Finite Group Databasebeta

← Group #99137

Character table — Group #99137

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444442244444444444444444444448888888888888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222-2-200000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000000000
χ2122222222-2-2-2-22222-2-2-2-222-2-222-2-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2222222222-2-2-2-22222-2-2-2-222-2-222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-2-2-222000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2222222-2-2-2-22200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ29222-2-22-2-22-22-222-2-222-2-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ30222-2-22-2-22-22-222-2-222-2-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ31222-2-22-2-22-22-222-2-222-2-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ32222-2-22-2-22-22-222-2-222-2-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ33222-2-22-2-22-22-2-2-222-2-2222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ34222-2-22-2-22-22-2-2-222-2-2222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ35222-2-22-2-22-22-2-2-222-2-222−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ36222-2-22-2-22-22-2-2-222-2-222−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ37222-2-22-2-2-22-2222-2-2-2-2222i−2i−2i2i2i−2i−2i2i0000000000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ38222-2-22-2-2-22-2222-2-2-2-2222i−2i−2i2i2i−2i−2i2i000000000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ39222-2-22-2-2-22-2222-2-2-2-222−2i2i2i−2i−2i2i2i−2i0000000000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ40222-2-22-2-2-22-2222-2-2-2-222−2i2i2i−2i−2i2i2i−2i000000000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ41222-2-22-2-2-22-22-2-22222-2-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ42222-2-22-2-2-22-22-2-22222-2-22i−2i−2i2i−2i2i2i−2i0000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ43222-2-22-2-2-22-22-2-22222-2-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ44222-2-22-2-2-22-22-2-22222-2-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4544-44-4-44-4000000004i−4i4i−4i0000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000000000
χ4644-44-4-44-4000000004i−4i4i−4i000000000000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000
χ4744-44-4-44-400000000−4i4i−4i4i0000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000
χ4844-44-4-44-400000000−4i4i−4i4i000000000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000
χ4944-4-44-4-44000000004i−4i−4i4i00000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000
χ5044-4-44-4-44000000004i−4i−4i4i0000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000
χ5144-4-44-4-4400000000−4i4i4i−4i00000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000
χ5244-4-44-4-4400000000−4i4i4i−4i0000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000
χ534-444-4-4-4400004i−4i4i−4i000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000000000000000
χ544-444-4-4-4400004i−4i4i−4i00000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000
χ554-444-4-4-440000−4i4i−4i4i000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000000000000000
χ564-444-4-4-440000−4i4i−4i4i00000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000
χ574-44-44-44-400004i−4i−4i4i0000000000000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000
χ584-44-44-44-400004i−4i−4i4i000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000
χ594-44-44-44-40000−4i4i4i−4i0000000000000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000
χ604-44-44-44-40000−4i4i4i−4i000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000
χ614-4-4444-4-444-4-40000000000000000004-4000000000000000000000000000000000000
χ624-4-4444-4-444-4-4000000000000000000-44000000000000000000000000000000000000
χ634-4-4444-4-4-4-44400000000000000004-400000000000000000000000000000000000000
χ644-4-4444-4-4-4-4440000000000000000-4400000000000000000000000000000000000000
χ654-4-4-4-44444-4-44000000000000000000004-40000000000000000000000000000000000
χ664-4-4-4-44444-4-4400000000000000000000-440000000000000000000000000000000000
χ674-4-4-4-4444-444-400000000000000000000004-400000000000000000000000000000000
χ684-4-4-4-4444-444-40000000000000000000000-4400000000000000000000000000000000

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