Finite Group DatabasebetaFinite Group Databasebeta| order | 16667 |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C2381⋊C7 |
| Fitting, socle, derived, Sylow | C2381 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C2381 | C7 |
| LCS | G ▷ C2381 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
7,2381|b^a=b^1944347 conjugacy classes — view the full character table.
| maximal subgroup of | D2381⋊C7, C2×C2381⋊C7 |
| maximal normal subgroup of | D2381⋊C7, C2×C2381⋊C7 |
| maximal quotient of | C2×C2381⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16667, 1);