Finite Group DatabasebetaFinite Group Databasebeta| order | 10726 |
| automorphism | Aut(G) order 27673080 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5363 |
| unambiguous semidirect product | C31⋊D173 |
| unambiguous semidirect product | C173⋊D31 |
| Fitting, socle, derived, Hall | C31×C173 ⋊ C2 |
| Sylow | C173 ⋊ D31 |
| Sylow | C31 ⋊ D173 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C173 | C2 |
| LCS | G ▷ C31×C173 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,31,173|b^a=b^30,c^a=c^1722683 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D173, C2×D5363, C3×D5363, … |
| maximal normal subgroup of | D31×D173, C2×D5363, C3×D5363, … |
| maximal quotient of | Dic5363, C2×D5363, C3×D5363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10726, 3);