Finite Group Databasebeta

← Group #100444

Character table — Group #100444

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222222244444444444444444444444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11ii−i−iii−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i1-1
χ1011111111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11ii−i−iii−i−i−i−i−i−iiiii−i−iii-1-111ii−i−i-11
χ1111111111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11−i−iii−i−iiiiiii−i−i−i−iii−i−i-1-111−i−iii-11
χ1211111111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11−i−iii−i−iii−i−i−i−iiiii−i−iii11-1-1−i−iii1-1
χ1311111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111ii−i−iii−i−iiiii−i−i−i−i−i−iii11-1-1−i−iii-11
χ1411111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111ii−i−iii−i−i−i−i−i−iiiiiii−i−i-1-111−i−iii1-1
χ1511111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111−i−iii−i−iiiiiii−i−i−i−i−i−iii-1-111ii−i−i1-1
χ1611111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111−i−iii−i−iii−i−i−i−iiiiiii−i−i11-1-1ii−i−i-11
χ1722222222222222-2-222-2-2-2-22-2-2222-2-222-2-2-2000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-22-2-22-2-222-2-222-2000000000000000000000000000000
χ19222222222222-2-222-2-22222-2-2-2-200000000-22222-2-2-2-20000000000000000000000
χ20222222222222-2-222-2-22222-2-2-2-200000000-2-2-2-2-222220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-222-20000000020000000000000000000000002i−2i2i−2i00
χ22222222222222-2-2-2-2-2-2-2-2-2-2-222-2000000002000000000000000000000000−2i2i−2i2i00
χ2322222222-2-2-2-222222222-2-2-222-222-2-2-2-222-2000000000000000000000000000000
χ2422222222-2-2-2-222222222-2-2-222-2-2-22222-2-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-222-2-22-2-220000000020000000000000000000000002-2-2200
χ2622222222-2-2-2-2-2-222-2-222-2-22-2-22000000002000000000000000000000000-222-200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000-22i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ292-22-222-2-200002-22i−2i2-22i−2i0002i−2i0002i−2i2-2000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i−1−i1−i−1+i0000000000
χ302-22-222-2-200002-22i−2i2-22i−2i0002i−2i0002i−2i2-200000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i1+i−1+i1−i0000000000
χ312-22-222-2-200002-22i−2i2-22i−2i0002i−2i000−2i2i-22000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i1+i−1+i1−i0000000000
χ322-22-222-2-200002-22i−2i2-22i−2i0002i−2i000−2i2i-2200000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i−1−i1−i−1+i0000000000
χ332-22-222-2-200002-2−2i2i2-2−2i2i000−2i2i0002i−2i-22000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i1−i−1−i1+i0000000000
χ342-22-222-2-200002-2−2i2i2-2−2i2i000−2i2i0002i−2i-2200000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i−1+i1+i−1−i0000000000
χ352-22-222-2-200002-2−2i2i2-2−2i2i000−2i2i000−2i2i2-2000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i−1+i1+i−1−i0000000000
χ362-22-222-2-200002-2−2i2i2-2−2i2i000−2i2i000−2i2i2-200000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i1−i−1−i1+i0000000000
χ372-2-222-22-222-2-200-2-200222-2000000000000000002-22-2i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2000000
χ382-2-222-22-222-2-200-2-200222-2000000000000000002-22-2−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2000000
χ392-2-222-22-222-2-200-2-200222-200000000000000000-22-22i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i2000000
χ402-2-222-22-222-2-200-2-200222-200000000000000000-22-22−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i2000000
χ412-2-222-22-2-2-222002200-2-22-2000000000000000002i−2i−2i2i2−22−2−22−220000−i2i2i2−i2000000
χ422-2-222-22-2-2-222002200-2-22-2000000000000000002i−2i−2i2i−22−222−22−20000i2−i2−i2i2000000
χ432-2-222-22-2-2-222002200-2-22-200000000000000000−2i2i2i−2i2−22−2−22−220000i2−i2−i2i2000000
χ442-2-222-22-2-2-222002200-2-22-200000000000000000−2i2i2i−2i−22−222−22−20000−i2i2i2−i2000000
χ45444-4-4-44-44-44-44400-4-40000-4004000000000000000000000000000000000000000
χ46444-4-4-44-44-44-4-4-400440000400-4000000000000000000000000000000000000000
χ47444-4-4-44-4-44-444400-4-40000400-4000000000000000000000000000000000000000
χ48444-4-4-44-4-44-44-4-400440000-4004000000000000000000000000000000000000000
χ4944-4-44-4-440000004i−4i00−4i4i000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ5044-4-44-4-440000004i−4i00−4i4i00000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ5144-4-44-4-44000000−4i4i004i−4i000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ5244-4-44-4-44000000−4i4i004i−4i00000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ534-444-4-4-4400004-400-44000000004i−4i0000000000000000000000000000000000000
χ544-444-4-4-4400004-400-4400000000−4i4i0000000000000000000000000000000000000
χ554-444-4-4-440000-44004-4000000000000004i−4i0000000000000000000000000000000
χ564-444-4-4-440000-44004-400000000000000−4i4i0000000000000000000000000000000
χ574-44-444-4-40000-444i−4i-444i−4i000−4i4i0000000000000000000000000000000000000000
χ584-44-444-4-40000-44−4i4i-44−4i4i0004i−4i0000000000000000000000000000000000000000
χ594-4-444-44-444-4-4004400-4-4-440000000000000000000000000000000000000000000
χ604-4-444-44-4-4-44400-4-40044-440000000000000000000000000000000000000000000
χ614-4-4-4-44444-4-440000000000000000000000022−2222−2200000000000000000000000000
χ624-4-4-4-44444-4-4400000000000000000000000−2222−222200000000000000000000000000
χ634-4-4-4-4444-444-4000000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ644-4-4-4-4444-444-400000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ6588-88-88-8-8000000000000000000000000000000000000000000000000000000000

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