Finite Group Databasebeta

← Group #252669

Character table — Group #252669

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444444444444444888888888888888822224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111-1-11-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1
χ911111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-1
χ1011111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1111-1-1-1-111
χ1111111111-1-1-1-111111111-1-1-1-1111111-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111
χ1211111111-1-1-1-111111111-1-1-1-1111111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-11-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1111-111-1-111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-11-111-1-1-1-111
χ1722222222222222-2-2-222-222-2-20000-2-222-22200000000000000000000000000-2-200000000
χ1822222222222222-2-2-222-222-2-20000-2-2-2-2-2-2-2000000000000000000000000002200000000
χ19222222222222-2-2222-2-22-2-2222222-2-200-20022-2-2-2-2000000000000000000000000000000
χ20222222222222-2-2222-2-22-2-222-2-2-2-2-2-200-200-2-22222000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-20000220020000000000000000000000000000002-22-20000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000022002000000000000000000000000000000-22-220000
χ2322222222-2-2-2-222-2-2-222-2-2-2220000-2-2222-2-2000000000000000000000000002-200000000
χ2422222222-2-2-2-222-2-2-222-2-2-2220000-2-2-2-222200000000000000000000000000-2200000000
χ2522222222-2-2-2-2-2-2222-2-2222-2-22222-2-200200-2-2-2-222000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-2222-2-2-2-2-2-2-2-2002002222-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-20000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-2000000000000000000000000000000-222-20000
χ292222-2-2-2-222-2-2-2-20002202-2000000002-202-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000
χ302222-2-2-2-222-2-2-2-20002202-2000000002-202-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000
χ312222-2-2-2-222-2-2-2-20002202-200000000-220-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000
χ322222-2-2-2-222-2-2-2-20002202-200000000-220-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000
χ332222-2-2-2-2-2-222-2-2000220-22000000002-20-22000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ342222-2-2-2-2-2-222-2-2000220-22000000002-20-22000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ352222-2-2-2-2-2-222-2-2000220-2200000000-2202-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ362222-2-2-2-2-2-222-2-2000220-2200000000-2202-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ3722-2-2-22-222-22-20022-200-2002-22i2i−2i−2i00000002i−2i0000000000002−22−22−22−20000000000i2−i2i2−i2
χ3822-2-2-22-222-22-20022-200-2002-22i2i−2i−2i00000002i−2i000000000000−22−22−22−220000000000−i2i2−i2i2
χ3922-2-2-22-222-22-20022-200-2002-2−2i−2i2i2i0000000−2i2i0000000000002−22−22−22−20000000000−i2i2−i2i2
χ4022-2-2-22-222-22-20022-200-2002-2−2i−2i2i2i0000000−2i2i000000000000−22−22−22−220000000000i2−i2i2−i2
χ4122-2-2-22-22-22-220022-200-200-222i2i−2i−2i0000000−2i2i0000000000002−22−2−22−220000000000i2−i2−i2i2
χ4222-2-2-22-22-22-220022-200-200-222i2i−2i−2i0000000−2i2i000000000000−22−222−22−20000000000−i2i2i2−i2
χ4322-2-2-22-22-22-220022-200-200-22−2i−2i2i2i00000002i−2i0000000000002−22−2−22−220000000000−i2i2i2−i2
χ4422-2-2-22-22-22-220022-200-200-22−2i−2i2i2i00000002i−2i000000000000−22−222−22−20000000000i2−i2−i2i2
χ452-2-2222-2-200002-22-222-2-200002i−2i2i−2i2-200000002i−2i0000002i−2i2i−2i00000000002-20000000000
χ462-2-2222-2-200002-22-222-2-200002i−2i2i−2i2-200000002i−2i000000−2i2i−2i2i0000000000-220000000000
χ472-2-2222-2-200002-22-222-2-20000−2i2i−2i2i2-20000000−2i2i0000002i−2i2i−2i0000000000-220000000000
χ482-2-2222-2-200002-22-222-2-20000−2i2i−2i2i2-20000000−2i2i000000−2i2i−2i2i00000000002-20000000000
χ492-2-2222-2-20000-222-22-22-200002i−2i2i−2i-220000000−2i2i002i−2i2i−2i0000000000002-2000000000000
χ502-2-2222-2-20000-222-22-22-200002i−2i2i−2i-220000000−2i2i00−2i2i−2i2i000000000000-22000000000000
χ512-2-2222-2-20000-222-22-22-20000−2i2i−2i2i-2200000002i−2i002i−2i2i−2i000000000000-22000000000000
χ522-2-2222-2-20000-222-22-22-20000−2i2i−2i2i-2200000002i−2i00−2i2i−2i2i0000000000002-2000000000000
χ534444-4-4-4-444-4-444000-4-40-440000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-44444000-4-404-40000000000000000000000000000000000000000000000000
χ5544-4-44-44-44-4-4400000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ5644-4-44-44-44-4-440000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5744-4-44-44-4-444-400000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ5844-4-44-44-4-444-40000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ5944-4-4-44-444-44-400-4-4400400-4400000000000000000000000000000000000000000000000
χ6044-4-4-44-44-44-4400-4-44004004-400000000000000000000000000000000000000000000000
χ614-44-4-444-40000004-4-400400004-4-440000000000000000000000000000000000000000000
χ624-44-4-444-40000004-4-40040000-444-40000000000000000000000000000000000000000000
χ634-44-4-444-4000000-44400-400000000000000000004i−4i000000000000000000000000000000
χ644-44-4-444-4000000-44400-40000000000000000000−4i4i000000000000000000000000000000
χ654-4-4444-4-400004-4-44-44-4400000000-4400000000000000000000000000000000000000000
χ664-4-4444-4-40000-44-44-4-444000000004-400000000000000000000000000000000000000000
χ674-4-44-4-44400004-4000-44000000000000000000000022−22−222200000000000000000000000000
χ684-4-44-4-44400004-4000-440000000000000000000000−222222−2200000000000000000000000000
χ694-4-44-4-4440000-440004-40000000000000000000000000022−22−22220000000000000000000000
χ704-4-44-4-4440000-440004-400000000000000000000000000−222222−220000000000000000000000
χ718-88-88-8-88000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).