Finite Group Databasebeta

← Group #98759

Character table — Group #98759

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222444444444444444444448888888888888888444444444444224444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-11-1-1-11-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-111-1-111-11-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111-1-1111-1-1-111ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1-1-111-1-111-11−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-11111-1-1-111-11-1−i−iii−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-111-1-111-11-1-1−i−iii−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111-1-1111-1-1-111−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1-1-111-1-111-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-11111-1-1-111-11-1ii−i−iii−i−i−i−iii
χ17222222222222-2-22222-2-2-2-2-2-222-2-200000000000000000000000022220-2000-2000000000000
χ18222222222222-2-22222-2-2-2-2-2-222-2-2000000000000000000000000-2-2-2-2020002000000000000
χ192222222222-2-22222-2-22222-2-2-2-2-2-20000000000000000000022220000000-2-20000000000000
χ202222222222-2-22222-2-22222-2-2-2-2-2-200000000000000000000-2-2-2-20000000220000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-222-2-222000000000000000022-2-200000000-202000000000000000
χ222222222222-2-2-2-222-2-2-2-2-2-222-2-2220000000000000000-2-2220000000020-2000000000000000
χ2322222222-2-22222-2-22222-2-222-2-2-2-20000000000000000222200000000-20-2000000000000000
χ2422222222-2-22222-2-22222-2-222-2-2-2-20000000000000000-2-2-2-200000000202000000000000000
χ2522222222-2-222-2-2-2-222-2-222-2-2-2-2220000000000000000000022-2-20000000-220000000000000
χ2622222222-2-222-2-2-2-222-2-222-2-2-2-22200000000000000000000-2-22200000002-20000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-2-2-2222200000000000000000000000022-2-20-20002000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-2-2-22222000000000000000000000000-2-22202000-2000000000000
χ29222-2-22-2-2002i−2i2i−2i002i−2i2i−2i002-200001+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i2i−2i2-2000000000000001−i−1+i1+i−1−i00000000
χ30222-2-22-2-2002i−2i2i−2i002i−2i2i−2i002-200001+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i−2i2i-2200000000000000−1+i1−i−1−i1+i00000000
χ31222-2-22-2-2002i−2i2i−2i002i−2i2i−2i002-20000−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i2i−2i2-200000000000000−1+i1−i−1−i1+i00000000
χ32222-2-22-2-2002i−2i2i−2i002i−2i2i−2i002-20000−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−2i2i-22000000000000001−i−1+i1+i−1−i00000000
χ33222-2-22-2-200−2i2i−2i2i00−2i2i−2i2i002-200001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i2i−2i-2200000000000000−1−i1+i−1+i1−i00000000
χ34222-2-22-2-200−2i2i−2i2i00−2i2i−2i2i002-200001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i−2i2i2-2000000000000001+i−1−i1−i−1+i00000000
χ35222-2-22-2-200−2i2i−2i2i00−2i2i−2i2i002-20000−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i2i−2i-22000000000000001+i−1−i1−i−1+i00000000
χ36222-2-22-2-200−2i2i−2i2i00−2i2i−2i2i002-20000−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−2i2i2-200000000000000−1−i1+i−1+i1−i00000000
χ3722-22-2-22-222-2-200-2-2220000002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000002i−2i2i−2i000000000000002−22−2
χ3822-22-2-22-222-2-200-2-2220000002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000−2i2i−2i2i00000000000000−22−22
χ3922-22-2-22-222-2-200-2-2220000002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000002i−2i2i−2i00000000000000−22−22
χ4022-22-2-22-222-2-200-2-2220000002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000−2i2i−2i2i000000000000002−22−2
χ4122-22-2-22-2-2-2220022-2-20000002-20022−2−222−2−2−2−222−2−222000000002i−2i−2i2i00000000000000−i2i2i2−i2
χ4222-22-2-22-2-2-2220022-2-20000002-20022−2−222−2−2−2−222−2−22200000000−2i2i2i−2i00000000000000i2−i2−i2i2
χ4322-22-2-22-2-2-2220022-2-20000002-200−2−222−2−22222−2−222−2−2000000002i−2i−2i2i00000000000000i2−i2−i2i2
χ4422-22-2-22-2-2-2220022-2-20000002-200−2−222−2−22222−2−222−2−200000000−2i2i2i−2i00000000000000−i2i2i2−i2
χ452-2-2222-2-22i−2i002i−2i2i−2i00−2i2i2-20000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i00002-22i−2i000000000000001−i−1+i1+i−1−i0000
χ462-2-2222-2-22i−2i002i−2i2i−2i00−2i2i2-20000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000-22−2i2i00000000000000−1+i1−i−1−i1+i0000
χ472-2-2222-2-22i−2i002i−2i2i−2i00−2i2i2-2000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i00002-22i−2i00000000000000−1+i1−i−1−i1+i0000
χ482-2-2222-2-22i−2i002i−2i2i−2i00−2i2i2-2000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000-22−2i2i000000000000001−i−1+i1+i−1−i0000
χ492-2-2222-2-2−2i2i00−2i2i−2i2i002i−2i2-20000001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i00002-2−2i2i000000000000001+i−1−i1−i−1+i0000
χ502-2-2222-2-2−2i2i00−2i2i−2i2i002i−2i2-20000001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000-222i−2i00000000000000−1−i1+i−1+i1−i0000
χ512-2-2222-2-2−2i2i00−2i2i−2i2i002i−2i2-2000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i00002-2−2i2i00000000000000−1−i1+i−1+i1−i0000
χ522-2-2222-2-2−2i2i00−2i2i−2i2i002i−2i2-2000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000-222i−2i000000000000001+i−1−i1−i−1+i0000
χ53444-4-44-4-4004i−4i−4i4i004i−4i−4i4i00-4400000000000000000000000000000000000000000000000000
χ54444-4-44-4-400−4i4i4i−4i00−4i4i4i−4i00-4400000000000000000000000000000000000000000000000000
χ5544-44-4-44-4444400-4-4-4-4000000-44000000000000000000000000000000000000000000000000
χ5644-44-4-44-4-4-4-4-4004444000000-44000000000000000000000000000000000000000000000000
χ5744-4-44-4-44004i−4i0000−4i4i00000000002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3000000000000000000000000000000
χ5844-4-44-4-44004i−4i0000−4i4i0000000000−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3000000000000000000000000000000
χ5944-4-44-4-4400−4i4i00004i−4i00000000002ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ000000000000000000000000000000
χ6044-4-44-4-4400−4i4i00004i−4i0000000000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ000000000000000000000000000000
χ614-444-4-4-444i−4i0000−4i4i0000000000002ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ624-444-4-4-444i−4i0000−4i4i000000000000−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ634-444-4-4-44−4i4i00004i−4i0000000000002ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ644-444-4-4-44−4i4i00004i−4i000000000000−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ654-44-44-44-40000000000000000004i−4i2ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ664-44-44-44-40000000000000000004i−4i−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ674-44-44-44-4000000000000000000−4i4i2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ684-44-44-44-4000000000000000000−4i4i−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ694-4-4444-4-44i−4i00−4i4i4i−4i004i−4i-440000000000000000000000000000000000000000000000000000
χ704-4-4444-4-4−4i4i004i−4i−4i4i00−4i4i-440000000000000000000000000000000000000000000000000000
χ714-4-4-4-44440000440000-4-4000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ724-4-4-4-44440000440000-4-400000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ734-4-4-4-44440000-4-4000044000000002-22-2-22-222-22-2-22-22000000000000000000000000000000
χ744-4-4-4-44440000-4-400004400000000-22-222-22-2-22-222-22-2000000000000000000000000000000

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