Finite Group DatabasebetaFinite Group Databasebeta| order | 10402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D743⋊C7 |
| unambiguous semidirect product | (C743⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C743 ⋊ C2×C7 |
| Hall | C743⋊C7 ⋊ C2 |
| Hall | D743 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C743 | C2×C7 |
| LCS | G ▷ C743 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,743|c^a=c^742,c^b=c^43367 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D743⋊C7, C3×D743⋊C7, C3⋊(D743⋊C7) |
| maximal normal subgroup of | C2×D743⋊C7, C3×D743⋊C7 |
| maximal quotient of | Dic743⋊C7, C2×D743⋊C7, C3×D743⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10402, 1);