Finite Group Databasebeta

← Group #97654

Character table — Group #97654

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444444444444888888888888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-11-1-11-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-11111
χ911111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-1-11ii−i−i
χ1011111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-1111-1−i−iii
χ1111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11-1-1111-1ii−i−i
χ1211111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-111-1-1-11−i−iii
χ1311111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11111-1-1-1−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-1-1-1111ii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-1-1-1-1111−i−iii
χ1611111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11111-1-1-1ii−i−i
χ172222222222222222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ182222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ192222222222-2-2-2-2-2-22222-2-222-2-222-2-2000000000000000000000000000000002200-200-20000
χ202222222222-2-2-2-2-2-22222-2-222-2-222-2-200000000000000000000000000000000-2-20020020000
χ212222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22200000000000000000000000000000000002-202-200000
χ222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2220000000000000000000000000000000000-220-2200000
χ2322222222-2-22222-2-222-2-2-2-222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ2422222222-2-22222-2-222-2-2-2-222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-22222-2-2222222-2-2-2-200000000000000000000000000000000002-20-2200000
χ2622222222-2-2-2-2-2-22222-2-2222222-2-2-2-20000000000000000000000000000000000-2202-200000
χ2722222222-2-2-2-2-2-222-2-2-2-222-2-2-2-22222000000000000000000000000000000002-200200-20000
χ2822222222-2-2-2-2-2-222-2-2-2-222-2-2-2-2222200000000000000000000000000000000-2200-20020000
χ292222-2-2-2-22222-2-22200-2-2-2-2000000002-22-2000022−2−222−2−20000000022−2−222−2−2000000000000
χ302222-2-2-2-22222-2-22200-2-2-2-2000000002-22-20000−2−222−2−22200000000−2−222−2−222000000000000
χ312222-2-2-2-22222-2-22200-2-2-2-200000000-22-22000022−2−222−2−200000000−2−222−2−222000000000000
χ322222-2-2-2-22222-2-22200-2-2-2-200000000-22-220000−2−222−2−2220000000022−2−222−2−2000000000000
χ332222-2-2-2-2-2-222-2-2-2-2002222000000002-2-220000i2i2−i2−i2−i2−i2i2i200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ342222-2-2-2-2-2-222-2-2-2-2002222000000002-2-220000−i2−i2i2i2i2i2−i2−i200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ352222-2-2-2-2-2-222-2-2-2-200222200000000-222-20000i2i2−i2−i2−i2−i2i2i200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ362222-2-2-2-2-2-222-2-2-2-200222200000000-222-20000−i2−i2i2i2i2i2−i2−i200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ372-22-22-2-222i−2i2-22-22i−2i002i−2i2i−2i0000000000002i−2i2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ382-22-22-2-222i−2i2-22-22i−2i002i−2i2i−2i0000000000002i−2i2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ392-22-22-2-222i−2i2-22-22i−2i002i−2i2i−2i000000000000−2i2i-221+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ402-22-22-2-222i−2i2-22-22i−2i002i−2i2i−2i000000000000−2i2i-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ412-22-22-2-22−2i2i2-22-2−2i2i00−2i2i−2i2i0000000000002i−2i-221−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ422-22-22-2-22−2i2i2-22-2−2i2i00−2i2i−2i2i0000000000002i−2i-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ432-22-22-2-22−2i2i2-22-2−2i2i00−2i2i−2i2i000000000000−2i2i2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ442-22-22-2-22−2i2i2-22-2−2i2i00−2i2i−2i2i000000000000−2i2i2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ452-22-2-222-22i−2i2-2-222i−2i2i−2i−2i2i−2i2i2i−2i2-22-22i−2i0000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000
χ462-22-2-222-22i−2i2-2-222i−2i2i−2i−2i2i−2i2i2i−2i2-22-22i−2i000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000
χ472-22-2-222-22i−2i2-2-222i−2i−2i2i−2i2i−2i2i−2i2i-22-22−2i2i000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000000000
χ482-22-2-222-22i−2i2-2-222i−2i−2i2i−2i2i−2i2i−2i2i-22-22−2i2i00000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000000000
χ492-22-2-222-22i−2i-222-2−2i2i2i−2i−2i2i2i−2i2i−2i-222-2−2i2i00000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000000
χ502-22-2-222-22i−2i-222-2−2i2i2i−2i−2i2i2i−2i2i−2i-222-2−2i2i0000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000000
χ512-22-2-222-22i−2i-222-2−2i2i−2i2i−2i2i2i−2i−2i2i2-2-222i−2i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ522-22-2-222-22i−2i-222-2−2i2i−2i2i−2i2i2i−2i−2i2i2-2-222i−2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ532-22-2-222-2−2i2i2-2-22−2i2i2i−2i2i−2i2i−2i2i−2i-22-222i−2i000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000000000
χ542-22-2-222-2−2i2i2-2-22−2i2i2i−2i2i−2i2i−2i2i−2i-22-222i−2i00000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000000000
χ552-22-2-222-2−2i2i2-2-22−2i2i−2i2i2i−2i2i−2i−2i2i2-22-2−2i2i0000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000
χ562-22-2-222-2−2i2i2-2-22−2i2i−2i2i2i−2i2i−2i−2i2i2-22-2−2i2i000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000
χ572-22-2-222-2−2i2i-222-22i−2i2i−2i2i−2i−2i2i2i−2i2-2-22−2i2i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ582-22-2-222-2−2i2i-222-22i−2i2i−2i2i−2i−2i2i2i−2i2-2-22−2i2i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ592-22-2-222-2−2i2i-222-22i−2i−2i2i2i−2i−2i2i−2i2i-222-22i−2i00000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000000
χ602-22-2-222-2−2i2i-222-22i−2i−2i2i2i−2i−2i2i−2i2i-222-22i−2i0000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000000
χ614444-4-4-4-444-4-444-4-400-4-4440000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-4-4-444440044-4-40000000000000000000000000000000000000000000000000000
χ6344-4-4-44-44000000004i−4i0000−4i4i00000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ6444-4-4-44-44000000004i−4i0000−4i4i0000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ6544-4-4-44-4400000000−4i4i00004i−4i00000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ6644-4-4-44-4400000000−4i4i00004i−4i0000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ674-44-44-4-444i−4i-44-44−4i4i004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ684-44-44-4-44−4i4i-44-444i−4i00−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ694-4-4444-4-400000000440000-4-400000000000000000000002-2-222-2-2200000000000000000000
χ704-4-4444-4-400000000440000-4-40000000000000000000000-222-2-222-200000000000000000000
χ714-4-4444-4-400000000-4-400004400000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ724-4-4444-4-400000000-4-40000440000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ7388-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000

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