Finite Group Databasebeta

← Group #100239

Character table — Group #100239

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222222444444448888888844444444444448888888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111111-1-1-1-111-1-1-1-1-11111-111-1-1-1-1-1-1iiii−i−i−i−i111-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ101111111111-1-1-1-111-1-1-1-1-11111-111-1-1-1-1-1-1iiii−i−i−i−i111-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i−i−iii-1-111-11
χ111111111111-1-1-1-111-1-1-1-1-11111-111-1-1-1-1-1-1−i−i−i−iiiii111-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiiiii−i−i-1-111-11
χ121111111111-1-1-1-111-1-1-1-1-11111-111-1-1-1-1-1-1−i−i−i−iiiii111-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−iii11-1-11-1
χ131111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i1-1-111iiii−i−i−i−iii−i−i−i−i−i−iiiii−i−iii11-1-1-11
χ141111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i1-1-111−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i-1-1111-1
χ151111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiii1-1-111iiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iii-1-1111-1
χ161111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiii1-1-111−i−i−i−iiiii−i−iiiiiii−i−i−i−iii−i−i11-1-1-11
χ17222222222222-2-22222-2-2222222-2-2-2-2-2-2-2-200000000-2-2-222000000000000000000000000000000
χ18222222222222-2-22222-2-22-2-2-2-22-2-2-2-2222200000000-222-2-2000000000000000000000000000000
χ192222222222-2-22222-2-222-22222-2-2-222222200000000-2-2-2-2-2000000000000000000000000000000
χ202222222222-2-22222-2-222-2-2-2-2-2-2-2-222-2-2-2-200000000-22222000000000000000000000000000000
χ2122222222-2-22222-2-22222-20000-222-2-2000022222222-2000000000000-2-2-2-2000000000000000000
χ2222222222-2-22222-2-22222-20000-222-2-20000-2-2-2-2-2-2-2-2-20000000000002222000000000000000000
χ2322222222-2-222-2-2-2-222-2-2-20000-2-2-222000000000000200000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ2422222222-2-222-2-2-2-222-2-2-20000-2-2-22200000000000020000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ2522222222-2-2-2-222-2-2-2-222200002-2-2-2-20000000000002000000000000000022-2-2-2-2220000000000
χ2622222222-2-2-2-222-2-2-2-222200002-2-2-2-200000000000020000000000000000-2-22222-2-20000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2200002222200002i2i2i2i−2i−2i−2i−2i-2000000000000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-220000222220000−2i−2i−2i−2i2i2i2i2i-20000000000002i2i−2i−2i000000000000000000
χ29222-22-2-2-2002i−2i2i−2i002i−2i2i−2i0000002-20000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000002−2i2−i200
χ30222-22-2-2-2002i−2i2i−2i002i−2i2i−2i0000002-20000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000−22−i2i200
χ31222-22-2-2-2002i−2i2i−2i002i−2i2i−2i0000002-2000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000−22−i2i200
χ32222-22-2-2-2002i−2i2i−2i002i−2i2i−2i0000002-2000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000002−2i2−i200
χ33222-22-2-2-200−2i2i−2i2i00−2i2i−2i2i0000002-20000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000−22i2−i200
χ34222-22-2-2-200−2i2i−2i2i00−2i2i−2i2i0000002-20000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000002−2−i2i200
χ35222-22-2-2-200−2i2i−2i2i00−2i2i−2i2i0000002-2000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000002−2−i2i200
χ36222-22-2-2-200−2i2i−2i2i00−2i2i−2i2i0000002-2000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000−22i2−i200
χ3722-22-22-2-22-2002i−2i2-200−2i2i022-2-20002i−2i2i2i−2i−2i00000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000001−i−1+i1+i−1−i000000
χ3822-22-22-2-22-2002i−2i2-200−2i2i022-2-20002i−2i2i2i−2i−2i0000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000−1+i1−i−1−i1+i000000
χ3922-22-22-2-22-2002i−2i2-200−2i2i0-2-2220002i−2i−2i−2i2i2i00000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000−1+i1−i−1−i1+i000000
χ4022-22-22-2-22-2002i−2i2-200−2i2i0-2-2220002i−2i−2i−2i2i2i0000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000001−i−1+i1+i−1−i000000
χ4122-22-22-2-22-200−2i2i2-2002i−2i022-2-2000−2i2i−2i−2i2i2i00000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000001+i−1−i1−i−1+i000000
χ4222-22-22-2-22-200−2i2i2-2002i−2i022-2-2000−2i2i−2i−2i2i2i0000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000−1−i1+i−1+i1−i000000
χ4322-22-22-2-22-200−2i2i2-2002i−2i0-2-222000−2i2i2i2i−2i−2i00000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000−1−i1+i−1+i1−i000000
χ4422-22-22-2-22-200−2i2i2-2002i−2i0-2-222000−2i2i2i2i−2i−2i0000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000001+i−1−i1−i−1+i000000
χ452-22-2-222-2222200-2-2-2-200-20000200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i202i−2i0000000000i2−i2i2−i22−22−22−22−20000000000
χ462-22-2-222-2222200-2-2-2-200-20000200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i202i−2i0000000000−i2i2−i2i2−22−22−22−220000000000
χ472-22-2-222-2222200-2-2-2-200-2000020000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20−2i2i0000000000i2−i2i2−i2−22−22−22−220000000000
χ482-22-2-222-2222200-2-2-2-200-2000020000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20−2i2i0000000000−i2i2−i2i22−22−22−22−20000000000
χ492-22-2-222-222-2-200-2-2220020000-200002i−2i2i−2i2−22−2−22−220−2i2i00000000002−2−22i2−i2i2−i2−i2i2−i2i20000000000
χ502-22-2-222-222-2-200-2-2220020000-200002i−2i2i−2i−22−222−22−20−2i2i0000000000−222−2−i2i2−i2i2i2−i2i2−i20000000000
χ512-22-2-222-222-2-200-2-2220020000-20000−2i2i−2i2i2−22−2−22−2202i−2i00000000002−2−22−i2i2−i2i2i2−i2i2−i20000000000
χ522-22-2-222-222-2-200-2-2220020000-20000−2i2i−2i2i−22−222−22−202i−2i0000000000−222−2i2−i2i2−i2−i2i2−i2i20000000000
χ532-22-2-222-2-2-2220022-2-20022-22-2-200000000i2−i2i2−i2i2−i2i2−i20002-200000000−i2i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000
χ542-22-2-222-2-2-2220022-2-20022-22-2-200000000−i2i2−i2i2−i2i2−i2i20002-200000000i2−i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000
χ552-22-2-222-2-2-2220022-2-2002-22-22-200000000i2−i2i2−i2i2−i2i2−i2000-2200000000−i2i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000
χ562-22-2-222-2-2-2220022-2-2002-22-22-200000000−i2i2−i2i2−i2i2−i2i2000-2200000000i2−i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000
χ572-22-2-222-2-2-2-2-200222200-22-22-22000000002−22−2−22−22000-2200000000−222−22−2−22−222−20000000000
χ582-22-2-222-2-2-2-2-200222200-22-22-2200000000−22−222−22−2000-22000000002−2−22−222−22−2−220000000000
χ592-22-2-222-2-2-2-2-200222200-2-22-222000000002−22−2−22−220002-200000000−222−2−222−22−2−220000000000
χ602-22-2-222-2-2-2-2-200222200-2-22-22200000000−22−222−22−20002-2000000002−2−222−2−22−222−20000000000
χ61444-44-4-4-4004i−4i−4i4i004i−4i−4i4i000000-440000000000000000000000000000000000000000000000000
χ62444-44-4-4-400−4i4i4i−4i00−4i4i4i−4i000000-440000000000000000000000000000000000000000000000000
χ6344-44-44-4-4-44004i−4i-4400−4i4i00000000−4i4i00000000000000000000000000000000000000000000000
χ6444-44-44-4-4-4400−4i4i-44004i−4i000000004i−4i00000000000000000000000000000000000000000000000
χ6544-4-4-4-4440000440000-4-40000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ6644-4-4-4-4440000440000-4-4000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ6744-4-4-4-4440000-4-40000440000000000000000000000000002-2-222-2-220000000000000000000000
χ6844-4-4-4-4440000-4-4000044000000000000000000000000000-222-2-222-20000000000000000000000
χ694-444-4-4-44004i−4i0000−4i4i00000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000
χ704-444-4-4-44004i−4i0000−4i4i0000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000
χ714-444-4-4-4400−4i4i00004i−4i00000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000
χ724-444-4-4-4400−4i4i00004i−4i0000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000
χ734-4-4-444-444-40000-44000000000000004-4-440000000000000000000000000000000000000000000
χ744-4-4-444-444-40000-4400000000000000-444-40000000000000000000000000000000000000000000
χ754-4-4-444-44-4400004-4000004-4-440000000000000000000000000000000000000000000000000000
χ764-4-4-444-44-4400004-400000-444-40000000000000000000000000000000000000000000000000000
χ778-8-888-88-8000000000000000000000000000000000000000000000000000000000000000000000

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