Finite Group Databasebeta

← Group #97646

Character table — Group #97646

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444444444444888888888888888888888888222444448888
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111-1-11-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-11111
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-11-1-1-11ii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11-1111-1−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-11-1111-1ii−i−i
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-11-1-1-11−i−iii
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii111-11-1-1-1−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-11-1111ii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-11-1111−i−iii
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i111-11-1-1-1ii−i−i
χ17222222222222-2-2-2-2-2-22222-2-222-2-2-2-200000000000000000000000000000000002-2-20020000
χ18222222222222-2-2-2-2-2-22222-2-222-2-2-2-20000000000000000000000000000000000-22200-20000
χ192222222222-2-22222-2-222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ202222222222-2-22222-2-222-2-2-2-2-2-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ212222222222-2-2-2-2-2-22222-2-222-2-222-2-2000000000000000000000000000000002-20002-200000
χ222222222222-2-2-2-2-2-22222-2-222-2-222-2-200000000000000000000000000000000-22000-2200000
χ2322222222-2-222222222-2-22222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-222222222-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ2522222222-2-222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000000000002-2000-2200000
χ2622222222-2-222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000-220002-200000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-222000000000000000000000000000000000022-200-20000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2220000000000000000000000000000000000-2-220020000
χ2922-22-2-22-2002i−2i22-2-22i−2i002i−2i2i−2i0000002i−2i2-200001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3022-22-2-22-2002i−2i22-2-22i−2i002i−2i2i−2i0000002i−2i2-20000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3122-22-2-22-2002i−2i22-2-22i−2i002i−2i2i−2i000000−2i2i-2200001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3222-22-2-22-2002i−2i22-2-22i−2i002i−2i2i−2i000000−2i2i-220000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3322-22-2-22-200−2i2i22-2-2−2i2i00−2i2i−2i2i0000002i−2i-2200001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ3422-22-2-22-200−2i2i22-2-2−2i2i00−2i2i−2i2i0000002i−2i-220000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3522-22-2-22-200−2i2i22-2-2−2i2i00−2i2i−2i2i000000−2i2i2-200001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3622-22-2-22-200−2i2i22-2-2−2i2i00−2i2i−2i2i000000−2i2i2-20000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ372-22-22-22-22i−2i2i−2i2-22-22i−2i2i−2i−2i2i−2i2i2-22-22i−2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000
χ382-22-22-22-22i−2i2i−2i2-22-22i−2i2i−2i−2i2i−2i2i2-22-22i−2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000
χ392-22-22-22-22i−2i2i−2i-22-22−2i2i2i−2i−2i2i2i−2i2-2-22−2i2i00000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000000
χ402-22-22-22-22i−2i2i−2i-22-22−2i2i2i−2i−2i2i2i−2i2-2-22−2i2i0000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000000
χ412-22-22-22-22i−2i−2i2i2-22-2−2i2i2i−2i2i−2i2i−2i-22-222i−2i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000
χ422-22-22-22-22i−2i−2i2i2-22-2−2i2i2i−2i2i−2i2i−2i-22-222i−2i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000
χ432-22-22-22-22i−2i−2i2i-22-222i−2i2i−2i2i−2i−2i2i-222-2−2i2i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ442-22-22-22-22i−2i−2i2i-22-222i−2i2i−2i2i−2i−2i2i-222-2−2i2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ452-22-22-22-2−2i2i2i−2i2-22-22i−2i−2i2i−2i2i−2i2i-22-22−2i2i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000
χ462-22-22-22-2−2i2i2i−2i2-22-22i−2i−2i2i−2i2i−2i2i-22-22−2i2i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000
χ472-22-22-22-2−2i2i2i−2i-22-22−2i2i−2i2i−2i2i2i−2i-222-22i−2i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ482-22-22-22-2−2i2i2i−2i-22-22−2i2i−2i2i−2i2i2i−2i-222-22i−2i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ492-22-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i2i−2i2i−2i2-22-2−2i2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000
χ502-22-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i2i−2i2i−2i2-22-2−2i2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000
χ512-22-22-22-2−2i2i−2i2i-22-222i−2i−2i2i2i−2i−2i2i2-2-222i−2i00000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000000
χ522-22-22-22-2−2i2i−2i2i-22-222i−2i−2i2i2i−2i−2i2i2-2-222i−2i0000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000000
χ532-2-2-2-222200222-2-222200-2-2-2-200000000002-22-2i2−i2−i2i2i2−i2−i2i200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ542-2-2-2-222200222-2-222200-2-2-2-200000000002-22-2−i2i2i2−i2−i2i2i2−i200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ552-2-2-2-222200222-2-222200-2-2-2-20000000000-22-22i2−i2−i2i2i2−i2−i2i200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ562-2-2-2-222200222-2-222200-2-2-2-20000000000-22-22−i2i2i2−i2−i2i2i2−i200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ572-2-2-2-222200-2-22-2-22-2-200222200000000002-2-222−2−22−222−2000000002−2−22−222−2000000000000
χ582-2-2-2-222200-2-22-2-22-2-200222200000000002-2-22−222−22−2−2200000000−222−22−2−22000000000000
χ592-2-2-2-222200-2-22-2-22-2-20022220000000000-222-22−2−22−222−200000000−222−22−2−22000000000000
χ602-2-2-2-222200-2-22-2-22-2-20022220000000000-222-2−222−22−2−22000000002−2−22−222−2000000000000
χ6144-44-4-44-4004i−4i-4-444−4i4i004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6244-44-4-44-400−4i4i-4-4444i−4i00−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6344-4-44-4-444400000000-4-4000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ6444-4-44-4-444400000000-4-400000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ6544-4-44-4-44-4-40000000044000000000000000000000000002-22-2-22-2200000000000000000000
χ6644-4-44-4-44-4-4000000004400000000000000000000000000-22-222-22-200000000000000000000
χ674-4-4444-4-44i−4i00000000−4i4i000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ684-4-4444-4-44i−4i00000000−4i4i00000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ694-4-4444-4-4−4i4i000000004i−4i000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ704-4-4444-4-4−4i4i000000004i−4i00000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ714-4-4-4-44440044-444-4-4-400-4-44400000000000000000000000000000000000000000000000000
χ724-4-4-4-444400-4-4-444-4440044-4-400000000000000000000000000000000000000000000000000
χ73888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000

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