Finite Group DatabasebetaFinite Group Databasebeta| order | 10676 |
| automorphism | Aut(G) order 13323648 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5338 |
| direct product | C2×D2669 |
| unambiguous semidirect product | (C2×C17)⋊D157 |
| unambiguous semidirect product | (C2×C157)⋊D17 |
| Fitting, socle | C2×C17×C157 ⋊ C2 |
| derived, Hall | C17×C157 ⋊ C22 |
| Sylow | C157 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2669 |
| commutator, cosocle, hypocenter | C17×C157 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C157 | C2 |
| LCS | G ▷ C17×C157 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17⋊(D157⋊C3), D3×D2669, C2×C3×D2669, … |
| maximal normal subgroup of | C2×C17⋊(D157⋊C3), C2×C3×D2669, D10676 |
| maximal quotient of | D3×D2669, C2×C3×D2669, C2×D8007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10676, 13);