Finite Group Databasebeta

← Group #97129

Character table — Group #97129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444222244444444444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222222222222222222-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-22200000000000000000000000000000000
χ2122222222-2-2-2-2222-2-2-2-2200002-22-200002-200000000000000000000002-22-200000000
χ2222222222-2-2-2-2222-2-2-2-2200002-22-200002-20000000000000000000000-22-2200000000
χ2322222222-2-2-2-2222-2-2-2-220000-22-220000-220000000000000000002-22-2000000000000
χ2422222222-2-2-2-2222-2-2-2-220000-22-220000-22000000000000000000-22-22000000000000
χ2522222222-2-2-2-2-2-2-22222-200002-22-20000-220000000000000000002-2-22000000000000
χ2622222222-2-2-2-2-2-2-22222-200002-22-20000-22000000000000000000-222-2000000000000
χ2722222222-2-2-2-2-2-2-22222-20000-22-2200002-200000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-22222-20000-22-2200002-20000000000000000000000-222-200000000
χ29222-2-22-2-222-2-222-222-2-2-222-2-20000002-200000000000000000000000000002−22−22−22−2
χ30222-2-22-2-222-2-222-222-2-2-222-2-20000002-20000000000000000000000000000−22−22−22−22
χ31222-2-22-2-222-2-222-222-2-2-2-2-222000000-2200000000000000000000000000002−22−2−22−22
χ32222-2-22-2-222-2-222-222-2-2-2-2-222000000-220000000000000000000000000000−22−222−22−2
χ33222-2-22-2-222-2-2-2-22-2-222222-2-2000000-220000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ34222-2-22-2-222-2-2-2-22-2-222222-2-2000000-220000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ35222-2-22-2-222-2-2-2-22-2-2222-2-2220000002-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ36222-2-22-2-222-2-2-2-22-2-2222-2-2220000002-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ3722-222-2-2-22-22-2000000002-22-222-2-22-200000022−2−222−2−222−2−222−2−20000000000000000
χ3822-222-2-2-22-22-2000000002-22-222-2-22-2000000−2−222−2−222−2−222−2−2220000000000000000
χ3922-222-2-2-22-22-2000000002-22-2-2-222-22000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ4022-222-2-2-22-22-2000000002-22-2-2-222-22000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ4122-222-2-2-22-22-200000000-22-2222-2-2-2200000022−2−222−2−2−2−222−2−2220000000000000000
χ4222-222-2-2-22-22-200000000-22-2222-2-2-22000000−2−222−2−22222−2−222−2−20000000000000000
χ4322-222-2-2-22-22-200000000-22-22-2-2222-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ4422-222-2-2-22-22-200000000-22-22-2-2222-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ45444-4-44-4-4-4-44444-4-4-444-4000000000000000000000000000000000000000000000000
χ46444-4-44-4-4-4-444-4-4444-4-44000000000000000000000000000000000000000000000000
χ4744-444-4-4-4-44-440000000000004-4-440000000000000000000000000000000000000000
χ4844-444-4-4-4-44-44000000000000-444-40000000000000000000000000000000000000000
χ4944-4-4-4-4444-4-44000000004-4-4400000000000000000000000000000000000000000000
χ5044-4-4-4-4444-4-4400000000-444-400000000000000000000000000000000000000000000
χ5144-4-4-4-444-444-400000000000000000000004-400000000000000000000000000000000
χ5244-4-4-4-444-444-40000000000000000000000-4400000000000000000000000000000000
χ534-444-4-44-400000004i−4i4i−4i00000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ544-444-4-44-400000004i−4i4i−4i0000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ554-444-4-44-40000000−4i4i−4i4i00000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ564-444-4-44-40000000−4i4i−4i4i0000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ574-44-44-4-4400000004i−4i−4i4i000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ584-44-44-4-4400000004i−4i−4i4i00000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ594-44-44-4-440000000−4i4i4i−4i000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ604-44-44-4-440000000−4i4i4i−4i00000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ614-4-44-44-4400004-440000-40000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ624-4-44-44-4400004-440000-4000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ634-4-44-44-440000-44-4000040000000000000000000000002-2-22-222-20000000000000000
χ644-4-44-44-440000-44-400004000000000000000000000000-222-22-2-220000000000000000
χ654-4-4-4444-400004-4-40000400000000000000002-2-22-222-2000000000000000000000000
χ664-4-4-4444-400004-4-4000040000000000000000-222-22-2-22000000000000000000000000
χ674-4-4-4444-40000-4440000-400000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ684-4-4-4444-40000-4440000-40000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.