Finite Group DatabasebetaFinite Group Databasebeta| order | 10676 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D157 |
| unambiguous semidirect product | (D17×C157)⋊C2 |
| unambiguous semidirect product | (C17×D157)⋊C2 |
| unambiguous semidirect product | D2669⋊C2 |
| Fitting, socle, derived, Hall | C17×C157 ⋊ C22 |
| Sylow | C157 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C157 | C22 |
| LCS | G ▷ C17×C157 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
800 conjugacy classes — view the full character table.
| maximal subgroup of | D17×D157⋊C3, C3×D17×D157, D51×D157, … |
| maximal normal subgroup of | D17×D157⋊C3, C3×D17×D157 |
| maximal quotient of | C3×D17×D157, D51×D157, D17×D471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10676, 12);