Finite Group Databasebeta

← Group #140819

Character table — Group #140819

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order1222444488888888244444888888888888161616161616161622448888161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-11-111-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-11-11-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-111111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i−i−iii
χ1111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i1-11-1-1-111ii−i−i−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-11-1111-1-1−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii1-11-1-1-111−i−iiiii−i−iii−i−i
χ1611111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-11-1111-1-1ii−i−iii−i−i−i−iii
χ172222222222222222-222-2-2-2-2-2-2-20000000000000000000000002-22-200000000
χ182222222222222222-222-2-2-2-2-2-2-2000000000000000000000000-22-2200000000
χ19222222222222-2-2-2-22-2-22-2-222-2-2000000000000000000000000000000002i−2i2i−2i
χ20222222222222-2-2-2-22-2-22-2-222-2-200000000000000000000000000000000−2i2i−2i2i
χ21222222222222-2-2-2-2-2-2-2-222-2-22222-2-222-2-20000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000
χ2322222222-2-2-2-222222-2-22-2-2-2-222000000000000000000000000000000002-2-22
χ2422222222-2-2-2-222222-2-22-2-2-2-22200000000000000000000000000000000-222-2
χ2522222222-2-2-2-22222-2-2-2-22222-2-222-2-2-2-2220000000000000000000000000000
χ2622222222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-222-2-2-222220000000000000000000000002i−2i−2i2i00000000
χ2822222222-2-2-2-2-2-2-2-2-222-2-2-22222000000000000000000000000−2i2i2i−2i00000000
χ292222-2-2-2-22i2i−2i−2i2i2i−2i−2i22-2-22-22i−2i2i−2i0000000000000000020-2002i−2i000000000000
χ302222-2-2-2-22i2i−2i−2i2i2i−2i−2i22-2-22-22i−2i2i−2i00000000000000000-20200−2i2i000000000000
χ312222-2-2-2-22i2i−2i−2i2i2i−2i−2i-22-22-22−2i2i−2i2i00000000000000000000000000002ζ6−2ζ62ζ2−2ζ20000
χ322222-2-2-2-22i2i−2i−2i2i2i−2i−2i-22-22-22−2i2i−2i2i0000000000000000000000000000−2ζ62ζ6−2ζ22ζ20000
χ332222-2-2-2-22i2i−2i−2i−2i−2i2i2i2-22-2-222i−2i−2i2i000000002ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ200000000000000000000
χ342222-2-2-2-22i2i−2i−2i−2i−2i2i2i2-22-2-222i−2i−2i2i00000000−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ200000000000000000000
χ352222-2-2-2-22i2i−2i−2i−2i−2i2i2i-2-2222-2−2i2i2i−2i000000000000000020-202i−2i00000000000000
χ362222-2-2-2-22i2i−2i−2i−2i−2i2i2i-2-2222-2−2i2i2i−2i0000000000000000-2020−2i2i00000000000000
χ372222-2-2-2-2−2i−2i2i2i2i2i−2i−2i2-22-2-22−2i2i2i−2i000000002ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ600000000000000000000
χ382222-2-2-2-2−2i−2i2i2i2i2i−2i−2i2-22-2-22−2i2i2i−2i00000000−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ600000000000000000000
χ392222-2-2-2-2−2i−2i2i2i2i2i−2i−2i-2-2222-22i−2i−2i2i000000000000000020-20−2i2i00000000000000
χ402222-2-2-2-2−2i−2i2i2i2i2i−2i−2i-2-2222-22i−2i−2i2i0000000000000000-20202i−2i00000000000000
χ412222-2-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-22-2−2i2i−2i2i0000000000000000020-200−2i2i000000000000
χ422222-2-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-22-2−2i2i−2i2i00000000000000000-202002i−2i000000000000
χ432222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-22-22-222i−2i2i−2i00000000000000000000000000002ζ2−2ζ22ζ6−2ζ60000
χ442222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-22-22-222i−2i2i−2i0000000000000000000000000000−2ζ22ζ2−2ζ62ζ60000
χ4544-4-44i−4i4i−4i00004ζ6−4ζ64ζ2−4ζ20000000000000000002ζ3−2ζ32ζ7−2ζ72ζ−2ζ2ζ5−2ζ500000000000000000000
χ4644-4-44i−4i4i−4i00004ζ6−4ζ64ζ2−4ζ2000000000000000000−2ζ32ζ3−2ζ72ζ7−2ζ2ζ−2ζ52ζ500000000000000000000
χ4744-4-44i−4i4i−4i0000−4ζ64ζ6−4ζ24ζ20000000000000000002ζ7−2ζ7−2ζ32ζ3−2ζ52ζ52ζ−2ζ00000000000000000000
χ4844-4-44i−4i4i−4i0000−4ζ64ζ6−4ζ24ζ2000000000000000000−2ζ72ζ72ζ3−2ζ32ζ5−2ζ5−2ζ2ζ00000000000000000000
χ4944-4-4−4i4i−4i4i00004ζ2−4ζ24ζ6−4ζ60000000000000000002ζ−2ζ−2ζ52ζ5−2ζ32ζ32ζ7−2ζ700000000000000000000
χ5044-4-4−4i4i−4i4i00004ζ2−4ζ24ζ6−4ζ6000000000000000000−2ζ2ζ2ζ5−2ζ52ζ3−2ζ3−2ζ72ζ700000000000000000000
χ5144-4-4−4i4i−4i4i0000−4ζ24ζ2−4ζ64ζ60000000000000000002ζ5−2ζ52ζ−2ζ2ζ7−2ζ72ζ3−2ζ300000000000000000000
χ5244-4-4−4i4i−4i4i0000−4ζ24ζ2−4ζ64ζ6000000000000000000−2ζ52ζ5−2ζ2ζ−2ζ72ζ7−2ζ32ζ300000000000000000000
χ534-4-4444-4-44i−4i4i−4i000000000000000022−22002i2−2i20000000000000000000000000000
χ544-4-4444-4-44i−4i4i−4i0000000000000000−222200−2i22i20000000000000000000000000000
χ554-4-4444-4-4−4i4i−4i4i000000000000000022−2200−2i22i20000000000000000000000000000
χ564-4-4444-4-4−4i4i−4i4i0000000000000000−2222002i2−2i20000000000000000000000000000
χ574-4-44-4-4444-4-440000000000000022−220022−22000000000000000000000000000000
χ584-4-44-4-4444-4-4400000000000000−222200−2222000000000000000000000000000000
χ594-4-44-4-444-444-40000000000000022−2200−2222000000000000000000000000000000
χ604-4-44-4-444-444-400000000000000−22220022−22000000000000000000000000000000
χ618-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.