Finite Group Databasebeta

← Group #264809

Character table — Group #264809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order12222244444444888844888888888888888888888822444444224444448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-1-1-1-11-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-1-1-11-1-11-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-11-1-11-1-1-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11111-111-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-111-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-111111-1-111-1-1
χ911111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-11-11-111-1-1-1-1111-1
χ1011111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-11-11-1-1-11-1-111-1-111-11
χ1111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-111111-1-111-1-1-11
χ1211111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11111-1-1-1-11111-1-11-1
χ1311111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11-11-1111-1-1-111-1-1-1-1-11
χ1411111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-11-11-1111-1-1-1-1-1-11-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-11-1-1-1-111-1-11111111-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1-1-111-1-11111-11
χ17222222-2-2-2222-222222-2-2-2-2-2-200000000220000000000220022000-200-200000000000
χ18222222-2-2-2222-222222-2-2-2-2-2-200000000220000000000-2-200-2-2000200200000000000
χ19222222-2-2-2222-22-2-2-2-2-2-2222200000000-2-200000000002200-2-2000200-200000000000
χ20222222-2-2-2222-22-2-2-2-2-2-2222200000000-2-20000000000-2-20022000-200200000000000
χ21222222-2-2-2-2-2-2-2-200002200002i2i2i2i−2i−2i−2i−2i00000000002-2002-200000000000000002i−2i00
χ22222222-2-2-2-2-2-2-2-200002200002i2i2i2i−2i−2i−2i−2i0000000000-2200-220000000000000000−2i2i00
χ23222222-2-2-2-2-2-2-2-20000220000−2i−2i−2i−2i2i2i2i2i00000000002-2002-20000000000000000−2i2i00
χ24222222-2-2-2-2-2-2-2-20000220000−2i−2i−2i−2i2i2i2i2i0000000000-2200-2200000000000000002i−2i00
χ252222-2-22-2-22-2-22222222-222-2-200000000-2-200000000000000000220-200-20000000000
χ262222-2-22-2-22-2-22222222-222-2-200000000-2-200000000000000000-2-2020020000000000
χ272222-2-22-2-22-2-222-2-2-2-22-2-2-2220000000022000000000000000002-20200-20000000000
χ282222-2-22-2-22-2-222-2-2-2-22-2-2-222000000002200000000000000000-220-20020000000000
χ292222-2-22-2-2-2222-20000-22000000000000002222-2-2-2-22200-2-20020000-2000000000000
χ302222-2-22-2-2-2222-20000-22000000000000002222-2-2-2-2-2-2002200-200002000000000000
χ312222-2-22-2-2-2222-20000-2200000000000000-2-2-2-222222200-2-200-200002000000000000
χ322222-2-22-2-2-2222-20000-2200000000000000-2-2-2-22222-2-200220020000-2000000000000
χ332222-2-2-2222-2-2-222222-22-2-22200000000-2-2000000002-200-22000000000000002-20000
χ342222-2-2-2222-2-2-222222-22-2-22200000000-2-200000000-22002-200000000000000-220000
χ352222-2-2-2222-2-2-22-2-2-2-2-2222-2-20000000022000000002-200-2200000000000000-220000
χ362222-2-2-2222-2-2-22-2-2-2-2-2222-2-2000000002200000000-22002-2000000000000002-20000
χ372-2-222-200022-20-22i2i−2i−2i000000i2i2−i2−i2i2i2−i2−i22i−2i22−2−222−2−2002i−2i002-2000000002−2i2−i2000000
χ382-2-222-200022-20-22i2i−2i−2i000000i2i2−i2−i2i2i2−i2−i22i−2i22−2−222−2−200−2i2i00-2200000000−22−i2i2000000
χ392-2-222-200022-20-22i2i−2i−2i000000−i2−i2i2i2−i2−i2i2i22i−2i−2−222−2−222002i−2i002-200000000−22−i2i2000000
χ402-2-222-200022-20-22i2i−2i−2i000000−i2−i2i2i2−i2−i2i2i22i−2i−2−222−2−22200−2i2i00-22000000002−2i2−i2000000
χ412-2-222-200022-20-2−2i−2i2i2i000000i2i2−i2−i2i2i2−i2−i2−2i2i−2−222−2−222002i−2i00-22000000002−2−i2i2000000
χ422-2-222-200022-20-2−2i−2i2i2i000000i2i2−i2−i2i2i2−i2−i2−2i2i−2−222−2−22200−2i2i002-200000000−22i2−i2000000
χ432-2-222-200022-20-2−2i−2i2i2i000000−i2−i2i2i2−i2−i2i2i2−2i2i22−2−222−2−2002i−2i00-2200000000−22i2−i2000000
χ442-2-222-200022-20-2−2i−2i2i2i000000−i2−i2i2i2−i2−i2i2i2−2i2i22−2−222−2−200−2i2i002-2000000002−2−i2i2000000
χ45444444444-4-4-44-40000-4-4000000000000000000000000000000000000000000000000
χ464444-4-4-444-444-4-400004-4000000000000000000000000000000000000000000000000
χ4744-4-400400000-4022−2222−220022−22002-22-22-22-20022−2222−22000000000000000000000000000000
χ4844-4-400400000-4022−2222−220022−2200-22-22-22-2200−2222−2222000000000000000000000000000000
χ4944-4-400400000-40−2222−222200−2222002-22-22-22-200−2222−2222000000000000000000000000000000
χ5044-4-400400000-40−2222−222200−222200-22-22-22-220022−2222−22000000000000000000000000000000
χ5144-4-400-4000004022−2222−2200−2222002i−2i2i−2i−2i2i−2i2i0000002i2−2i22i2−2i200000000000000000000000000
χ5244-4-400-4000004022−2222−2200−222200−2i2i−2i2i2i−2i2i−2i000000−2i22i2−2i22i200000000000000000000000000
χ5344-4-400-40000040−2222−22220022−22002i−2i2i−2i−2i2i−2i2i000000−2i22i2−2i22i200000000000000000000000000
χ5444-4-400-40000040−2222−22220022−2200−2i2i−2i2i2i−2i2i−2i0000002i2−2i22i2−2i200000000000000000000000000
χ554-44-40004i−4i000002i2−2i2−2i22i2000022−222ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3002-2-22−2i2i2i−2i00000000000000000000000000
χ564-44-40004i−4i000002i2−2i2−2i22i2000022−22−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300-222-22i−2i−2i2i00000000000000000000000000
χ574-44-40004i−4i00000−2i22i22i2−2i20000−22222ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300-222-22i−2i−2i2i00000000000000000000000000
χ584-44-40004i−4i00000−2i22i22i2−2i20000−2222−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3002-2-22−2i2i2i−2i00000000000000000000000000
χ594-44-4000−4i4i000002i2−2i2−2i22i20000−22222ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ002-2-222i−2i−2i2i00000000000000000000000000
χ604-44-4000−4i4i000002i2−2i2−2i22i20000−2222−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00-222-2−2i2i2i−2i00000000000000000000000000
χ614-44-4000−4i4i00000−2i22i22i2−2i2000022−222ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00-222-2−2i2i2i−2i00000000000000000000000000
χ624-44-4000−4i4i00000−2i22i22i2−2i2000022−22−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ002-2-222i−2i−2i2i00000000000000000000000000
χ634-4-444-4000-4-440400000000002222−22−22−22−222222000000000000000000000000000000000000
χ644-4-444-4000-4-44040000000000−22−2222222222−22−22000000000000000000000000000000000000
χ654-4-44-440004-440-44i4i−4i−4i00000000000000−4i4i0000000000000000000000000000000000
χ664-4-44-440004-440-4−4i−4i4i4i000000000000004i−4i0000000000000000000000000000000000
χ674-4-44-44000-44-404000000000000000000002222−22−22−22−22222200000000000000000000000000
χ684-4-44-44000-44-40400000000000000000000−22−2222222222−22−2200000000000000000000000000

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