Finite Group Databasebeta

← Group #134594

Character table — Group #134594

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order1222224444444488888888444444444488888888888844448888888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-1111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ10111111-1-1111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ11111111-1-1111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111ii−i−iii−i−i-1-111−i−iii−i−iii
χ12111111-1-1111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111−i−iii−i−iii-1-111ii−i−iii−i−i
χ13111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ14111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ15111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ16111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ1722222222222222-2-22222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ19222222-2-2222-2-2222222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000
χ20222222-2-2222-2-2222-2-2-2-222-2-22222-2-2-2-2-2-2-2-222-2-22222000000000000000000000000
χ212222-2-22222-2-2-2-2220000222-20000000022-2-2-2-20000000000000000002i−2i2i−2i00000000
χ222222-2-22222-2-2-2-2220000222-20000000022-2-2-2-2000000000000000000−2i2i−2i2i00000000
χ232222-2-22222-2-2-2-2-2-20000-2-22-200000000-2-222220000002-22-200000000000000000000
χ242222-2-22222-2-2-2-2-2-20000-2-22-200000000-2-22222000000-22-2200000000000000000000
χ252222-2-222-2-22-2-2200222200-2200000000000000-2-222-2-20000000000000000i2−i2i2−i2i2−i2i2−i2
χ262222-2-222-2-22-2-2200222200-2200000000000000-2-222-2-20000000000000000−i2i2−i2i2−i2i2−i2i2
χ272222-2-222-2-22-2-2200-2-2-2-200-220000000000000022-2-2220000000000000000i2−i2i2−i2−i2i2−i2i2
χ282222-2-222-2-22-2-2200-2-2-2-200-220000000000000022-2-2220000000000000000−i2i2−i2i2i2−i2i2−i2
χ292222-2-2-2-222-222-222000022-2200000000-2-222-2-20000002-2-2200000000000000000000
χ302222-2-2-2-222-222-222000022-2200000000-2-222-2-2000000-222-200000000000000000000
χ312222-2-2-2-222-222-2-2-20000-2-2-220000000022-2-2220000000000000000002i−2i−2i2i00000000
χ322222-2-2-2-222-222-2-2-20000-2-2-220000000022-2-222000000000000000000−2i2i2i−2i00000000
χ332222-2-2-2-2-2-22222002222002-200000000000000-2-2-2-22200000000000000002−2−222−2−22
χ342222-2-2-2-2-2-22222002222002-200000000000000-2-2-2-2220000000000000000−222−2−222−2
χ352222-2-2-2-2-2-2222200-2-2-2-2002-2000000000000002222-2-200000000000000002−2−22−222−2
χ362222-2-2-2-2-2-2222200-2-2-2-2002-2000000000000002222-2-20000000000000000−222−22−2−22
χ3722-2-22-2002-2200-22222-2-2-2-200000022-2-200002-22-2000000002−22−22−22−2000000000000
χ3822-2-22-2002-2200-22222-2-2-2-200000022-2-200002-22-200000000−22−22−22−22000000000000
χ3922-2-22-2002-2200-222-2-222-2-2000000-2-22200002-2-22000000002−22−2−22−22000000000000
χ4022-2-22-2002-2200-222-2-222-2-2000000-2-22200002-2-2200000000−22−222−22−2000000000000
χ4122-2-22-2002-2200-2-2-222-2-222000000-2-2220000-222-200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ4222-2-22-2002-2200-2-2-222-2-222000000-2-2220000-222-200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ4322-2-22-2002-2200-2-2-2-2-2222200000022-2-20000-22-2200000000i2−i2−i2i2−i2i2i2−i2000000000000
χ4422-2-22-2002-2200-2-2-2-2-2222200000022-2-20000-22-2200000000−i2i2i2−i2i2−i2−i2i2000000000000
χ4544444444-4-4-444-400000000-4-400000000000000000000000000000000000000000000
χ46444444-4-4-4-4-4-4-4-4000000004400000000000000000000000000000000000000000000
χ4744-4-44-400-44-400400000000004i4i−4i−4i0000000000000000000000000000000000000000
χ4844-4-44-400-44-40040000000000−4i−4i4i4i0000000000000000000000000000000000000000
χ4944-4-4-44004-4-4004440000-4-400000000000000-44000000000000000000000000000000
χ5044-4-4-44004-4-4004-4-4000044000000000000004-4000000000000000000000000000000
χ5144-4-4-4400-44400-40044-4-4000000000000000000-440000000000000000000000000000
χ5244-4-4-4400-44400-400-4-4440000000000000000004-40000000000000000000000000000
χ534-44-400000004-4022−222i2−2i22i2−2i222−22002i−2i2i−2i2i−2i2i−2i0022−220000002i2−2i2000000000000000000000000
χ544-44-400000004-4022−22−2i22i2−2i22i222−2200−2i2i−2i2i−2i2i−2i2i0022−22000000−2i22i2000000000000000000000000
χ554-44-400000004-40−22222i2−2i22i2−2i2−222200−2i2i−2i2i−2i2i−2i2i00−22220000002i2−2i2000000000000000000000000
χ564-44-400000004-40−2222−2i22i2−2i22i2−2222002i−2i2i−2i2i−2i2i−2i00−2222000000−2i22i2000000000000000000000000
χ574-44-40000000-44022−222i2−2i22i2−2i222−2200−2i2i−2i2i2i−2i2i−2i00−2222000000−2i22i2000000000000000000000000
χ584-44-40000000-44022−22−2i22i2−2i22i222−22002i−2i2i−2i−2i2i−2i2i00−22220000002i2−2i2000000000000000000000000
χ594-44-40000000-440−22222i2−2i22i2−2i2−2222002i−2i2i−2i−2i2i−2i2i0022−22000000−2i22i2000000000000000000000000
χ604-44-40000000-440−2222−2i22i2−2i22i2−222200−2i2i−2i2i2i−2i2i−2i0022−220000002i2−2i2000000000000000000000000
χ614-4-44004i−4i00000022−222i2−2i2−2i22i2−2222002-2-222i−2i−2i2i2i2−2i200000022−2200000000000000000000000000
χ624-4-44004i−4i00000022−22−2i22i22i2−2i2−222200-222-2−2i2i2i−2i2i2−2i2000000−222200000000000000000000000000
χ634-4-44004i−4i000000−22222i2−2i2−2i22i222−2200-222-2−2i2i2i−2i−2i22i200000022−2200000000000000000000000000
χ644-4-44004i−4i000000−2222−2i22i22i2−2i222−22002-2-222i−2i−2i2i−2i22i2000000−222200000000000000000000000000
χ654-4-4400−4i4i00000022−222i2−2i2−2i22i2−222200-222-22i−2i−2i2i−2i22i2000000−222200000000000000000000000000
χ664-4-4400−4i4i00000022−22−2i22i22i2−2i2−2222002-2-22−2i2i2i−2i−2i22i200000022−2200000000000000000000000000
χ674-4-4400−4i4i000000−22222i2−2i2−2i22i222−22002-2-22−2i2i2i−2i2i2−2i2000000−222200000000000000000000000000
χ684-4-4400−4i4i000000−2222−2i22i22i2−2i222−2200-222-22i−2i−2i2i2i2−2i200000022−2200000000000000000000000000

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