Finite Group Databasebeta

← Group #424649

Character table — Group #424649

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12224444222222444444888822224444444444444444888888888844448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1
χ5111111111111111111111111-1-111-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ911111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1111111111111111111111-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111-1-1
χ1211111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-111
χ1311111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-11111
χ17222222222-2-2-2-222-2-2-2-2222220000000022-2-2000000000000-2-200000000000000002-2
χ18222222222-2-2-2-222-2-2-2-22222200000000-2-222000000000000-2-20000000000000000-22
χ19222222222-2-2-2-222-2-2-2-22-2-2-2-20000000022-2-2000000000000220000000000000000-22
χ20222222222-2-2-2-222-2-2-2-22-2-2-2-200000000-2-2220000000000002200000000000000002-2
χ212222-2-2-2-2222222-2-2-2-2-2-20000000000002-22-2000000002i2i−2i−2i002i2i−2i−2i00000000000000
χ222222-2-2-2-2222222-2-2-2-2-2-20000000000002-22-200000000−2i−2i2i2i00−2i−2i2i2i00000000000000
χ232222-2-2-2-2222222-2-2-2-2-2-2000000000000-22-22000000002i2i−2i−2i00−2i−2i2i2i00000000000000
χ242222-2-2-2-2222222-2-2-2-2-2-2000000000000-22-2200000000−2i−2i2i2i002i2i−2i−2i00000000000000
χ252222-2-2-2-22-2-2-2-22-22222-20000002200-2-22-2-22000022-2-2000000000000000000000000
χ262222-2-2-2-22-2-2-2-22-22222-20000002200-2-2-222-20000-2-222000000000000000000000000
χ272222-2-2-2-22-2-2-2-22-22222-2000000-2-200222-2-220000-2-222000000000000000000000000
χ282222-2-2-2-22-2-2-2-22-22222-2000000-2-20022-222-2000022-2-2000000000000000000000000
χ292222-2-2-2-2-222-2-2-222-2-22222-2-200000000000022-2-2000000002-20000002-20000000000
χ302222-2-2-2-2-222-2-2-222-2-22222-2-2000000000000-2-222000000002-2000000-220000000000
χ312222-2-2-2-2-222-2-2-222-2-222-2-22200000000000022-2-200000000-22000000-220000000000
χ322222-2-2-2-2-222-2-2-222-2-222-2-222000000000000-2-22200000000-220000002-20000000000
χ332222-2-2-2-2-2-2-222-22-222-2222-2-22200-2-2000000000000000000-2200002-2000000000000
χ342222-2-2-2-2-2-2-222-22-222-2222-2-2-2-20022000000000000000000-220000-22000000000000
χ352222-2-2-2-2-2-2-222-22-222-22-2-2222200-2-20000000000000000002-20000-22000000000000
χ362222-2-2-2-2-2-2-222-22-222-22-2-222-2-200220000000000000000002-200002-2000000000000
χ3722-2-222-2-222-22-2-2222-2-2-200002-22-22-22-2000000000000000000000000002-200000000
χ3822-2-222-2-222-22-2-2222-2-2-200002-2-222-2-2200000000000000000000000000-2200000000
χ3922-2-222-2-222-22-2-2222-2-2-20000-222-2-222-200000000000000000000000000-2200000000
χ4022-2-222-2-222-22-2-2222-2-2-20000-22-22-22-22000000000000000000000000002-200000000
χ4122-2-222-2-2-2-222-22-22-22-2200000000000000002i−2i2i−2i00000000002-22-200000000002i−2i00
χ4222-2-222-2-2-2-222-22-22-22-2200000000000000002i−2i2i−2i0000000000-22-220000000000−2i2i00
χ4322-2-222-2-2-2-222-22-22-22-220000000000000000−2i2i−2i2i00000000002-22-20000000000−2i2i00
χ4422-2-222-2-2-2-222-22-22-22-220000000000000000−2i2i−2i2i0000000000-22-2200000000002i−2i00
χ4522-2-2-2-2222-22-22-2-222-2-220000002-200-2200002i−2i−2i2i00000000000000000000002i−2i0000
χ4622-2-2-2-2222-22-22-2-222-2-220000002-200-220000−2i2i2i−2i0000000000000000000000−2i2i0000
χ4722-2-2-2-2222-22-22-2-222-2-22000000-22002-200002i−2i−2i2i0000000000000000000000−2i2i0000
χ4822-2-2-2-2222-22-22-2-222-2-22000000-22002-20000−2i2i2i−2i00000000000000000000002i−2i0000
χ4922-2-2-2-222-2-222-222-22-22-200002-200-22000000000000000000002i−2i−2i2i0000002i−2i000000
χ5022-2-2-2-222-2-222-222-22-22-200002-200-2200000000000000000000−2i2i2i−2i000000−2i2i000000
χ5122-2-2-2-222-2-222-222-22-22-20000-22002-2000000000000000000002i−2i−2i2i000000−2i2i000000
χ5222-2-2-2-222-2-222-222-22-22-20000-22002-200000000000000000000−2i2i2i−2i0000002i−2i000000
χ5344444444-444-4-4-4-4-444-4-4000000000000000000000000000000000000000000000000
χ5444444444-4-4-444-4-44-4-44-4000000000000000000000000000000000000000000000000
χ5544-4-444-4-44-44-44-44-4-444-4000000000000000000000000000000000000000000000000
χ5644-4-444-4-4-44-4-444-4-44-444000000000000000000000000000000000000000000000000
χ5744-4-4-4-44444-44-4-4-4-4-4444000000000000000000000000000000000000000000000000
χ5844-4-4-4-444-44-4-44444-44-4-4000000000000000000000000000000000000000000000000
χ594-44-44i−4i4i−4i0000000000002i2−2i222−2200000000000000002-22i−2i2ζ−2ζ2ζ3−2ζ300000000000000000000
χ604-44-44i−4i4i−4i0000000000002i2−2i222−220000000000000000-22−2i2i−2ζ2ζ−2ζ32ζ300000000000000000000
χ614-44-44i−4i4i−4i000000000000−2i22i2−222200000000000000002-22i−2i−2ζ2ζ−2ζ32ζ300000000000000000000
χ624-44-44i−4i4i−4i000000000000−2i22i2−22220000000000000000-22−2i2i2ζ−2ζ2ζ3−2ζ300000000000000000000
χ634-44-4−4i4i−4i4i0000000000002i2−2i2−222200000000000000002-2−2i2i2ζ3−2ζ32ζ−2ζ00000000000000000000
χ644-44-4−4i4i−4i4i0000000000002i2−2i2−22220000000000000000-222i−2i−2ζ32ζ3−2ζ2ζ00000000000000000000
χ654-44-4−4i4i−4i4i000000000000−2i22i222−2200000000000000002-2−2i2i−2ζ32ζ3−2ζ2ζ00000000000000000000
χ664-44-4−4i4i−4i4i000000000000−2i22i222−220000000000000000-222i−2i2ζ3−2ζ32ζ−2ζ00000000000000000000
χ678-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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