Finite Group Databasebeta

← Group #98754

Character table — Group #98754

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222444444444444444444448888888888888888224444444444244444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-11111
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
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-111-1-111-1-11-1ii−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−i11-1-1-1-111-1-111-1-1111-1ii−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-1-11111-1-1-1-1111-11-1-11−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-1-111-1-11111-1-1-11-11-11−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−iiiiiiiii11-1-111-1-111-1-111-1-11-1−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−iiiiiiiii11-1-1-1-111-1-111-1-1111-1−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-1-11111-1-1-1-1111-11-1-11ii−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-1-111-1-11111-1-1-11-11-11ii−i−iii−i−i−i−iii
χ17222222222222-2-22222-2-222-2-2-2-2-2-20000000000000000000022220000-200-200000000000000
χ18222222222222-2-22222-2-222-2-2-2-2-2-200000000000000000000-2-2-2-20000200200000000000000
χ192222222222-2-22222-2-222-2-222-2-2-2-200000000000000002222000000000000-2-2000000000000
χ202222222222-2-22222-2-222-2-222-2-2-2-20000000000000000-2-2-2-200000000000022000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000022-2-20-22000000000000000
χ222222222222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000-2-22202-2000000000000000
χ2322222222-2-22222-2-22222-2-2-2-222-2-200000000000000000000000022220-2-2000000000000000
χ2422222222-2-22222-2-22222-2-2-2-222-2-2000000000000000000000000-2-2-2-2022000000000000000
χ2522222222-2-222-2-2-2-222-2-2-2-222-2-222000000000000000022-2-2000000000000-22000000000000
χ2622222222-2-222-2-2-2-222-2-2-2-222-2-2220000000000000000-2-2220000000000002-2000000000000
χ2722222222-2-2-2-222-2-2-2-22222-2-2-2-2220000000000000000000022-2-20000-200200000000000000
χ2822222222-2-2-2-222-2-2-2-22222-2-2-2-22200000000000000000000-2-2220000200-200000000000000
χ2922-22-2-22-22i−2i002i−2i2i−2i002i−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+i2-22i−2i000000000000001+i−1−i1−i−1+i00000000
χ3022-22-2-22-22i−2i002i−2i2i−2i002i−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-22−2i2i00000000000000−1−i1+i−1+i1−i00000000
χ3122-22-2-22-22i−2i002i−2i2i−2i002i−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−i2-22i−2i00000000000000−1−i1+i−1+i1−i00000000
χ3222-22-2-22-22i−2i002i−2i2i−2i002i−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-22−2i2i000000000000001+i−1−i1−i−1+i00000000
χ3322-22-2-22-2−2i2i00−2i2i−2i2i00−2i2i002-200001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i2-2−2i2i000000000000001−i−1+i1+i−1−i00000000
χ3422-22-2-22-2−2i2i00−2i2i−2i2i00−2i2i002-200001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i-222i−2i00000000000000−1+i1−i−1−i1+i00000000
χ3522-22-2-22-2−2i2i00−2i2i−2i2i00−2i2i002-20000−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i2-2−2i2i00000000000000−1+i1−i−1−i1+i00000000
χ3622-22-2-22-2−2i2i00−2i2i−2i2i00−2i2i002-20000−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i-222i−2i000000000000001−i−1+i1+i−1−i00000000
χ3722-2-22-2-222i−2i2i−2i00−2i2i2i−2i002-20000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00002i−2i2-2000000000000001−i−1+i1+i−1−i0000
χ3822-2-22-2-222i−2i2i−2i00−2i2i2i−2i002-20000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000−2i2i-2200000000000000−1+i1−i−1−i1+i0000
χ3922-2-22-2-222i−2i2i−2i00−2i2i2i−2i002-2000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00002i−2i2-200000000000000−1+i1−i−1−i1+i0000
χ4022-2-22-2-222i−2i2i−2i00−2i2i2i−2i002-2000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000−2i2i-22000000000000001−i−1+i1+i−1−i0000
χ4122-2-22-2-22−2i2i−2i2i002i−2i−2i2i002-20000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00002i−2i-2200000000000000−1−i1+i−1+i1−i0000
χ4222-2-22-2-22−2i2i−2i2i002i−2i−2i2i002-20000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000−2i2i2-2000000000000001+i−1−i1−i−1+i0000
χ4322-2-22-2-22−2i2i−2i2i002i−2i−2i2i002-2000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00002i−2i-22000000000000001+i−1−i1−i−1+i0000
χ4422-2-22-2-22−2i2i−2i2i002i−2i−2i2i002-2000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000−2i2i2-200000000000000−1−i1+i−1+i1−i0000
χ452-2-2-2-222200222200-2-2-2-200002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000002-22-200000000000000i2−i2i2−i2
χ462-2-2-2-222200222200-2-2-2-200002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000-22-2200000000000000−i2i2−i2i2
χ472-2-2-2-222200222200-2-2-2-200002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000002-22-200000000000000−i2i2−i2i2
χ482-2-2-2-222200222200-2-2-2-200002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000-22-2200000000000000i2−i2i2−i2
χ492-2-2-2-222200-2-2-2-200222200002-2002−22−22−22−2−22−22−22−22000000002-2-22000000000000002−2−22
χ502-2-2-2-222200-2-2-2-200222200002-2002−22−22−22−2−22−22−22−2200000000-222-200000000000000−222−2
χ512-2-2-2-222200-2-2-2-200222200002-200−22−22−22−222−22−22−22−2000000002-2-2200000000000000−222−2
χ522-2-2-2-222200-2-2-2-200222200002-200−22−22−22−222−22−22−22−200000000-222-2000000000000002−2−22
χ53444-4-44-4-4440000-4-400000000000022-2-2-2-22222-2-2-2-222000000000000000000000000000000
χ54444-4-44-4-4440000-4-4000000000000-2-22222-2-2-2-22222-2-2000000000000000000000000000000
χ55444-4-44-4-4-4-40000440000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ56444-4-44-4-4-4-4000044000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ5744-44-4-44-44i−4i00−4i4i4i−4i00−4i4i00-4400000000000000000000000000000000000000000000000000
χ5844-44-4-44-4−4i4i004i−4i−4i4i004i−4i00-4400000000000000000000000000000000000000000000000000
χ5944-4-44-4-444i−4i−4i4i00−4i4i−4i4i00-440000000000000000000000000000000000000000000000000000
χ6044-4-44-4-44−4i4i4i−4i004i−4i4i−4i00-440000000000000000000000000000000000000000000000000000
χ614-444-4-4-44004i−4i0000−4i4i00000000002ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ624-444-4-4-44004i−4i0000−4i4i0000000000−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ634-444-4-4-4400−4i4i00004i−4i00000000002ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ644-444-4-4-4400−4i4i00004i−4i0000000000−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ654-44-44-44-400004i−4i0000−4i4i000000002ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ000000000000000000000000000000
χ664-44-44-44-400004i−4i0000−4i4i00000000−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ000000000000000000000000000000
χ674-44-44-44-40000−4i4i00004i−4i000000002ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000
χ684-44-44-44-40000−4i4i00004i−4i00000000−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000
χ694-4-4444-4-40000000000000000004i−4i2ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ704-4-4444-4-40000000000000000004i−4i−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ714-4-4444-4-4000000000000000000−4i4i2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ724-4-4444-4-4000000000000000000−4i4i−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ734-4-4-4-44440044-4-400-4-4440000-44000000000000000000000000000000000000000000000000
χ744-4-4-4-444400-4-4440044-4-40000-44000000000000000000000000000000000000000000000000

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