Finite Group Databasebeta

← Group #97015

Character table — Group #97015

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222444444444444444444448888888888888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-11-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-11-1-1-111-1-1-11-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-11-1-1-1-111-1-11-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-111-1-1-11-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-11-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i111-1-1-1-1-1-1111ii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-1-1-111111-1-1−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-111-1-111-11-1−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111111-1-1-1-11ii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111111-1-1-1-11−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11-111-1-111-11-1ii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-111111-1-1ii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii111-1-1-1-1-1-1111−i−iii
χ17222222222222-2-22222-2-222-2-2-2-2-2-20000000000000000000000002002-20000-2000000
χ18222222222222-2-22222-2-222-2-2-2-2-2-2000000000000000000000000-200-2200002000000
χ192222222222-2-22222-2-222-2-222-2-2-2-2000000000000000000000000020002-2000-200000
χ202222222222-2-22222-2-222-2-222-2-2-2-20000000000000000000000000-2000-22000200000
χ212222222222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000200002-200-20000
χ222222222222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000-20000-220020000
χ2322222222-2-22222-2-22222-2-2-2-222-2-20000000000000000000000000020000-2200-20000
χ2422222222-2-22222-2-22222-2-2-2-222-2-200000000000000000000000000-200002-20020000
χ2522222222-2-222-2-2-2-222-2-2-2-222-2-22200000000000000000000000002000-22000-200000
χ2622222222-2-222-2-2-2-222-2-2-2-222-2-2220000000000000000000000000-20002-2000200000
χ2722222222-2-2-2-222-2-2-2-22222-2-2-2-222000000000000000000000000200-220000-2000000
χ2822222222-2-2-2-222-2-2-2-22222-2-2-2-222000000000000000000000000-2002-200002000000
χ292-2-2-2222-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-22-22i−2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ302-2-2-2222-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-22-22i−2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ312-2-2-2222-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i2-2-22-22−2i2i00000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000
χ322-2-2-2222-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i2-2-22-22−2i2i0000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000
χ332-2-2-2222-22i−2i−2i2i2i−2i2i−2i−2i2i2i−2i-222-2-22−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000000000000
χ342-2-2-2222-22i−2i−2i2i2i−2i2i−2i−2i2i2i−2i-222-2-22−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000000000000
χ352-2-2-2222-22i−2i−2i2i−2i2i2i−2i−2i2i−2i2i-22-222-22i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000000000000000000
χ362-2-2-2222-22i−2i−2i2i−2i2i2i−2i−2i2i−2i2i-22-222-22i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000000000000000000
χ372-2-2-2222-2−2i2i2i−2i2i−2i−2i2i2i−2i2i−2i-22-222-2−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000000000000000000
χ382-2-2-2222-2−2i2i2i−2i2i−2i−2i2i2i−2i2i−2i-22-222-2−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000000000000000000
χ392-2-2-2222-2−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i-222-2-222i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000000000000
χ402-2-2-2222-2−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i-222-2-222i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000000000000
χ412-2-2-2222-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i2-2-22-222i−2i00000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000
χ422-2-2-2222-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i2-2-22-222i−2i0000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000
χ432-2-2-2222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-22-2−2i2i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ442-2-2-2222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-22-2−2i2i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ45444-44-4-4-40000440000-4-4000000002-22-22-22-200000000000000000000000000000000
χ46444-44-4-4-40000440000-4-400000000-22-22-22-2200000000000000000000000000000000
χ47444-44-4-4-40000-4-4000044000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ48444-44-4-4-40000-4-400004400000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ4944-44-44-4-400440000-4-4000000000000000000000000002-22-22-22-20000000000000000
χ5044-44-44-4-400440000-4-400000000000000000000000000-22-22-22-220000000000000000
χ5144-44-44-4-400-4-4000044000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ5244-44-44-4-400-4-400004400000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ5344-4-4-4-4444i−4i0000−4i4i000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ5444-4-4-4-4444i−4i0000−4i4i00000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ5544-4-4-4-444−4i4i00004i−4i000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ5644-4-4-4-444−4i4i00004i−4i00000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ574-444-4-44-4440000-4-4000000000000000000002-2-222-2-22000000000000000000000000
χ584-444-4-44-4440000-4-400000000000000000000-222-2-222-2000000000000000000000000
χ594-444-4-44-4-4-4000044000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ604-444-4-44-4-4-400004400000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ614-44-4-44-44004i−4i0000−4i4i000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ624-44-4-44-44004i−4i0000−4i4i00000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ634-44-4-44-4400−4i4i00004i−4i000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ644-44-4-44-4400−4i4i00004i−4i00000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ654-4-444-4-4400004i−4i0000−4i4i000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ664-4-444-4-4400004i−4i0000−4i4i00000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ674-4-444-4-440000−4i4i00004i−4i000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ684-4-444-4-440000−4i4i00004i−4i00000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000

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