Finite Group Databasebeta

← Group #138228

Character table — Group #138228

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222222222222444444444444444444444444444444444488888888
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
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ91111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ121111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ131111111111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ141111111111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ151111111111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111111111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000000000
χ192222222222-2-2-2-222-2-22222-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-222-2-22200000000000000000000000000000000
χ212222-2-2-2-22222-2-2-2-22-222-2-222-2-200000000000000000000000000000000002−22−22−22−2
χ222222-2-2-2-22222-2-2-2-22-222-2-222-2-20000000000000000000000000000000000−22−22−22−22
χ232222-2-2-2-22222-2-2-2-22-2-2-222-2-2220000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ242222-2-2-2-22222-2-2-2-22-2-2-222-2-2220000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ252222-2-2-2-222-2-222-2-2-2222-2-2-2-2220000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ262222-2-2-2-222-2-222-2-2-2222-2-2-2-2220000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ272222-2-2-2-222-2-222-2-2-22-2-22222-2-200000000000000000000000000000000002−2−22−222−2
χ282222-2-2-2-222-2-222-2-2-22-2-22222-2-20000000000000000000000000000000000−222−22−2−22
χ292222-2-2-2-2-2-222-2-222-22000000002i2i−2i−2i2i−2i00001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000000000000000
χ302222-2-2-2-2-2-222-2-222-22000000002i2i−2i−2i2i−2i0000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000000000000000
χ312222-2-2-2-2-2-222-2-222-2200000000−2i−2i2i2i−2i2i00001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000000000000000
χ322222-2-2-2-2-2-222-2-222-2200000000−2i−2i2i2i−2i2i0000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000000000000000
χ332222-2-2-2-2-2-2-2-222222-2000000002i2i−2i−2i−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000000000000000
χ342222-2-2-2-2-2-2-2-222222-2000000002i2i−2i−2i−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000000000000000
χ352222-2-2-2-2-2-2-2-222222-200000000−2i−2i2i2i2i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000000000
χ362222-2-2-2-2-2-2-2-222222-200000000−2i−2i2i2i2i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000000000
χ3722-2-222-2-22-200002-2002-22-200002i−2i2i−2i00002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ3822-2-222-2-22-200002-2002-22-200002i−2i2i−2i00002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ3922-2-222-2-22-200002-2002-22-20000−2i2i−2i2i0000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4022-2-222-2-22-200002-2002-22-20000−2i2i−2i2i0000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4122-2-222-2-22-200002-200-22-2200002i−2i2i−2i0000−2i2i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i0000000000000000
χ4222-2-222-2-22-200002-200-22-2200002i−2i2i−2i0000−2i2i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i0000000000000000
χ4322-2-222-2-22-200002-200-22-220000−2i2i−2i2i00002i−2i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i0000000000000000
χ4422-2-222-2-22-200002-200-22-220000−2i2i−2i2i00002i−2i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i0000000000000000
χ4522-2-2-2-222-2200002-20000002-22-22-2-22002-20000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ4622-2-2-2-222-2200002-20000002-22-22-2-22002-2000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ4722-2-2-2-222-2200002-20000002-22-2-222-200-22002i−2i−2i2i00000000−2i2i2i−2i0000000000000000
χ4822-2-2-2-222-2200002-20000002-22-2-222-200-2200−2i2i2i−2i000000002i−2i−2i2i0000000000000000
χ4922-2-2-2-222-2200002-2000000-22-222-2-2200-22002-2-22000000002-2-220000000000000000
χ5022-2-2-2-222-2200002-2000000-22-222-2-2200-2200-222-200000000-222-20000000000000000
χ5122-2-2-2-222-2200002-2000000-22-22-222-2002-20000002-2-222-2-2200000000000000000000
χ5222-2-2-2-222-2200002-2000000-22-22-222-2002-2000000-222-2-222-200000000000000000000
χ5344444444-4-44444-4-4-4-400000000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ5544-4-444-4-4-440000-440000004-4-44000000000000000000000000000000000000000000
χ5644-4-444-4-4-440000-44000000-444-4000000000000000000000000000000000000000000
χ5744-4-4-4-4444-40000-44004-4-440000000000000000000000000000000000000000000000
χ5844-4-4-4-4444-40000-4400-444-40000000000000000000000000000000000000000000000
χ594-44-44-44-4004-44-40000000000000000000000000000000000000000002i−2i2i−2i00000000
χ604-44-44-44-4004-44-4000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ614-44-44-44-400-44-440000000000000000000000000000000000000000002i−2i−2i2i00000000
χ624-44-44-44-400-44-44000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ634-44-4-44-44004-4-44000000000000000000000000000000000000002-22-2000000000000
χ644-44-4-44-44004-4-4400000000000000000000000000000000000000-22-22000000000000
χ654-44-4-44-4400-444-4000000000000000000000000000000000000002-2-22000000000000
χ664-44-4-44-4400-444-400000000000000000000000000000000000000-222-2000000000000
χ678-8-888-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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