Finite Group Databasebeta

← Group #97657

Character table — Group #97657

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444422444444888888888888888888888888444444448888
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111
χ911111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-1111-1-1-1ii−i−i
χ1011111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-1-1111−i−iii
χ1111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11-1-1-1111ii−i−i
χ1211111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-1111-1-1-1−i−iii
χ1311111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1111-11-1-1−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-1-11-111ii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-1-1-11-111−i−iii
χ1611111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1111-11-1-1ii−i−i
χ1722222222222222-2-22222-2-222-2-2-2-2-2-222-2-2-2-222000000000000000000000000000000000000
χ1822222222222222-2-22222-2-222-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000
χ192222222222-2-2-2-222-2-22222-2-222-2-2-2-200000000000000000000000000000000002-2002-20000
χ202222222222-2-2-2-222-2-22222-2-222-2-2-2-20000000000000000000000000000000000-2200-220000
χ212222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-22222000000000000000000000000000000002200-2-2000000
χ222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222200000000000000000000000000000000-2-20022000000
χ2322222222-2-2222222-2-2-2-222-2-2-2-2-2-22222-2-222-2-2000000000000000000000000000000000000
χ2422222222-2-2222222-2-2-2-222-2-2-2-2-2-222-2-222-2-222000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-22222-2-22222-2-222-2-2000000000000000000000000000000002-200-22000000
χ2622222222-2-2-2-2-2-22222-2-22222-2-222-2-200000000000000000000000000000000-22002-2000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-22200000000000000000000000000000000002-200-220000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2220000000000000000000000000000000000-22002-20000
χ2922-2-22-2-222222-2-200-2-2-2-20022000000002i−2i2i−2i00i2i2−i2−i2i2i2−i2−i20000000022−2−222−2−2000000000000
χ3022-2-22-2-222222-2-200-2-2-2-20022000000002i−2i2i−2i00−i2−i2i2i2−i2−i2i2i200000000−2−222−2−222000000000000
χ3122-2-22-2-222222-2-200-2-2-2-2002200000000−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i200000000−2−222−2−222000000000000
χ3222-2-22-2-222222-2-200-2-2-2-2002200000000−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i20000000022−2−222−2−2000000000000
χ3322-2-22-2-22-2-222-2-200222200-2-2000000002i−2i−2i2i0022−2−2−2−22200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ3422-2-22-2-22-2-222-2-200222200-2-2000000002i−2i−2i2i00−2−22222−2−200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ3522-2-22-2-22-2-222-2-200222200-2-200000000−2i2i2i−2i0022−2−2−2−22200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ3622-2-22-2-22-2-222-2-200222200-2-200000000−2i2i2i−2i00−2−22222−2−200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ372-22-222-2-22i−2i2-22-2002i−2i2i−2i002i−2i0000002-200002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ382-22-222-2-22i−2i2-22-2002i−2i2i−2i002i−2i0000002-200002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ392-22-222-2-22i−2i2-22-2002i−2i2i−2i002i−2i000000-220000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ402-22-222-2-22i−2i2-22-2002i−2i2i−2i002i−2i000000-220000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ412-22-222-2-2−2i2i2-22-200−2i2i−2i2i00−2i2i0000002-20000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ422-22-222-2-2−2i2i2-22-200−2i2i−2i2i00−2i2i0000002-20000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ432-22-222-2-2−2i2i2-22-200−2i2i−2i2i00−2i2i000000-2200002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ442-22-222-2-2−2i2i2-22-200−2i2i−2i2i00−2i2i000000-2200002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ452-2-222-22-22i−2i2-2-222i−2i−2i2i−2i2i2i−2i2i−2i2-22-22i−2i0000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000
χ462-2-222-22-22i−2i2-2-222i−2i−2i2i−2i2i2i−2i2i−2i2-22-22i−2i000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000
χ472-2-222-22-22i−2i2-2-22−2i2i−2i2i−2i2i−2i2i2i−2i-22-22−2i2i000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000000000000000
χ482-2-222-22-22i−2i2-2-22−2i2i−2i2i−2i2i−2i2i2i−2i-22-22−2i2i00000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000000000
χ492-2-222-22-22i−2i-222-22i−2i2i−2i−2i2i2i−2i−2i2i2-2-22−2i2i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ502-2-222-22-22i−2i-222-22i−2i2i−2i−2i2i2i−2i−2i2i2-2-22−2i2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ512-2-222-22-22i−2i-222-2−2i2i2i−2i−2i2i−2i2i−2i2i-222-22i−2i00000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000000
χ522-2-222-22-22i−2i-222-2−2i2i2i−2i−2i2i−2i2i−2i2i-222-22i−2i0000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000000
χ532-2-222-22-2−2i2i2-2-222i−2i2i−2i2i−2i2i−2i−2i2i-22-222i−2i000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000000000
χ542-2-222-22-2−2i2i2-2-222i−2i2i−2i2i−2i2i−2i−2i2i-22-222i−2i00000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000000000
χ552-2-222-22-2−2i2i2-2-22−2i2i2i−2i2i−2i−2i2i−2i2i2-22-2−2i2i0000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000
χ562-2-222-22-2−2i2i2-2-22−2i2i2i−2i2i−2i−2i2i−2i2i2-22-2−2i2i000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000
χ572-2-222-22-2−2i2i-222-22i−2i−2i2i2i−2i2i−2i2i−2i-222-2−2i2i00000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000000
χ582-2-222-22-2−2i2i-222-22i−2i−2i2i2i−2i2i−2i2i−2i-222-2−2i2i0000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000000
χ592-2-222-22-2−2i2i-222-2−2i2i−2i2i2i−2i−2i2i2i−2i2-2-222i−2i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ602-2-222-22-2−2i2i-222-2−2i2i−2i2i2i−2i−2i2i2i−2i2-2-222i−2i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ6144-44-44-4-4000000440000-4-40000000000000000000000002-22-22-22-200000000000000000000
χ6244-44-44-4-4000000440000-4-4000000000000000000000000-22-22-22-2200000000000000000000
χ6344-44-44-4-4000000-4-40000440000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ6444-44-44-4-4000000-4-4000044000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ6544-4-44-4-4444-4-4440044-4-400-4-400000000000000000000000000000000000000000000000000
χ6644-4-44-4-44-4-4-4-44400-4-444004400000000000000000000000000000000000000000000000000
χ674-444-4-4-440000004i−4i0000−4i4i0000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ684-444-4-4-440000004i−4i0000−4i4i000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ694-444-4-4-44000000−4i4i00004i−4i0000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ704-444-4-4-44000000−4i4i00004i−4i000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ714-44-444-4-44i−4i-44-4400−4i4i4i−4i00−4i4i00000000000000000000000000000000000000000000000000
χ724-44-444-4-4−4i4i-44-44004i−4i−4i4i004i−4i00000000000000000000000000000000000000000000000000
χ73888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000

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