Finite Group Databasebeta

← Group #97713

Character table — Group #97713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444442244444444888888888888888824444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-11-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-111-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-11-1-1-1-11-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-111-1-111-11−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1-11-11-111-1-1-11ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-11-1-111111-1−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-11-11-111-1-1-11−i−iiiii−i−i
χ1411111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-11-1-111111-1ii−i−i−i−iii
χ1511111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-11-1-1-1-11-1−i−iii−i−iii
χ1611111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-111-1-111-11ii−i−iii−i−i
χ172222222222222222-2-222-2-2-2-2-2-2000000000000000020-2000002-20000000000
χ182222222222222222-2-222-2-2-2-2-2-20000000000000000-20200000-220000000000
χ192222222222-2-222-2-222-2-2-2-222-2-200000000000000000002-200000-2200000000
χ202222222222-2-222-2-222-2-2-2-222-2-20000000000000000000-22000002-200000000
χ212222222222-2-222-2-2-2-2-2-222-2-222000000000000000002000-22-2000000000000
χ222222222222-2-222-2-2-2-2-2-222-2-22200000000000000000-20002-22000000000000
χ2322222222-2-222-2-22222-2-2-2-2-2-22200000000000000000002200000-2-200000000
χ2422222222-2-222-2-22222-2-2-2-2-2-2220000000000000000000-2-2000002200000000
χ2522222222-2-222-2-222-2-2-2-22222-2-2000000000000000002000-2-22000000000000
χ2622222222-2-222-2-222-2-2-2-22222-2-200000000000000000-200022-2000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000020-200000-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-222220000000000000000-202000002-20000000000
χ292-222-22-2-22i−2i2i−2i2i−2i2i−2i2-22-22-22i−2i2i−2i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ302-222-22-2-22i−2i2i−2i2i−2i2i−2i2-22-22-22i−2i2i−2i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ312-222-22-2-22i−2i2i−2i2i−2i2i−2i-222-2-22−2i2i−2i2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000000
χ322-222-22-2-22i−2i2i−2i2i−2i2i−2i-222-2-22−2i2i−2i2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000000
χ332-222-22-2-22i−2i−2i2i2i−2i−2i2i2-2-22-222i−2i−2i2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000000000000000
χ342-222-22-2-22i−2i−2i2i2i−2i−2i2i2-2-22-222i−2i−2i2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000000000000000
χ352-222-22-2-22i−2i−2i2i2i−2i−2i2i-22-222-2−2i2i2i−2i00000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ362-222-22-2-22i−2i−2i2i2i−2i−2i2i-22-222-2−2i2i2i−2i0000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ372-222-22-2-2−2i2i2i−2i−2i2i2i−2i2-2-22-22−2i2i2i−2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000000000000000
χ382-222-22-2-2−2i2i2i−2i−2i2i2i−2i2-2-22-22−2i2i2i−2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000000000000000
χ392-222-22-2-2−2i2i2i−2i−2i2i2i−2i-22-222-22i−2i−2i2i00000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ402-222-22-2-2−2i2i2i−2i−2i2i2i−2i-22-222-22i−2i−2i2i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ412-222-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-22-2−2i2i−2i2i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ422-222-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-22-2−2i2i−2i2i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ432-222-22-2-2−2i2i−2i2i−2i2i−2i2i-222-2-222i−2i2i−2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000000
χ442-222-22-2-2−2i2i−2i2i−2i2i−2i2i-222-2-222i−2i2i−2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000000
χ45444-4-4-44-4004400-4-40000000000000000002-22-22-22-200000000000000000000
χ46444-4-4-44-4004400-4-4000000000000000000-22-22-22-2200000000000000000000
χ47444-4-4-44-400-4-400440000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ48444-4-4-44-400-4-40044000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ4944-4-4-44-444i−4i00−4i4i0000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000
χ5044-4-4-44-444i−4i00−4i4i000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000
χ5144-4-4-44-44−4i4i004i−4i0000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000
χ5244-4-4-44-44−4i4i004i−4i000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000
χ534-44-44-4-44004i−4i00−4i4i0000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ544-44-44-4-44004i−4i00−4i4i000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ554-44-44-4-4400−4i4i004i−4i0000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ564-44-44-4-4400−4i4i004i−4i000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ574-4-4-4444-44400-4-40000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ584-4-4-4444-44400-4-4000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ594-4-4-4444-4-4-400440000000000002-2-222-2-220000000000000000000000000000
χ604-4-4-4444-4-4-40044000000000000-222-2-222-20000000000000000000000000000
χ6188-888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-8-88-8-888000000000000000000000000000000000000000000000000000000

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