Finite Group Databasebeta

← Group #134607

Character table — Group #134607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order1222224444444488888888444444444488888888888822448888888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-11111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-11-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-1-11111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-11-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-1-11111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111-1-1-11111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-11-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-11-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-11-1111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-11-1111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ19222222-2-2-22222-222222222-2-2-2-2-2-22222-2-2-2-222-2-2-2-222000000000000000000000000
χ20222222-2-2-22222-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000
χ212222-2-222-222-2-2-2000022222-20000000022-2-2-2-200000000002i−2i2i−2i0000000000000000
χ222222-2-222-222-2-2-2000022222-20000000022-2-2-2-20000000000−2i2i−2i2i0000000000000000
χ232222-2-222-222-2-2-20000-2-2-2-22-200000000-2-222220000002-2-2200000000000000000000
χ242222-2-222-222-2-2-20000-2-2-2-22-200000000-2-22222000000-222-200000000000000000000
χ252222-2-222-2-2-222-222220000-220000000000000022-2-2-2-20000000000000000i2−i2i2−i2i2−i2i2−i2
χ262222-2-222-2-2-222-222220000-220000000000000022-2-2-2-20000000000000000−i2i2−i2i2−i2i2−i2i2
χ272222-2-222-2-2-222-2-2-2-2-20000-2200000000000000-2-222220000000000000000i2−i2i2−i2−i2i2−i2i2
χ282222-2-222-2-2-222-2-2-2-2-20000-2200000000000000-2-222220000000000000000−i2i2−i2i2i2−i2i2−i2
χ292222-2-2-2-2222-2-2200002222-2200000000-2-222-2-200000022-2-200000000000000000000
χ302222-2-2-2-2222-2-2200002222-2200000000-2-222-2-2000000-2-22200000000000000000000
χ312222-2-2-2-2222-2-220000-2-2-2-2-220000000022-2-22200000000002i−2i−2i2i0000000000000000
χ322222-2-2-2-2222-2-220000-2-2-2-2-220000000022-2-2220000000000−2i2i2i−2i0000000000000000
χ332222-2-2-2-22-2-2222222200002-200000000000000-2-222-2-200000000000000002−2−222−2−22
χ342222-2-2-2-22-2-2222222200002-200000000000000-2-222-2-20000000000000000−222−2−222−2
χ352222-2-2-2-22-2-2222-2-2-2-200002-20000000000000022-2-22200000000000000002−2−22−222−2
χ362222-2-2-2-22-2-2222-2-2-2-200002-20000000000000022-2-2220000000000000000−222−22−2−22
χ372-2-222-20002-22-202i2i−2i−2i22-2-20000002i2i−2i−2i00002-200002i−2i00000000i2−i2i2−i22−22−200000000
χ382-2-222-20002-22-202i2i−2i−2i22-2-20000002i2i−2i−2i00002-200002i−2i00000000−i2i2−i2i2−22−2200000000
χ392-2-222-20002-22-202i2i−2i−2i-2-222000000−2i−2i2i2i0000-2200002i−2i000000002−2−22−i2i2i2−i200000000
χ402-2-222-20002-22-202i2i−2i−2i-2-222000000−2i−2i2i2i0000-2200002i−2i00000000−222−2i2−i2−i2i200000000
χ412-2-222-20002-22-20−2i−2i2i2i22-2-2000000−2i−2i2i2i00002-20000−2i2i00000000i2−i2i2−i2−22−2200000000
χ422-2-222-20002-22-20−2i−2i2i2i22-2-2000000−2i−2i2i2i00002-20000−2i2i00000000−i2i2−i2i22−22−200000000
χ432-2-222-20002-22-20−2i−2i2i2i-2-2220000002i2i−2i−2i0000-220000−2i2i000000002−2−22i2−i2−i2i200000000
χ442-2-222-20002-22-20−2i−2i2i2i-2-2220000002i2i−2i−2i0000-220000−2i2i00000000−222−2−i2i2i2−i200000000
χ45444444444-4-4-4-4400000000-4-400000000000000000000000000000000000000000000
χ46444444-4-4-4-4-4-4-4-4000000004400000000000000000000000000000000000000000000
χ4744-4-4000040000-422−2222−2222−2222−220022-2-22-22-20022−22000022−2200000000000000000000000000
χ4844-4-4000040000-422−2222−22−2222−222200-2-222-22-2200−2222000022−2200000000000000000000000000
χ4944-4-4000040000-4−2222−222222−2222−2200-2-222-22-220022−220000−222200000000000000000000000000
χ5044-4-4000040000-4−2222−2222−2222−22220022-2-22-22-200−22220000−222200000000000000000000000000
χ5144-4-40000-40000422−2222−2222−2222−2200-2-2222-22-200−22220000−222200000000000000000000000000
χ5244-4-40000-40000422−2222−22−2222−22220022-2-2-22-220022−220000−222200000000000000000000000000
χ5344-4-40000-400004−2222−222222−2222−220022-2-2-22-2200−2222000022−2200000000000000000000000000
χ5444-4-40000-400004−2222−2222−2222−222200-2-2222-22-20022−22000022−2200000000000000000000000000
χ554-44-4004i−4i0000002i2−2i2−2i22i222−22−2222002-22-22i−2i−2i2i2i2−2i2000022−220000000000000000000000000000
χ564-44-4004i−4i0000002i2−2i2−2i22i2−222222−2200-22-22−2i2i2i−2i−2i22i2000022−220000000000000000000000000000
χ574-44-4004i−4i000000−2i22i22i2−2i222−22−222200-22-22−2i2i2i−2i2i2−2i20000−22220000000000000000000000000000
χ584-44-4004i−4i000000−2i22i22i2−2i2−222222−22002-22-22i−2i−2i2i−2i22i20000−22220000000000000000000000000000
χ594-44-400−4i4i0000002i2−2i2−2i22i222−22−222200-22-222i−2i−2i2i−2i22i20000−22220000000000000000000000000000
χ604-44-400−4i4i0000002i2−2i2−2i22i2−222222−22002-22-2−2i2i2i−2i2i2−2i20000−22220000000000000000000000000000
χ614-44-400−4i4i000000−2i22i22i2−2i222−22−2222002-22-2−2i2i2i−2i−2i22i2000022−220000000000000000000000000000
χ624-44-400−4i4i000000−2i22i22i2−2i2−222222−2200-22-222i−2i−2i2i2i2−2i2000022−220000000000000000000000000000
χ634-4-444-4000-44-44000000000004-4-440000000000000000000000000000000000000000
χ644-4-444-4000-44-4400000000000-444-40000000000000000000000000000000000000000
χ654-4-44-440004-4-440000044-4-400000000000000-44000000000000000000000000000000
χ664-4-44-440004-4-4400000-4-444000000000000004-4000000000000000000000000000000
χ674-4-44-44000-444-404i4i−4i−4i000000000000000000000000−4i4i000000000000000000000000
χ684-4-44-44000-444-40−4i−4i4i4i0000000000000000000000004i−4i000000000000000000000000

Here i is the imaginary unit (i² = −1).