Finite Group DatabasebetaFinite Group Databasebeta| order | 10478 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C13⋊D403 |
| unambiguous semidirect product | C31⋊(C13⋊D13) |
| Fitting, socle, derived, Hall | C132×C31 ⋊ C2 |
| Sylow | C132 ⋊ D31 |
| Sylow | C31 ⋊ C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C31 | C2 |
| LCS | G ▷ C132×C31 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,13^2,31|b^a=b^12,c^a=c^12,d^a=d^302621 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×D403, D31×C13⋊D13, C2×C13⋊D403, … |
| maximal normal subgroup of | D13×D403, D31×C13⋊D13, C2×C13⋊D403, … |
| maximal quotient of | C31⋊#10621725, C2×C13⋊D403, C3×C13⋊D403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10478, 6);