Finite Group Databasebeta

← Group #349010

Character table — Group #349010

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442222444444444444444444444444444444444888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-11-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-11-1
χ611111111111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-11
χ711111111111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-111-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ811111111111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-111-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ91111111111111111-1-1-1-111111-1-1-1-111111-1-111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ101111111111111111-1-1-1-111111-1-1-1-111111-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ111111111111111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ131111111111111111-1-1-1-1-1-11-1-11111-1-111111-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-11-1-11111-1-111111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-11-1-11111-1-11-1-11111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-11-1-11111-1-11-1-11111-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-2222222-2222222-2-2-200-2-200-2000000-2-2000000000000000000000000
χ182222222222-2-222-2-22222-2-2-2-2-2-2-2-2-222-20022002000000-2-2000000000000000000000000
χ192222222222-2-222-2-2-2-2-2-222-222-2-2-2-2-2-2-2002200-200000022000000000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-2-2-2-2222222-200-2-200200000022000000000000000000000000
χ2122222222-2-222-2-222000022-2-2-20000-2-2-22200-2-2222000000-2-20000000000000000000000
χ2222222222-2-222-2-222000022-2-2-20000-2-2-2-2-200222-2-2000000220000000000000000000000
χ2322222222-2-222-2-2220000-2-2-222000022-2220022-2-2-2000000-2-20000000000000000000000
χ2422222222-2-222-2-2220000-2-2-222000022-2-2-200-2-2-222000000220000000000000000000000
χ2522222222-2-2-2-2-2-2-2-20000222-2-20000222000000-20022-2-2000022-2-2000000000000000000
χ2622222222-2-2-2-2-2-2-2-20000222-2-20000222000000-200-2-2220000-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-22220000-2-2200000020022-2-20000-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-22220000-2-22000000200-2-222000022-2-2000000000000000000
χ2922-22-2-2-222222-2-2-2-2000000-2002i2i−2i−2i002002i−2i2i−2i02i−2i000000002-22-2000000000000000000
χ3022-22-2-2-222222-2-2-2-2000000-2002i2i−2i−2i002002i−2i−2i2i0−2i2i00000000-22-22000000000000000000
χ3122-22-2-2-222222-2-2-2-2000000-200−2i−2i2i2i00200−2i2i2i−2i02i−2i00000000-22-22000000000000000000
χ3222-22-2-2-222222-2-2-2-2000000-200−2i−2i2i2i00200−2i2i−2i2i0−2i2i000000002-22-2000000000000000000
χ3322-22-2-2-2222-2-2-2-2220000002002i2i−2i−2i00-22-2−2i2i000002i−2i2i−2i002-20000000000000000000000
χ3422-22-2-2-2222-2-2-2-2220000002002i2i−2i−2i00-2-22−2i2i00000−2i2i−2i2i00-220000000000000000000000
χ3522-22-2-2-2222-2-2-2-222000000200−2i−2i2i2i00-22-22i−2i00000−2i2i−2i2i002-20000000000000000000000
χ3622-22-2-2-2222-2-2-2-222000000200−2i−2i2i2i00-2-222i−2i000002i−2i2i−2i00-220000000000000000000000
χ3722-22-2-2-22-2-22222-2-222-2-200200000000-200002i−2i0−2i2i2i−2i−2i2i2-2000000000000000000000000
χ3822-22-2-2-22-2-22222-2-222-2-200200000000-20000−2i2i02i−2i−2i2i2i−2i2-2000000000000000000000000
χ3922-22-2-2-22-2-22222-2-2-2-22200200000000-200002i−2i0−2i2i−2i2i2i−2i-22000000000000000000000000
χ4022-22-2-2-22-2-22222-2-2-2-22200200000000-20000−2i2i02i−2i2i−2i−2i2i-22000000000000000000000000
χ4122-22-2-2-22-2-2-2-2222222-2-200-20000000022-200000000000-22-22-222-2000000000000000000
χ4222-22-2-2-22-2-2-2-2222222-2-200-2000000002-2200000000000-222-22-2-22000000000000000000
χ4322-22-2-2-22-2-2-2-22222-2-22200-20000000022-2000000000002-2-222-2-22000000000000000000
χ4422-22-2-2-22-2-2-2-22222-2-22200-2000000002-22000000000002-22-2-222-2000000000000000000
χ4522-2-2-222-22-2002-2002-22-22i−2i02i−2i2i−2i2i−2i000000000000000000000000i2i2−i2−i222−2−2i2−i22−2000000
χ4622-2-2-222-22-2002-2002-22-22i−2i02i−2i2i−2i2i−2i000000000000000000000000−i2−i2i2i2−2−222−i2i2−22000000
χ4722-2-2-222-22-2002-2002-22-2−2i2i0−2i2i−2i2i−2i2i000000000000000000000000i2i2−i2−i2−2−222i2−i2−22000000
χ4822-2-2-222-22-2002-2002-22-2−2i2i0−2i2i−2i2i−2i2i000000000000000000000000−i2−i2i2i222−2−2−i2i22−2000000
χ4922-2-2-222-22-2002-200-22-222i−2i02i−2i−2i2i−2i2i000000000000000000000000i2i2−i2−i222−2−2−i2i2−22000000
χ5022-2-2-222-22-2002-200-22-222i−2i02i−2i−2i2i−2i2i000000000000000000000000−i2−i2i2i2−2−222i2−i22−2000000
χ5122-2-2-222-22-2002-200-22-22−2i2i0−2i2i2i−2i2i−2i000000000000000000000000i2i2−i2−i2−2−222−i2i22−2000000
χ5222-2-2-222-22-2002-200-22-22−2i2i0−2i2i2i−2i2i−2i000000000000000000000000−i2−i2i2i222−2−2i2−i2−22000000
χ53444-44-4-4-44-400-44000000000004-4-44000000000000000000000000000000000000000000
χ54444-44-4-4-44-400-4400000000000-444-4000000000000000000000000000000000000000000
χ55444-44-4-4-4-44004-4004-4-44000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-44004-400-444-4000000000000000000000000000000000000000000000000000
χ5744-4-4-444-4-4400-440000004i−4i0−4i4i0000000000000000000000000000000000000000000000
χ5844-4-4-444-4-4400-44000000−4i4i04i−4i0000000000000000000000000000000000000000000000
χ594-44-4-4-444004-4004-40000000000000000000000000000000000000000022−2222−220000000000
χ604-44-4-4-444004-4004-400000000000000000000000000000000000000000−2222−22220000000000
χ614-44-4-4-44400-4400-44000000000000000000000000000000000000022−2222−2200000000000000
χ624-44-4-4-44400-4400-440000000000000000000000000000000000000−2222−222200000000000000
χ634-4-444-44-40000000000000000000004i−4i00000000000000000000002i−2i−2i2i2-2-220000000000
χ644-4-444-44-40000000000000000000004i−4i0000000000000000000000−2i2i2i−2i-222-20000000000
χ654-4-444-44-4000000000000000000000−4i4i00000000000000000000002i−2i−2i2i-222-20000000000
χ664-4-444-44-4000000000000000000000−4i4i0000000000000000000000−2i2i2i−2i2-2-220000000000
χ674-4-4-444-44004-400-44000000000000000000000000000000000000000000000000022−220000
χ684-4-4-444-44004-400-440000000000000000000000000000000000000000000000000−22220000
χ694-4-4-444-4400-44004-400000000000000000000000000000000000000000000000000022−2200
χ704-4-4-444-4400-44004-4000000000000000000000000000000000000000000000000000−222200
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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