Finite Group Databasebeta

← Group #100504

Character table — Group #100504

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888844444888888888888888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
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
χ51111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1111-1-1-1-1111-1-1-11111-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-1111-1-1-1-1111-1-1-11111-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ1111111111-1-1-1-1111-1-1-1-1111-1-1-11111-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ1211111111-1-1-1-1111-1-1-1-1111-1-1-11111-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ1311111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-11111-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ1411111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-11111-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ1511111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-11111-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-11111-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ17222222222222-2-2-22222-222-2-2-200000000-222222222-20000-2-2-2-200000000000000000000000000
χ18222222222222-2-2-22222-222-2-2-200000000-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ192222222222-2-222222-2-22-2-22-2-22222-2-2-2-2200000000-2-2-222000000000000000000000000000000
χ202222222222-2-222222-2-22-2-22-2-2-2-2-2-22222200000000-222-2-2000000000000000000000000000000
χ212222222222-2-2-2-2-222-2-2-2-2-2-22200000000-2000000002000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ222222222222-2-2-2-2-222-2-2-2-2-2-22200000000-200000000200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2322222222-2-222222-2-2222-2-2-22222222222-200000000-2-2-2-2-2000000000000000000000000000000
χ2422222222-2-222222-2-2222-2-2-222-2-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000
χ2522222222-2-222-2-2-2-2-222-2-2-22-2-20000000020000000020000000022-2-2-2-222000000000000000000
χ2622222222-2-222-2-2-2-2-222-2-2-22-2-200000000200000000200000000-2-22222-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222220000000022i2i2i2i−2i−2i−2i−2i-20000−2i−2i2i2i00000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222000000002−2i−2i−2i−2i2i2i2i2i-200002i2i−2i−2i00000000000000000000000000
χ2922-2-222-2-22i−2i2i−2i0002i−2i2i−2i02-20000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00002−2i2−i200
χ3022-2-222-2-22i−2i2i−2i0002i−2i2i−2i02-20000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000−22−i2i200
χ3122-2-222-2-22i−2i2i−2i0002i−2i2i−2i02-2000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000−22−i2i200
χ3222-2-222-2-22i−2i2i−2i0002i−2i2i−2i02-2000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002−2i2−i200
χ3322-2-222-2-2−2i2i−2i2i000−2i2i−2i2i02-20000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−22i2−i200
χ3422-2-222-2-2−2i2i−2i2i000−2i2i−2i2i02-20000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00002−2−i2i200
χ3522-2-222-2-2−2i2i−2i2i000−2i2i−2i2i02-2000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00002−2−i2i200
χ3622-2-222-2-2−2i2i−2i2i000−2i2i−2i2i02-2000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000−22i2−i200
χ372-22-22-2-2200222-2-200-2-220002-222-2-222-2-200000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000
χ382-22-22-2-2200222-2-200-2-220002-222-2-222-2-200000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000
χ392-22-22-2-2200222-2-200-2-220002-2-2-222-2-22200000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000
χ402-22-22-2-2200222-2-200-2-220002-2-2-222-2-22200000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000
χ412-22-22-2-2200-2-22-2-200222000-2222-2-2-2-222000000000000000000000000002−22−2−22−222−2−22000000
χ422-22-22-2-2200-2-22-2-200222000-2222-2-2-2-22200000000000000000000000000−22−222−22−2−222−2000000
χ432-22-22-2-2200-2-22-2-200222000-22-2-22222-2-2000000000000000000000000002−22−2−22−22−222−2000000
χ442-22-22-2-2200-2-22-2-200222000-22-2-22222-2-200000000000000000000000000−22−222−22−22−2−22000000
χ452-2-22-22-22220022-2-2-200-200-2002i−2i2i−2i00002i2−i2i2−i2i2−i2i2−i20002i−2ii2−i2i2−i22−22−22−22−2000000000000000000
χ462-2-22-22-22220022-2-2-200-200-2002i−2i2i−2i00002−i2i2−i2i2−i2i2−i2i20002i−2i−i2i2−i2i2−22−22−22−22000000000000000000
χ472-2-22-22-22220022-2-2-200-200-200−2i2i−2i2i00002i2−i2i2−i2i2−i2i2−i2000−2i2ii2−i2i2−i2−22−22−22−22000000000000000000
χ482-2-22-22-22220022-2-2-200-200-200−2i2i−2i2i00002−i2i2−i2i2−i2i2−i2i2000−2i2i−i2i2−i2i22−22−22−22−2000000000000000000
χ492-2-22-22-222200-2-22-2-20020020000002-22-2-2i2−i2i2−i2i2−i2i2−i202-200−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ502-2-22-22-222200-2-22-2-20020020000002-22-2-2−i2i2−i2i2−i2i2−i2i202-200i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ512-2-22-22-222200-2-22-2-2002002000000-22-22-2i2−i2i2−i2i2−i2i2−i20-2200−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ522-2-22-22-222200-2-22-2-2002002000000-22-22-2−i2i2−i2i2−i2i2−i2i20-2200i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ532-2-22-22-22-2-20022-22200-2002002i−2i2i−2i0000-22−22−2−22−22000−2i2i2−2−22−i2i2−i2i2i2−i2i2−i2000000000000000000
χ542-2-22-22-22-2-20022-22200-2002002i−2i2i−2i0000-2−22−222−22−2000−2i2i−222−2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ552-2-22-22-22-2-20022-22200-200200−2i2i−2i2i0000-22−22−2−22−220002i−2i2−2−22i2−i2i2−i2−i2i2−i2i2000000000000000000
χ562-2-22-22-22-2-20022-22200-200200−2i2i−2i2i0000-2−22−222−22−20002i−2i−222−2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ572-2-22-22-22-2-200-2-222200200-20000002-22-222−22−2−22−220-2200−222−2−222−22−2−22000000000000000000
χ582-2-22-22-22-2-200-2-222200200-20000002-22-22−22−222−22−20-22002−2−222−2−22−222−2000000000000000000
χ592-2-22-22-22-2-200-2-222200200-2000000-22-2222−22−2−22−2202-200−222−22−2−22−222−2000000000000000000
χ602-2-22-22-22-2-200-2-222200200-2000000-22-222−22−222−22−202-2002−2−22−222−22−2−22000000000000000000
χ6144-4-444-4-44i−4i−4i4i0004i−4i−4i4i0-440000000000000000000000000000000000000000000000000000000
χ6244-4-444-4-4−4i4i4i−4i000−4i4i4i−4i0-440000000000000000000000000000000000000000000000000000000
χ6344-4-4-4-44400004-440000-4000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ6444-4-4-4-44400004-440000-400000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ6544-4-4-4-4440000-44-4000040000000004-4-4400000000000000000000000000000000000000000000
χ6644-4-4-4-4440000-44-400004000000000-444-400000000000000000000000000000000000000000000
χ674-44-44-4-440044-44400-4-4-4000-440000000000000000000000000000000000000000000000000000
χ684-44-44-4-4400-4-4-4440044-40004-40000000000000000000000000000000000000000000000000000
χ694-44-4-444-44i−4i00000−4i4i000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000
χ704-44-4-444-44i−4i00000−4i4i00000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000
χ714-44-4-444-4−4i4i000004i−4i000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000
χ724-44-4-444-4−4i4i000004i−4i00000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000
χ734-4-444-44-4004i−4i00000−4i4i00000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000
χ744-4-444-44-4004i−4i00000−4i4i0000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000
χ754-4-444-44-400−4i4i000004i−4i00000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000
χ764-4-444-44-400−4i4i000004i−4i0000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000
χ778888-8-8-8-8000000000000000000000000000000000000000000000000000000000000000000000

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