Finite Group Databasebeta

← Group #267745

Character table — Group #267745

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444422224488888888888888882224444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11111-111-1-1-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-11-1-11111
χ91111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ101111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111-1-11-1-111-1-1
χ121111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-111-1-111
χ131111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-111
χ141111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11111111-1-1
χ151111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-111-1-11-1-1-1-1111-1-111
χ161111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111-11111-1-1-111-1-1
χ17222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-22200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-222222222-2-2-2-222-2-200000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ2122222222-2-22222-2-2-2-22-222-2-200002-20000000000000000000000002-2-200002000000
χ2222222222-2-22222-2-2-2-22-222-2-200002-2000000000000000000000000-2220000-2000000
χ2322222222-2-22222-2-2-2-2-22-2-2220000-220000000000000000000000000002-20002-20000
χ2422222222-2-22222-2-2-2-2-22-2-2220000-22000000000000000000000000000-22000-220000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-22200002-20000000000000000000000002-220000-2000000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-22200002-2000000000000000000000000-22-200002000000
χ2722222222-2-2-2-2-2-2-2-222-2222-2-20000-220000000000000000000000000002-2000-220000
χ2822222222-2-2-2-2-2-2-2-222-2222-2-20000-22000000000000000000000000000-220002-20000
χ292222-2-2-2-22-200002-200002i−2i2i−2i2i2i−2i−2i00002-20022−2−2i2i2−i2−i2i2i2−i2−i222−2−20000000000000000
χ302222-2-2-2-22-200002-200002i−2i2i−2i2i2i−2i−2i00002-200−2−222−i2−i2i2i2−i2−i2i2i2−2−2220000000000000000
χ312222-2-2-2-22-200002-200002i−2i2i−2i−2i−2i2i2i0000-220022−2−2i2i2−i2−i2−i2−i2i2i2−2−2220000000000000000
χ322222-2-2-2-22-200002-200002i−2i2i−2i−2i−2i2i2i0000-2200−2−222−i2−i2i2i2i2i2−i2−i222−2−20000000000000000
χ332222-2-2-2-22-200002-20000−2i2i−2i2i2i2i−2i−2i0000-220022−2−2−i2−i2i2i2i2i2−i2−i2−2−2220000000000000000
χ342222-2-2-2-22-200002-20000−2i2i−2i2i2i2i−2i−2i0000-2200−2−222i2i2−i2−i2−i2−i2i2i222−2−20000000000000000
χ352222-2-2-2-22-200002-20000−2i2i−2i2i−2i−2i2i2i00002-20022−2−2−i2−i2i2i2−i2−i2i2i222−2−20000000000000000
χ362222-2-2-2-22-200002-20000−2i2i−2i2i−2i−2i2i2i00002-200−2−222i2i2−i2−i2i2i2−i2−i2−2−2220000000000000000
χ3722-2-222-2-22222-2-2-2-22-20000002i−2i2i−2i0000002i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3822-2-222-2-22222-2-2-2-22-20000002i−2i2i−2i0000002i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ3922-2-222-2-22222-2-2-2-22-2000000−2i2i−2i2i000000−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4022-2-222-2-22222-2-2-2-22-2000000−2i2i−2i2i000000−2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ4122-2-222-2-222-2-222-2-2-220000002i−2i2i−2i000000−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ4222-2-222-2-222-2-222-2-2-220000002i−2i2i−2i000000−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4322-2-222-2-222-2-222-2-2-22000000−2i2i−2i2i0000002i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ4422-2-222-2-222-2-222-2-2-22000000−2i2i−2i2i0000002i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4522-2-2-2-2222-20000-22002200002-2-22-2-22-2000000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ4622-2-2-2-2222-20000-22002200002-2-22-2-22-200000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ4722-2-2-2-2222-20000-2200220000-222-2-2-2-22000000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ4822-2-2-2-2222-20000-2200220000-222-2-2-2-2200000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ4922-2-2-2-2222-20000-2200-2-200002-2-2222-2200002-2-2200002-2-2200000000000000000000
χ5022-2-2-2-2222-20000-2200-2-200002-2-2222-220000-222-20000-222-200000000000000000000
χ5122-2-2-2-2222-20000-2200-2-20000-222-2222-200002-2-220000-222-200000000000000000000
χ5222-2-2-2-2222-20000-2200-2-20000-222-2222-20000-222-200002-2-2200000000000000000000
χ534444-4-4-4-4-440000-4400004i−4i−4i4i00000000000000000000000000000000000000000000
χ544444-4-4-4-4-440000-440000−4i4i4i−4i00000000000000000000000000000000000000000000
χ5544-4-444-4-4-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ5644-4-444-4-4-4-4-4-444444-400000000000000000000000000000000000000000000000000
χ5744-4-4-4-444-4400004-4004-400000000-4400000000000000000000000000000000000000
χ5844-4-4-4-444-4400004-400-44000000004-400000000000000000000000000000000000000
χ594-44-4-444-4004-44-4000000000000000000000000000000000000002-2000002-20000000
χ604-44-4-444-4004-44-400000000000000000000000000000000000000-2200000-220000000
χ614-44-4-444-400-44-44000000000000000000000000000000000000002-200000-220000000
χ624-44-4-444-400-44-4400000000000000000000000000000000000000-22000002-20000000
χ634-4-44-44-44004-4-44000000000000000000000000000000000000000000000000002-22-2
χ644-4-44-44-44004-4-4400000000000000000000000000000000000000000000000000-22-22
χ654-4-44-44-4400-444-4000000000000000000000000000000000000000000000000002-2-22
χ664-4-44-44-4400-444-400000000000000000000000000000000000000000000000000-222-2
χ678-88-88-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-888-88-8000000000000000000000000000000000000000000000000000000000000

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