Finite Group Databasebeta

← Group #98053

Character table — Group #98053

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11-111111111
χ51111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-11-1-1-11-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-11111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-1-11ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-1-11−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i1-111-11-1-1−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii1-111-11-1-1ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111-1-111-1-11-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11-1-1111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-111-1-11-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11-1-1111−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-111-1-11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-11-111-11-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111-1-111-1-11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-111-11-1ii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-2-2000022220000000000000000000-2000-200000000
χ18222222222222222222-2-2-2-2-2-2-20000-2-2-2-200000000000000000002000200000000
χ192222222222-2-222-2-2-2-22-2222-2-2222200000000000000000000-200000-2000000000
χ202222222222-2-222-2-2-2-22-2222-2-2-2-2-2-2000000000000000000002000002000000000
χ212222222222-2-222-2-2-2-2-22-2-2-2220000000000000000000000000220-2-20000000000
χ222222222222-2-222-2-2-2-2-22-2-2-2220000000000000000000000000-2-20220000000000
χ2322222222-2-222-2-222-2-22-2-2-22-2200000000000000000000000002-20-220000000000
χ2422222222-2-222-2-222-2-22-2-2-22-220000000000000000000000000-2202-20000000000
χ2522222222-2-222-2-222-2-2-2222-22-222-2-200000000000000000000-2000002000000000
χ2622222222-2-222-2-222-2-2-2222-22-2-2-22200000000000000000000200000-2000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-222-2000022-2-200000000000000000002000-200000000
χ2822222222-2-2-2-2-2-2-2-22222-2-222-20000-2-2220000000000000000000-2000200000000
χ2922-2-22-2-222200-2-20000-202-22002i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ3022-2-22-2-222200-2-20000-202-22002i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ3122-2-22-2-222200-2-20000-202-2200−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ3222-2-22-2-222200-2-20000-202-2200−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ3322-2-22-2-22-2-200220000202-2-2002i−2i−2i2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ3422-2-22-2-22-2-200220000202-2-2002i−2i−2i2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ3522-2-22-2-22-2-200220000202-2-200−2i2i2i−2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ3622-2-22-2-22-2-200220000202-2-200−2i2i2i−2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ372-22-222-2-22i−2i2i−2i2i−2i2i−2i2-2000000000002-22i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000001+i−1−i1−i−1+i
χ382-22-222-2-22i−2i2i−2i2i−2i2i−2i2-2000000000002-22i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000−1−i1+i−1+i1−i
χ392-22-222-2-22i−2i2i−2i2i−2i2i−2i2-200000000000-22−2i2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000−1−i1+i−1+i1−i
χ402-22-222-2-22i−2i2i−2i2i−2i2i−2i2-200000000000-22−2i2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000001+i−1−i1−i−1+i
χ412-22-222-2-2−2i2i−2i2i−2i2i−2i2i2-2000000000002-2−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000001−i−1+i1+i−1−i
χ422-22-222-2-2−2i2i−2i2i−2i2i−2i2i2-2000000000002-2−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000−1+i1−i−1−i1+i
χ432-22-222-2-2−2i2i−2i2i−2i2i−2i2i2-200000000000-222i−2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000−1+i1−i−1−i1+i
χ442-22-222-2-2−2i2i−2i2i−2i2i−2i2i2-200000000000-222i−2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000001−i−1+i1+i−1−i
χ45444-4-4-44-4004400-4-4000000000000000000000000000000000000000002-22-20000
χ46444-4-4-44-4004400-4-400000000000000000000000000000000000000000-22-220000
χ47444-4-4-44-400-4-40044000000000000000000000000000000000000000002i−2i−2i2i0000
χ48444-4-4-44-400-4-4004400000000000000000000000000000000000000000−2i2i2i−2i0000
χ4944-4-44-4-444400-4-4000040-44-4000000000000000000000000000000000000000000
χ5044-4-44-4-44-4-400440000-40-444000000000000000000000000000000000000000000
χ514-444-4-4-44004i−4i00−4i4i000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ524-444-4-4-44004i−4i00−4i4i00000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ534-444-4-4-4400−4i4i004i−4i000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ544-444-4-4-4400−4i4i004i−4i00000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ554-44-444-4-44i−4i−4i4i4i−4i−4i4i-4400000000000000000000000000000000000000000000000
χ564-44-444-4-4−4i4i4i−4i−4i4i4i−4i-4400000000000000000000000000000000000000000000000
χ574-4-444-44-44i−4i00−4i4i0000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ584-4-444-44-44i−4i00−4i4i000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ594-4-444-44-4−4i4i004i−4i0000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ604-4-444-44-4−4i4i004i−4i000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ614-4-4-4-4444000000000004000-40000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ624-4-4-4-4444000000000004000-4000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ634-4-4-4-444400000000000-400040000000002-2-222-2-22000000000000000000000000
χ644-4-4-4-444400000000000-40004000000000-222-2-222-2000000000000000000000000
χ6588-88-88-8-8000000000000000000000000000000000000000000000000000000000

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