Finite Group Databasebeta

← Group #511571

Character table — Group #511571

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244444444444444444444444488888888888888883232323232323232
order122222224444888888882222224444448888888888881616161616161616161616161616161622444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111
χ51111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1
χ911111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-11-1
χ1011111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-111-11
χ1111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-11-11
χ1211111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-11-11-1
χ1311111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-1-11
χ1411111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-111-1
χ1511111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-1111-1
χ1611111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-11
χ17222222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-2-2-22222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-2000000000000000000000000
χ2122222222-2-2-2-200000000222222-2-2-2-2-2-200000000000022−2−222−2−222−2−222−2−200000000
χ2222222222-2-2-2-200000000222222-2-2-2-2-2-2000000000000−2−222−2−222−2−222−2−22200000000
χ2322222222-2-2-2-20000000022-2-2-2-2-2-2222200000000000022−2−222−2−2−2−222−2−22200000000
χ2422222222-2-2-2-20000000022-2-2-2-2-2-22222000000000000−2−222−2−22222−2−222−2−200000000
χ2522222222-2-2-2-200000000-2-222-2-222-2-22200000000000022−2−2−2−22222−2−2−2−22200000000
χ2622222222-2-2-2-200000000-2-222-2-222-2-222000000000000−2−22222−2−2−2−22222−2−200000000
χ2722222222-2-2-2-200000000-2-2-2-2222222-2-200000000000022−2−2−2−222−2−22222−2−200000000
χ2822222222-2-2-2-200000000-2-2-2-2222222-2-2000000000000−2−22222−2−222−2−2−2−22200000000
χ292-2-2-2-222200002222−2−2−2−22-22-22-200000022−2−222−2−222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ302-2-2-2-222200002222−2−2−2−22-22-22-200000022−2−222−2−222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ312-2-2-2-222200002222−2−2−2−22-2-22-2200000022−2−2−2−222−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ322-2-2-2-222200002222−2−2−2−22-2-22-2200000022−2−2−2−222−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ332-2-2-2-222200002222−2−2−2−2-222-2-22000000−2−22222−2−2−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ342-2-2-2-222200002222−2−2−2−2-222-2-22000000−2−22222−2−2−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ352-2-2-2-222200002222−2−2−2−2-22-222-2000000−2−222−2−22222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ362-2-2-2-222200002222−2−2−2−2-22-222-2000000−2−222−2−22222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ372-2-2-2-22220000−2−2−2−222222-22-22-2000000−2−222−2−222−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ382-2-2-2-22220000−2−2−2−222222-22-22-2000000−2−222−2−222−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ392-2-2-2-22220000−2−2−2−222222-2-22-22000000−2−22222−2−222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ402-2-2-2-22220000−2−2−2−222222-2-22-22000000−2−22222−2−222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ412-2-2-2-22220000−2−2−2−22222-222-2-2200000022−2−2−2−22222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ422-2-2-2-22220000−2−2−2−22222-222-2-2200000022−2−2−2−22222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ432-2-2-2-22220000−2−2−2−22222-22-222-200000022−2−222−2−2−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ442-2-2-2-22220000−2−2−2−22222-22-222-200000022−2−222−2−2−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ45444-4-44-4-400002222−22−222222−22−2200000000004i−4i000000002i2−2i22i2−2i2000000000000000000000000
χ46444-4-44-4-400002222−22−222222−22−220000000000−4i4i00000000−2i22i2−2i22i2000000000000000000000000
χ47444-4-44-4-40000−22−222222−22−22222200000000004i−4i00000000−2i22i2−2i22i2000000000000000000000000
χ48444-4-44-4-40000−22−222222−22−2222220000000000−4i4i000000002i2−2i22i2−2i2000000000000000000000000
χ4944-44-4-44-4000022−2222−2222−2222−22000000004i−4i0000002i2−2i22i2−2i20000000000000000000000000000
χ5044-44-4-44-4000022−2222−2222−2222−2200000000−4i4i000000−2i22i2−2i22i20000000000000000000000000000
χ5144-44-4-44-40000−2222−2222−2222−2222000000004i−4i000000−2i22i2−2i22i20000000000000000000000000000
χ5244-44-4-44-40000−2222−2222−2222−222200000000−4i4i0000002i2−2i22i2−2i20000000000000000000000000000
χ5344-4-44-4-4444-4-4000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ5444-4-44-4-4444-4-400000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ5544-4-44-4-44-4-4444-4-444-4-44000000000000000000000000000000000000000000000000
χ5644-4-44-4-44-4-444-444-4-444-4000000000000000000000000000000000000000000000000
χ574-444-4-4-44000022−22−2222−222222−220000004i−4i00002i2−2i2−2i22i200000000000000000000000000000000
χ584-444-4-4-44000022−22−2222−222222−22000000−4i4i0000−2i22i22i2−2i200000000000000000000000000000000
χ594-444-4-4-440000−222222−2222−22−22220000004i−4i0000−2i22i22i2−2i200000000000000000000000000000000
χ604-444-4-4-440000−222222−2222−22−2222000000−4i4i00002i2−2i2−2i22i200000000000000000000000000000000
χ614-44-44-44-44-44-40000000000000000000000004i−4i−4i4i0000000000000000000000000000
χ624-44-44-44-44-44-4000000000000000000000000−4i4i4i−4i0000000000000000000000000000
χ634-44-44-44-4-44-444-44-4-44-44000000000000000000000000000000000000000000000000
χ644-44-44-44-4-44-44-44-444-44-4000000000000000000000000000000000000000000000000
χ654-4-4444-4-44-4-4444-4-4-4-444000000000000000000000000000000000000000000000000
χ664-4-4444-4-44-4-44-4-44444-4-4000000000000000000000000000000000000000000000000
χ674-4-4444-4-4-444-400000000000000000000000000004i−4i−4i4i000000000000000000000000
χ684-4-4444-4-4-444-40000000000000000000000000000−4i4i4i−4i000000000000000000000000

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