Finite Group Databasebeta

← Group #512158

Character table — Group #512158

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222244444444444444444444444444444488888888888888816161616323232323232
order12442444442222244444444488888888888888882444444888888882488444888
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-11-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ51111111111-1-1111-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1111-1-111-1-111-1-11111-11-1-11-1
χ61111111111-1-1111-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1111-1-111-1-111-1-1-1-1-1-11-111-11
χ71111111111-1-1111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1111-1-1-1-111-1-1111111-1-11-1-11
χ81111111111-1-1111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1111-1-1-1-111-1-111-1-1-1-111-111-1
χ911111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-111-1-11-11-11-1
χ1011111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-111-11-11-11
χ1111111-1-1-1-111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-11
χ1211111-1-1-1-111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111-1
χ1311111-1-1-1-11-1-1111-1-1111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1111
χ1411111-1-1-1-11-1-1111-1-1111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-111111-1-1-1
χ1511111-1-1-1-11-1-1111-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-11111-1-1-1-111-1-1-1111-1-1
χ1611111-1-1-1-11-1-1111-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-11111-1-1-1-1-1-1111-1-1-111
χ172222222222002-2-20000002-2-20000222200002222002-2-20000-2-200-2-20000000000
χ182222222222002-2-20000002-2-20000-2-2-2-20000-2-2-2-2002-2-200002200220000000000
χ19222222222200-22-2000000-22-2222200002222000000-22-200-2-200-2-2000000000000
χ20222222222200-22-2000000-22-2-2-2-2-20000-2-2-2-2000000-22-200220022000000000000
χ21222222222222-2-22222222-2-220000000000000000-2-2-2-22-2-2000000000000000000
χ222222222222-2-2-2-22-2-2-2-2-2-2-2-22000000000000000022-2-2222000000000000000000
χ2322222-2-2-2-22002-2-20000002-2-2000022220000-2-2-2-200-22200002200-2-20000000000
χ2422222-2-2-2-22002-2-20000002-2-20000-2-2-2-20000222200-2220000-2-200220000000000
χ2522222-2-2-2-2200-22-2000000-22-222220000-2-2-2-20000002-22002200-2-2000000000000
χ2622222-2-2-2-2200-22-2000000-22-2-2-2-2-2000022220000002-2200-2-20022000000000000
χ2722222-2-2-2-2222-2-2222-2-2-2-2-2-2200000000000000002222-2-2-2000000000000000000
χ2822222-2-2-2-22-2-2-2-22-2-22222-2-220000000000000000-2-222-222000000000000000000
χ2922-2-220000-20022-20022-2-2-2-222i2i−2i−2i2i2i−2i−2i000000002-20000000002i−2i2i−2i0000000000
χ3022-2-220000-20022-20022-2-2-2-22−2i−2i2i2i−2i−2i2i2i000000002-2000000000−2i2i−2i2i0000000000
χ3122-2-220000-20022-200-2-222-2-222i2i−2i−2i−2i−2i2i2i00000000-220000000002i−2i−2i2i0000000000
χ3222-2-220000-20022-200-2-222-2-22−2i−2i2i2i2i2i−2i−2i00000000-22000000000−2i2i2i−2i0000000000
χ3322-2-220000-200-2-2-20022-2-2222000000002i2i−2i−2i2i2i−2i−2i-22000002i−2i2i−2i00000000000000
χ3422-2-220000-200-2-2-20022-2-222200000000−2i−2i2i2i−2i−2i2i2i-2200000−2i2i−2i2i00000000000000
χ3522-2-220000-200-2-2-200-2-222222000000002i2i−2i−2i−2i−2i2i2i2-2000002i−2i−2i2i00000000000000
χ3622-2-220000-200-2-2-200-2-22222200000000−2i−2i2i2i2i2i−2i−2i2-200000−2i2i2i−2i00000000000000
χ3722-2-220000-2222-22-2-20000-22-200002i2i−2i−2i2i2i−2i−2i0000000002-2−2i2i0000−2i2i0000000000
χ3822-2-220000-2222-22-2-20000-22-20000−2i−2i2i2i−2i−2i2i2i0000000002-22i−2i00002i−2i0000000000
χ3922-2-220000-222-222-2-200002-2-22i2i−2i−2i000000002i2i−2i−2i00000-2200−2i2i−2i2i000000000000
χ4022-2-220000-222-222-2-200002-2-2−2i−2i2i2i00000000−2i−2i2i2i00000-22002i−2i2i−2i000000000000
χ4122-2-220000-2-2-22-22220000-22-200002i2i−2i−2i−2i−2i2i2i000000000-222i−2i0000−2i2i0000000000
χ4222-2-220000-2-2-22-22220000-22-20000−2i−2i2i2i2i2i−2i−2i000000000-22−2i2i00002i−2i0000000000
χ4322-2-220000-2-2-2-2222200002-2-22i2i−2i−2i00000000−2i−2i2i2i000002-2002i−2i−2i2i000000000000
χ4422-2-220000-2-2-2-2222200002-2-2−2i−2i2i2i000000002i2i−2i−2i000002-200−2i2i2i−2i000000000000
χ4544-4-4-44i4i−4i−4i40000000000000000000000000000000000000000000002-22i−2i000000
χ4644-4-4-44i4i−4i−4i4000000000000000000000000000000000000000000000-22−2i2i000000
χ4744-4-4-4−4i−4i4i4i40000000000000000000000000000000000000000000002-2−2i2i000000
χ4844-4-4-4−4i−4i4i4i4000000000000000000000000000000000000000000000-222i−2i000000
χ494-44i−4i02+2i−2−2i2−2i−2+2i02-20002i−2i2-22i−2i0002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000
χ504-44i−4i02+2i−2−2i2−2i−2+2i02-20002i−2i2-22i−2i000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000
χ514-44i−4i02+2i−2−2i2−2i−2+2i0-22000−2i2i-22−2i2i0002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000
χ524-44i−4i02+2i−2−2i2−2i−2+2i0-22000−2i2i-22−2i2i000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000
χ534-44i−4i0−2−2i2+2i−2+2i2−2i02-20002i−2i-22−2i2i0002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000
χ544-44i−4i0−2−2i2+2i−2+2i2−2i02-20002i−2i-22−2i2i000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000
χ554-44i−4i0−2−2i2+2i−2+2i2−2i0-22000−2i2i2-22i−2i0002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000
χ564-44i−4i0−2−2i2+2i−2+2i2−2i0-22000−2i2i2-22i−2i000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000
χ574-4−4i4i02−2i−2+2i2+2i−2−2i02-2000−2i2i2-2−2i2i0002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000
χ584-4−4i4i02−2i−2+2i2+2i−2−2i02-2000−2i2i2-2−2i2i000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000
χ594-4−4i4i02−2i−2+2i2+2i−2−2i0-220002i−2i-222i−2i0002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000
χ604-4−4i4i02−2i−2+2i2+2i−2−2i0-220002i−2i-222i−2i000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000
χ614-4−4i4i0−2+2i2−2i−2−2i2+2i02-2000−2i2i-222i−2i0002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000
χ624-4−4i4i0−2+2i2−2i−2−2i2+2i02-2000−2i2i-222i−2i000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000
χ634-4−4i4i0−2+2i2−2i−2−2i2+2i0-220002i−2i2-2−2i2i0002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000
χ644-4−4i4i0−2+2i2−2i−2−2i2+2i0-220002i−2i2-2−2i2i000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000
χ658888-80000-80000000000000000000000000000000000000000000000000000000

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