Finite Group Databasebeta

← Group #97644

Character table — Group #97644

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444422444444888888888888888888888888222444448888
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
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11-1-11ii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-111-1−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111-111-1ii−i−i
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-11-1-11−i−iii
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1ii−i−i
χ1722222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-222-2-2000000000000000000000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-222-2-222000000000000000000000000000000000000
χ19222222222222-2-22222-2-22222-2-2-2-2-2-222-2-2-2-222000000000000000000000000000000000000
χ20222222222222-2-22222-2-22222-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000
χ2122222222-2-2-2-22222-2-22222-2-2-2-222-2-200000000000000000000000000000000002-2-20020000
χ2222222222-2-2-2-22222-2-22222-2-2-2-222-2-20000000000000000000000000000000000-22200-20000
χ2322222222-2-2-2-222-2-22222-2-22222-2-2-2-2000000000000000000000000000000002-20002-200000
χ2422222222-2-2-2-222-2-22222-2-22222-2-2-2-200000000000000000000000000000000-22000-2200000
χ2522222222-2-2-2-2-2-222-2-2-2-222-2-222-2-222000000000000000000000000000000002-2000-2200000
χ2622222222-2-2-2-2-2-222-2-2-2-222-2-222-2-22200000000000000000000000000000000-220002-200000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2222200000000000000000000000000000000002-2200-20000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222220000000000000000000000000000000000-22-20020000
χ2922-222-2-2-222-2-2002i−2i2i−2i002i−2i2i−2i000000002i−2i2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3022-222-2-2-222-2-2002i−2i2i−2i002i−2i2i−2i000000002i−2i2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3122-222-2-2-222-2-2002i−2i2i−2i002i−2i2i−2i00000000−2i2i-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3222-222-2-2-222-2-2002i−2i2i−2i002i−2i2i−2i00000000−2i2i-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3322-222-2-2-222-2-200−2i2i−2i2i00−2i2i−2i2i000000002i−2i-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ3422-222-2-2-222-2-200−2i2i−2i2i00−2i2i−2i2i000000002i−2i-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3522-222-2-2-222-2-200−2i2i−2i2i00−2i2i−2i2i00000000−2i2i2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3622-222-2-2-222-2-200−2i2i−2i2i00−2i2i−2i2i00000000−2i2i2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ372-222-22-2-22-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2-22-22i−2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000
χ382-222-22-2-22-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2-22-22i−2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000
χ392-222-22-2-22-22-22i−2i−2i2i−2i2i2i−2i2i−2i2i−2i-22-222i−2i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000
χ402-222-22-2-22-22-22i−2i−2i2i−2i2i2i−2i2i−2i2i−2i-22-222i−2i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000
χ412-222-22-2-22-22-2−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i-22-22−2i2i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000
χ422-222-22-2-22-22-2−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i-22-22−2i2i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000
χ432-222-22-2-22-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2-22-2−2i2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000
χ442-222-22-2-22-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2-22-2−2i2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000
χ452-222-22-2-2-22-222i−2i2i−2i−2i2i2i−2i−2i2i2i−2i-222-2−2i2i00000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000000
χ462-222-22-2-2-22-222i−2i2i−2i−2i2i2i−2i−2i2i2i−2i-222-2−2i2i0000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000000
χ472-222-22-2-2-22-222i−2i−2i2i2i−2i2i−2i2i−2i−2i2i2-2-22−2i2i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ482-222-22-2-2-22-222i−2i−2i2i2i−2i2i−2i2i−2i−2i2i2-2-22−2i2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ492-222-22-2-2-22-22−2i2i2i−2i−2i2i−2i2i−2i2i2i−2i2-2-222i−2i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ502-222-22-2-2-22-22−2i2i2i−2i−2i2i−2i2i−2i2i2i−2i2-2-222i−2i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ512-222-22-2-2-22-22−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i-222-22i−2i00000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000000
χ522-222-22-2-2-22-22−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i-222-22i−2i0000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000000
χ532-2-22-2-2222-2-2200222200-2-2-2-20000002-200002-2i2−i2−i2i2i2−i2−i2i200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ542-2-22-2-2222-2-2200222200-2-2-2-20000002-200002-2−i2i2i2−i2−i2i2i2−i200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ552-2-22-2-2222-2-2200222200-2-2-2-2000000-220000-22i2−i2−i2i2i2−i2−i2i200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ562-2-22-2-2222-2-2200222200-2-2-2-2000000-220000-22−i2i2i2−i2−i2i2i2−i200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ572-2-22-2-2222-2-2200-2-2-2-20022220000002-20000-222−2−22−222−2000000002−2−22−222−2000000000000
χ582-2-22-2-2222-2-2200-2-2-2-20022220000002-20000-22−222−22−2−2200000000−222−22−2−22000000000000
χ592-2-22-2-2222-2-2200-2-2-2-2002222000000-2200002-22−2−22−222−200000000−222−22−2−22000000000000
χ602-2-22-2-2222-2-2200-2-2-2-2002222000000-2200002-2−222−22−2−22000000002−2−22−222−2000000000000
χ61444-4-4-44-400004i−4i0000−4i4i000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ62444-4-4-44-400004i−4i0000−4i4i00000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ63444-4-4-44-40000−4i4i00004i−4i000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ64444-4-4-44-40000−4i4i00004i−4i00000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ6544-444-4-4-4-4-444004i−4i−4i4i004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6644-444-4-4-4-4-44400−4i4i4i−4i00−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ674-44-44-4-440000440000-4-4000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ684-44-44-4-440000440000-4-400000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ694-44-44-4-440000-4-4000044000000000000000000000000002-2-222-2-2200000000000000000000
χ704-44-44-4-440000-4-400004400000000000000000000000000-222-2-222-200000000000000000000
χ714-4-44-4-444-444-40044-4-400-4-44400000000000000000000000000000000000000000000000000
χ724-4-44-4-444-444-400-4-4440044-4-400000000000000000000000000000000000000000000000000
χ7388-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000

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