Finite Group DatabasebetaFinite Group Databasebeta| order | 10726 |
| isoclinism | isoclinic class of D173 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D173 |
| unambiguous semidirect product | C173⋊(C2×C31) |
| Fitting, socle, Hall | C31×C173 ⋊ C2 |
| derived, Sylow | C173 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D173 |
| commutator, cosocle, hypocenter | C173 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C173 | C2 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C31 | |
8 conjugacy classes of subgroups.
2728 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#10621924, C31⋊#10621924, D31×D173, … |
| maximal normal subgroup of | C31×#10621924, C31⋊#10621924, D31×D173, … |
| maximal quotient of | C31×Dic173, C2×C31×D173, C3×C31×D173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10726, 2);