Finite Group Databasebeta

← Group #101080

Character table — Group #101080

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ121111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ131111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ192222222222-2-222-2-2-2-22222-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-222222222-2-222-2-200000000000000000000000000000000
χ2122222222-2-222-2-222-2-20000000022-2-22-200000000000022-2-222-2-20000000000000000
χ2222222222-2-222-2-222-2-20000000022-2-22-2000000000000-2-222-2-2220000000000000000
χ2322222222-2-222-2-222-2-200000000-2-222-22000022-2-222-2-2000000000000000000000000
χ2422222222-2-222-2-222-2-200000000-2-222-220000-2-222-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2220000000022-2-2-2200002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2220000000022-2-2-220000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22200000000-2-2222-20000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-22200000000-2-2222-2000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2922-2-222-2-22-2002-2000000002i2i−2i−2i2i−2i2i−2i002-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ3022-2-222-2-22-2002-2000000002i2i−2i−2i2i−2i2i−2i002-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ3122-2-222-2-22-2002-2000000002i2i−2i−2i−2i2i−2i2i00-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ3222-2-222-2-22-2002-2000000002i2i−2i−2i−2i2i−2i2i00-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ3322-2-222-2-22-2002-200000000−2i−2i2i2i2i−2i2i−2i00-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ3422-2-222-2-22-2002-200000000−2i−2i2i2i2i−2i2i−2i00-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ3522-2-222-2-22-2002-200000000−2i−2i2i2i−2i2i−2i2i002-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ3622-2-222-2-22-2002-200000000−2i−2i2i2i−2i2i−2i2i002-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ3722-2-222-2-2-2200-2200002i2i−2i−2i00002i−2i−2i2i00002-21−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ3822-2-222-2-2-2200-2200002i2i−2i−2i00002i−2i−2i2i00002-2−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ3922-2-222-2-2-2200-2200002i2i−2i−2i0000−2i2i2i−2i0000-221+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ4022-2-222-2-2-2200-2200002i2i−2i−2i0000−2i2i2i−2i0000-22−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ4122-2-222-2-2-2200-220000−2i−2i2i2i00002i−2i−2i2i0000-221−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ4222-2-222-2-2-2200-220000−2i−2i2i2i00002i−2i−2i2i0000-22−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ4322-2-222-2-2-2200-220000−2i−2i2i2i0000−2i2i2i−2i00002-21+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ4422-2-222-2-2-2200-220000−2i−2i2i2i0000−2i2i2i−2i00002-2−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ452-22-22-2-22-2-22222-2-22-22-22-22-22-20000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ462-22-22-2-22-2-22222-2-22-22-22-22-22-20000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ472-22-22-2-22-2-22222-2-22-2-22-22-22-220000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ482-22-22-2-22-2-22222-2-22-2-22-22-22-220000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ492-22-22-2-22-2-2-2-22222-222-22-2-22-2200000000000000000000000000000000002−2−222−2−22
χ502-22-22-2-22-2-2-2-22222-222-22-2-22-220000000000000000000000000000000000−222−2−222−2
χ512-22-22-2-22-2-2-2-22222-22-22-222-22-200000000000000000000000000000000002−2−22−222−2
χ522-22-22-2-22-2-2-2-22222-22-22-222-22-20000000000000000000000000000000000−222−22−2−22
χ534444-4-4-4-4004-4004-400000000000000000000000000000000000000002-22-200000000
χ544444-4-4-4-4004-4004-40000000000000000000000000000000000000000-22-2200000000
χ554444-4-4-4-400-4400-4400000000000000000000000000000000000000002-2-2200000000
χ564444-4-4-4-400-4400-440000000000000000000000000000000000000000-222-200000000
χ574-44-44-4-444444-4-4-4-4-4400000000000000000000000000000000000000000000000000
χ584-44-44-4-4444-4-4-4-4444-400000000000000000000000000000000000000000000000000
χ594-44-4-444-4004-400-440000000000000000000000000000000000002i−2i2i−2i000000000000
χ604-44-4-444-4004-400-44000000000000000000000000000000000000−2i2i−2i2i000000000000
χ614-44-4-444-400-44004-40000000000000000000000000000000000002i−2i−2i2i000000000000
χ624-44-4-444-400-44004-4000000000000000000000000000000000000−2i2i2i−2i000000000000
χ634-4-444-44-44-400-4400004i−4i−4i4i0000000000000000000000000000000000000000000000
χ644-4-444-44-44-400-440000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ654-4-444-44-4-44004-4000000004i−4i−4i4i000000000000000000000000000000000000000000
χ664-4-444-44-4-44004-400000000−4i4i4i−4i000000000000000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-88-88-88000000000000000000000000000000000000000000000000000000000000

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