Finite Group DatabasebetaFinite Group Databasebeta| order | 10003 |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1429⋊C7 |
| Fitting, socle, derived, Sylow | C1429 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1429 | C7 |
| LCS | G ▷ C1429 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
7,1429|b^a=b^792211 conjugacy classes — view the full character table.
| maximal subgroup of | D1429⋊C7, C2×C1429⋊C7, (C1429⋊C3)⋊C7, … |
| maximal normal subgroup of | D1429⋊C7, C2×C1429⋊C7, (C1429⋊C3)⋊C7, … |
| maximal quotient of | C2×C1429⋊C7, C3×C1429⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10003, 1);