Finite Group Databasebeta

← Group #98019

Character table — Group #98019

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
χ311111111111111111111111111111-1-1-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111
χ51111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-11111-1-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-11111-1-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-11111-1-1-1111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-1-11111-1-1-1111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-11111-1-1-11-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-11111-1-1-11-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-11111-1-1-11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-11111-1-1-11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222222222-222-2-2-2-2-2-2000022220000000000000000-200-2000000000000
χ182222222222222222-222-2-2-2-2-2-20000-2-2-2-200000000000000002002000000000000
χ192222222222-2-2-222-22-2-222-22-2-222-2-2000000000000000000000-220000000000000
χ202222222222-2-2-222-22-2-222-22-2-2-2-2220000000000000000000002-20000000000000
χ212222222222-2-2-222-2-2-2-2-2-22-22200000000000000000000000000002-22-200000000
χ222222222222-2-2-222-2-2-2-2-2-22-2220000000000000000000000000000-22-2200000000
χ2322222222-2-2222-2-222-2-2-2-2-22-2200000000000000000000000000002-2-2200000000
χ2422222222-2-2222-2-222-2-2-2-2-22-220000000000000000000000000000-222-200000000
χ2522222222-2-2222-2-22-2-2-2222-22-22222000000000000000000000-2-20000000000000
χ2622222222-2-2222-2-22-2-2-2222-22-2-2-2-2-2000000000000000000000220000000000000
χ2722222222-2-2-2-2-2-2-2-2222-2-2222-2000022-2-20000000000000000-2002000000000000
χ2822222222-2-2-2-2-2-2-2-2222-2-2222-20000-2-2220000000000000000200-2000000000000
χ2922-2-222-2-2222-2-2-2-2202-200000000002i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i20000000000002−22−2
χ3022-2-222-2-2222-2-2-2-2202-200000000002i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i2000000000000−22−22
χ3122-2-222-2-2222-2-2-2-2202-20000000000−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i2000000000000−22−22
χ3222-2-222-2-2222-2-2-2-2202-20000000000−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i20000000000002−22−2
χ3322-2-222-2-2-2-2-22222-202-200000000002i−2i−2i2i0000000022−2−2−2−222000000000000−i2i2i2−i2
χ3422-2-222-2-2-2-2-22222-202-200000000002i−2i−2i2i00000000−2−22222−2−2000000000000i2−i2−i2i2
χ3522-2-222-2-2-2-2-22222-202-20000000000−2i2i2i−2i0000000022−2−2−2−222000000000000i2−i2−i2i2
χ3622-2-222-2-2-2-2-22222-202-20000000000−2i2i2i−2i00000000−2−22222−2−2000000000000−i2i2i2−i2
χ372-2-2-2-22220022-200-20002-220-202-22-20000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-2-2-2-22220022-200-20002-220-202-22-20000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-2-2-2-22220022-200-20002-220-20-22-220000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-2-2-2-22220022-200-20002-220-20-22-220000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-2-2-2-222200-2-220020002-2-20202-2-22000022−2−2−2−2222−22−2−22−220000000000000000
χ422-2-2-2-222200-2-220020002-2-20202-2-220000−2−22222−2−2−22−222−22−20000000000000000
χ432-2-2-2-222200-2-220020002-2-2020-222-2000022−2−2−2−222−22−222−22−20000000000000000
χ442-2-2-2-222200-2-220020002-2-2020-222-20000−2−22222−2−22−22−2−22−220000000000000000
χ45444-4-4-44-400000000400000-400000000002-22-22-22-2000000000000000000000000
χ46444-4-4-44-400000000400000-40000000000-22-22-22-22000000000000000000000000
χ47444-4-4-44-400000000-400000400000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ48444-4-4-44-400000000-40000040000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4944-4-444-4-444-444-4-4-40-440000000000000000000000000000000000000000000000
χ5044-4-444-4-4-4-44-4-44440-440000000000000000000000000000000000000000000000
χ514-444-44-4-4004-4400-400000000000000000000000002-2-222-2-220000000000000000
χ524-444-44-4-4004-4400-40000000000000000000000000-222-2-222-20000000000000000
χ534-444-44-4-400-44-400400000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ544-444-44-4-400-44-40040000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ554-44-44-4-444i−4i0004i−4i0000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ564-44-44-4-444i−4i0004i−4i000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ574-44-44-4-44−4i4i000−4i4i0000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ584-44-44-4-44−4i4i000−4i4i000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ594-4-444-44-44i−4i000−4i4i0000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ604-4-444-44-44i−4i000−4i4i000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ614-4-444-44-4−4i4i0004i−4i0000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ624-4-444-44-4−4i4i0004i−4i000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ634-4-4-4-44440044-400-4000-44-40400000000000000000000000000000000000000000
χ644-4-4-4-444400-4-44004000-4440-400000000000000000000000000000000000000000
χ6588-88-8-8-88000000000000000000000000000000000000000000000000000000000

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