Finite Group Databasebeta

← Group #136366

Character table — Group #136366

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488882244444888824888888888161616161616161688888888881616161644
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111-1-111-1-111111-1-11-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111-1-111-1-111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ71111111111111111-1-111-1-111111-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111-1-111-1-111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111-1-1111-11-11111111-1-1-1-1-1-111-11-111-1-1ii−i−i1111-1-1-1-1i−iii−i−iii−i−i11-1-1i−i
χ101111-1-1111-11-11111111-1-1-1-1-1-111-11-111-1-1ii−i−i-1-1-1-11111i−iii−i−i−i−iii-1-111−ii
χ111111-1-1111-11-11111111-1-1-1-1-1-111-11-111-1-1−i−iii1111-1-1-1-1−ii−i−iii−i−iii11-1-1−ii
χ121111-1-1111-11-11111111-1-1-1-1-1-111-11-111-1-1−i−iii-1-1-1-11111−ii−i−iiiii−i−i-1-111i−i
χ131111-1-1111-11-11111-1-11-111-1-1-1111-1-1-1-111ii−i−i1111-1-1-1-1i−i−i−iiiii−i−i-1-111−ii
χ141111-1-1111-11-11111-1-11-111-1-1-1111-1-1-1-111ii−i−i-1-1-1-11111i−i−i−iii−i−iii11-1-1i−i
χ151111-1-1111-11-11111-1-11-111-1-1-1111-1-1-1-111−i−iii1111-1-1-1-1−iiii−i−i−i−iii-1-111i−i
χ161111-1-1111-11-11111-1-11-111-1-1-1111-1-1-1-111−i−iii-1-1-1-11111−iiii−i−iii−i−i11-1-1−ii
χ17222222222222-2-2-2-22222222-2-2-2-222-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-2-2-222-2-22-2-2-2-2-2-2-222220000000000000000000000000000
χ1922222222-2-2-2-2000022-2-2-2-2200002-2000000000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i200
χ2022222222-2-2-2-2000022-2-2-2-2200002-2000000000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i200
χ2122222222-2-2-2-20000-2-2-2-22220000-22000000000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i200
χ2222222222-2-2-2-20000-2-2-2-22220000-22000000000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i200
χ23222222-2-22222222200-2-200-222-2-200-20000222200000000-2-200000000000000
χ24222222-2-22222222200-2-200-222-2-200-20000-2-2-2-2000000002200000000000000
χ25222222-2-22222-2-2-2-200-2-200-2-2-2220020000000000000000002-22-20000000000
χ26222222-2-22222-2-2-2-200-2-200-2-2-222002000000000000000000-22-220000000000
χ272222-2-2222-22-2-2-2-2-2222-2-2-2-222-2-2-222-2-2220000000000000000000000000000
χ282222-2-2222-22-2-2-2-2-2-2-22-222-222-2-22-2222-2-20000000000000000000000000000
χ292222-2-222-22-22000022-2222-20000-2-2000000000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i200
χ302222-2-222-22-22000022-2222-20000-2-2000000000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i200
χ312222-2-222-22-220000-2-2-22-2-2-2000022000000000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i200
χ322222-2-222-22-220000-2-2-22-2-2-2000022000000000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i200
χ332222-2-2-2-22-22-2222200-22002-2-2-2-200200002i2i−2i−2i00000000−2i2i00000000000000
χ342222-2-2-2-22-22-2222200-22002-2-2-2-20020000−2i−2i2i2i000000002i−2i00000000000000
χ352222-2-2-2-22-22-2-2-2-2-200-22002222200-20000000000000000002i−2i−2i2i0000000000
χ362222-2-2-2-22-22-2-2-2-2-200-22002222200-2000000000000000000−2i2i2i−2i0000000000
χ372-2-222-200-2-22222-2-200000002-20000000002-22-2i2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2000000
χ382-2-222-200-2-22222-2-200000002-20000000002-22-2−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2000000
χ392-2-222-200-2-22222-2-200000002-2000000000-22-22i2−i2i2−i2i2−i2i2−i2000000−i2i2−i2i2000000
χ402-2-222-200-2-22222-2-200000002-2000000000-22-22−i2i2−i2i2−i2i2−i2i2000000i2−i2i2−i2000000
χ412-2-22-2200-222-222-2-20000000-220000000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2000000−222−2000000
χ422-2-22-2200-222-222-2-20000000-220000000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20000002−2−22000000
χ432-2-22-2200-222-222-2-20000000-22000000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20000002−2−22000000
χ442-2-22-2200-222-222-2-20000000-22000000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2000000−222−2000000
χ45444444-4-4-4-4-4-40000004400-4000000000000000000000000000000000000000
χ464444-4-4-4-4-44-440000004-4004000000000000000000000000000000000000000
χ4744-4-4004-400002i2−2i22i2−2i200004i−4i0002i2−2i20000022−220000000000000000000000000000
χ4844-4-4004-400002i2−2i22i2−2i20000−4i4i0002i2−2i200000−22220000000000000000000000000000
χ4944-4-4004-40000−2i22i2−2i22i200004i−4i000−2i22i200000−22220000000000000000000000000000
χ5044-4-4004-40000−2i22i2−2i22i20000−4i4i000−2i22i20000022−220000000000000000000000000000
χ5144-4-400-4400002i2−2i22i2−2i24-40000000−2i22i20002i2−2i2000000000000000000000000000000
χ5244-4-400-4400002i2−2i22i2−2i2-440000000−2i22i2000−2i22i2000000000000000000000000000000
χ5344-4-400-440000−2i22i2−2i22i24-400000002i2−2i2000−2i22i2000000000000000000000000000000
χ5444-4-400-440000−2i22i2−2i22i2-4400000002i2−2i20002i2−2i2000000000000000000000000000000
χ554-4-444-40044-4-4000000000000000000000000002-2-222-2-220000000000000000
χ564-4-444-40044-4-400000000000000000000000000-222-2-222-20000000000000000
χ574-4-444-400-4-444-4-4440000000-440000000000000000000000000000000000000
χ584-4-44-44004-4-44000000000000000000000000002-2-22-222-20000000000000000
χ594-4-44-44004-4-4400000000000000000000000000-222-22-2-220000000000000000
χ604-4-44-4400-444-4-4-44400000004-40000000000000000000000000000000000000
χ618-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ628-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

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