Finite Group Databasebeta

← Group #349786

Character table — Group #349786

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442222444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-11-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-11-1
χ611111111111111111111-1-11-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-111-11
χ711111111111111111111-1-11-1-1-1-1-1-1-1-11-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ811111111111111111111-1-11-1-1-1-1-1-1-1-11-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ91111111111111111-1-1-1-111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ101111111111111111-1-1-1-111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ131111111111111111-1-1-1-1-1-11-1-11111-1-11-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-11-1-11111-1-11-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-11-1-11111-1-11-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-11-1-11111-1-11-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-2222222-2222222-2-2-2-200-2-200000000-2-2000000000000000000000000
χ182222222222-2-222-2-22222-2-2-2-2-2-2-2-2-222-2200-2-20000000022000000000000000000000000
χ192222222222-2-222-2-2-2-2-2-222-222-2-2-2-2-2-2-2-200220000000022000000000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-2-2-2-2222222-22002200000000-2-2000000000000000000000000
χ2122222222-2-222-2-222000022-2-2-20000-2-2-222200-2-222000000-2-20000000000000000000000
χ2222222222-2-222-2-222000022-2-2-20000-2-2-22-2-20022-2-2000000220000000000000000000000
χ2322222222-2-222-2-2220000-2-2-222000022-2-2220022-2-2000000-2-20000000000000000000000
χ2422222222-2-222-2-2220000-2-2-222000022-2-2-2-200-2-222000000220000000000000000000000
χ2522222222-2-2-2-2-2-2-2-20000222-2-20000222-20000000022-2-2000022-2-2000000000000000000
χ2622222222-2-2-2-2-2-2-2-20000222-2-20000222-200000000-2-2220000-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-22220000-2-2220000000022-2-20000-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-22220000-2-22200000000-2-222000022-2-2000000000000000000
χ2922-22-2-2-222-2002-20022-2-22i−2i02i−2i2i2i−2i−2i000000000000000000000000i2i2−i2−i222−2−2i2−i22−2000000
χ3022-22-2-2-222-2002-20022-2-22i−2i02i−2i2i2i−2i−2i000000000000000000000000−i2−i2i2i2−2−222−i2i2−22000000
χ3122-22-2-2-222-2002-20022-2-2−2i2i0−2i2i−2i−2i2i2i000000000000000000000000i2i2−i2−i2−2−222i2−i2−22000000
χ3222-22-2-2-222-2002-20022-2-2−2i2i0−2i2i−2i−2i2i2i000000000000000000000000−i2−i2i2i222−2−2−i2i22−2000000
χ3322-22-2-2-222-2002-200-2-2222i−2i02i−2i−2i−2i2i2i000000000000000000000000i2i2−i2−i222−2−2−i2i2−22000000
χ3422-22-2-2-222-2002-200-2-2222i−2i02i−2i−2i−2i2i2i000000000000000000000000−i2−i2i2i2−2−222i2−i22−2000000
χ3522-22-2-2-222-2002-200-2-222−2i2i0−2i2i2i2i−2i−2i000000000000000000000000i2i2−i2−i2−2−222−i2i22−2000000
χ3622-22-2-2-222-2002-200-2-222−2i2i0−2i2i2i2i−2i−2i000000000000000000000000−i2−i2i2i222−2−2i2−i2−22000000
χ3722-2-222-2-22222-2-2-2-22-22-200200000000-20002-22-22-22-22-200000000000000000000000000
χ3822-2-222-2-22222-2-2-2-22-22-200200000000-20002-2-22-22-22-2200000000000000000000000000
χ3922-2-222-2-22222-2-2-2-2-22-2200200000000-2000-222-22-2-22-2200000000000000000000000000
χ4022-2-222-2-22222-2-2-2-2-22-2200200000000-2000-22-22-222-22-200000000000000000000000000
χ4122-2-222-2-222-2-2-2-2222-22-200-200000000202i−2i-2200000000002i−2i2i−2i2i−2i000000000000000000
χ4222-2-222-2-222-2-2-2-2222-22-200-20000000020−2i2i-220000000000−2i2i−2i2i−2i2i000000000000000000
χ4322-2-222-2-222-2-2-2-222-22-2200-200000000202i−2i2-200000000002i−2i−2i2i−2i2i000000000000000000
χ4422-2-222-2-222-2-2-2-222-22-2200-20000000020−2i2i2-20000000000−2i2i2i−2i2i−2i000000000000000000
χ4522-2-222-2-2-2-22222-2-2000000-2002i−2i2i−2i002000002-2-2200002i−2i002i−2i−2i2i000000000000000000
χ4622-2-222-2-2-2-22222-2-2000000-2002i−2i2i−2i00200000-222-200002i−2i00−2i2i2i−2i000000000000000000
χ4722-2-222-2-2-2-22222-2-2000000-200−2i2i−2i2i002000002-2-220000−2i2i00−2i2i2i−2i000000000000000000
χ4822-2-222-2-2-2-22222-2-2000000-200−2i2i−2i2i00200000-222-20000−2i2i002i−2i−2i2i000000000000000000
χ4922-2-222-2-2-2-2-2-222220000002002i−2i2i−2i00-202i−2i000000-222-2−2i2i−2i2i0000000000000000000000
χ5022-2-222-2-2-2-2-2-222220000002002i−2i2i−2i00-20−2i2i0000002-2-22−2i2i2i−2i0000000000000000000000
χ5122-2-222-2-2-2-2-2-22222000000200−2i2i−2i2i00-202i−2i0000002-2-222i−2i−2i2i0000000000000000000000
χ5222-2-222-2-2-2-2-2-22222000000200−2i2i−2i2i00-20−2i2i000000-222-22i−2i2i−2i0000000000000000000000
χ53444-4-4-44-44-400-44004-4-44000000000000000000000000000000000000000000000000000
χ54444-4-4-44-44-400-4400-444-4000000000000000000000000000000000000000000000000000
χ55444-4-4-44-4-44004-4000000000004-4-44000000000000000000000000000000000000000000
χ56444-4-4-44-4-44004-400000000000-444-4000000000000000000000000000000000000000000
χ5744-44-4-4-44-4400-440000004i−4i0−4i4i0000000000000000000000000000000000000000000000
χ5844-44-4-4-44-4400-44000000−4i4i04i−4i0000000000000000000000000000000000000000000000
χ594-4444-4-4-4004-4004-40000000000000000000000000000000000000000022−2222−220000000000
χ604-4444-4-4-4004-4004-400000000000000000000000000000000000000000−2222−22220000000000
χ614-4444-4-4-400-4400-44000000000000000000000000000000000000022−2222−2200000000000000
χ624-4444-4-4-400-4400-440000000000000000000000000000000000000−2222−222200000000000000
χ634-4-44-444-40000000000000000000004i−4i00000000000000000000002i−2i−2i2i2-2-220000000000
χ644-4-44-444-40000000000000000000004i−4i0000000000000000000000−2i2i2i−2i-222-20000000000
χ654-4-44-444-4000000000000000000000−4i4i00000000000000000000002i−2i−2i2i-222-20000000000
χ664-4-44-444-4000000000000000000000−4i4i0000000000000000000000−2i2i2i−2i2-2-220000000000
χ674-4-4-44-444004-400-44000000000000000000000000000000000000000000000000022−220000
χ684-4-4-44-444004-400-440000000000000000000000000000000000000000000000000−22220000
χ694-4-4-44-44400-44004-400000000000000000000000000000000000000000000000000022−2200
χ704-4-4-44-44400-44004-4000000000000000000000000000000000000000000000000000−222200
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

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