … |
| maximal quotient of | Dic5365, C2×D5365, C3×D5365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10730, 8);