Finite Group Databasebeta

← Group #357613

Character table — Group #357613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222222288888888888888888888888888881111222222222222228888888888888888888888888888
order12222222224444444422224444444488888888888888882222222222444444442222444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i1111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii1111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ121111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ131111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−i−i−iii−i−iii1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−i−i−iii−i−iii
χ141111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i
χ151111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-2-2-2222-2-22-2-20000000000000000000000002i−2i2i−2i222222-2-2-2-2222-2-22-2-20000000000000000000000002i−2i2i−2i
χ18222222-2-2-2-2222-2-22-2-2000000000000000000000000−2i2i−2i2i222222-2-2-2-2222-2-22-2-2000000000000000000000000−2i2i−2i2i
χ19222222-2-2-2-2-2-2-222-2220000000000000000000000002-2-22222222-2-2-2-2-2-2-222-2220000000000000000000000002-2-22
χ20222222-2-2-2-2-2-2-222-222000000000000000000000000-222-2222222-2-2-2-2-2-2-222-222000000000000000000000000-222-2
χ212222-2-222-2-222-22-2-22-2000000000000000000002i−2i2i−2i00002222-2-222-2-222-22-2-22-2000000000000000000002i−2i2i−2i0000
χ222222-2-222-2-222-22-2-22-200000000000000000000−2i2i−2i2i00002222-2-222-2-222-22-2-22-200000000000000000000−2i2i−2i2i0000
χ232222-2-222-2-2-2-22-222-22000000000000000000002-2-2200002222-2-222-2-2-2-22-222-22000000000000000000002-2-220000
χ242222-2-222-2-2-2-22-222-2200000000000000000000-222-200002222-2-222-2-2-2-22-222-2200000000000000000000-222-20000
χ252222-2-2-2-22222-2-22-2-2200002-22-2000000000000000000002222-2-2-2-22222-2-22-2-2200002-22-200000000000000000000
χ262222-2-2-2-22222-2-22-2-220000-22-22000000000000000000002222-2-2-2-22222-2-22-2-220000-22-2200000000000000000000
χ272222-2-2-2-222-2-222-222-200002-2-22000000000000000000002222-2-2-2-222-2-222-222-200002-2-2200000000000000000000
χ282222-2-2-2-222-2-222-222-20000-222-2000000000000000000002222-2-2-2-222-2-222-222-20000-222-200000000000000000000
χ2922-2-22-22-22-22-2222-2-2-22-22-200000000000000000000000022-2-22-22-22-22-2222-2-2-22-22-2000000000000000000000000
χ3022-2-22-22-22-22-2222-2-2-2-22-2200000000000000000000000022-2-22-22-22-22-2222-2-2-2-22-22000000000000000000000000
χ3122-2-22-22-22-2-22-2-2-22222-2-2200000000000000000000000022-2-22-22-22-2-22-2-2-22222-2-22000000000000000000000000
χ3222-2-22-22-22-2-22-2-2-2222-222-200000000000000000000000022-2-22-22-22-2-22-2-2-2222-222-2000000000000000000000000
χ3322-2-22-2-22-222-22-2-2-22200000000000000002-22-20000000022-2-22-2-22-222-22-2-2-22200000000000000002-22-200000000
χ3422-2-22-2-22-222-22-2-2-2220000000000000000-22-220000000022-2-22-2-22-222-22-2-2-2220000000000000000-22-2200000000
χ3522-2-22-2-22-22-22-2222-2-200000000000000002i−2i−2i2i0000000022-2-22-2-22-22-22-2222-2-200000000000000002i−2i−2i2i00000000
χ3622-2-22-2-22-22-22-2222-2-20000000000000000−2i2i2i−2i0000000022-2-22-2-22-22-22-2222-2-20000000000000000−2i2i2i−2i00000000
χ3722-2-2-222-2-222-2-22-22-220000000000002-22-200000000000022-2-2-222-2-222-2-22-22-220000000000002-22-2000000000000
χ3822-2-2-222-2-222-2-22-22-22000000000000-22-2200000000000022-2-2-222-2-222-2-22-22-22000000000000-22-22000000000000
χ3922-2-2-222-2-22-222-22-22-20000000000002i−2i−2i2i00000000000022-2-2-222-2-22-222-22-22-20000000000002i−2i−2i2i000000000000
χ4022-2-2-222-2-22-222-22-22-2000000000000−2i2i2i−2i00000000000022-2-2-222-2-22-222-22-22-2000000000000−2i2i2i−2i000000000000
χ4122-2-2-22-222-22-2-2-2222-2000000002i−2i2i−2i000000000000000022-2-2-22-222-22-2-2-2222-2000000002i−2i2i−2i0000000000000000
χ4222-2-2-22-222-22-2-2-2222-200000000−2i2i−2i2i000000000000000022-2-2-22-222-22-2-2-2222-200000000−2i2i−2i2i0000000000000000
χ4322-2-2-22-222-2-2222-2-2-22000000002i−2i−2i2i000000000000000022-2-2-22-222-2-2222-2-2-22000000002i−2i−2i2i0000000000000000
χ4422-2-2-22-222-2-2222-2-2-2200000000−2i2i2i−2i000000000000000022-2-2-22-222-2-2222-2-2-2200000000−2i2i2i−2i0000000000000000
χ458-88-80000000000000000000000000000000000000000008-88-8000000000000000000000000000000000000000000
χ468-8-880000000000000000000000000000000000000000008-8-88000000000000000000000000000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ48111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ491111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ501111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ51111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ52111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ53111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ54111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ551111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iii
χ561111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i
χ571111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ581111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ591111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−i−i−iii−i−iii-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i
χ601111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii
χ611111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ621111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ63222222-2-2-2-2222-2-22-2-20000000000000000000000002i−2i2i−2i-2-2-2-2-2-22222-2-2-222-222000000000000000000000000−2i2i−2i2i
χ64222222-2-2-2-2222-2-22-2-2000000000000000000000000−2i2i−2i2i-2-2-2-2-2-22222-2-2-222-2220000000000000000000000002i−2i2i−2i
χ65222222-2-2-2-2-2-2-222-2220000000000000000000000002-2-22-2-2-2-2-2-22222222-2-22-2-2000000000000000000000000-222-2
χ66222222-2-2-2-2-2-2-222-222000000000000000000000000-222-2-2-2-2-2-2-22222222-2-22-2-20000000000000000000000002-2-22
χ672222-2-222-2-222-22-2-22-2000000000000000000002i−2i2i−2i0000-2-2-2-222-2-222-2-22-222-2200000000000000000000−2i2i−2i2i0000
χ682222-2-222-2-222-22-2-22-200000000000000000000−2i2i−2i2i0000-2-2-2-222-2-222-2-22-222-22000000000000000000002i−2i2i−2i0000
χ692222-2-222-2-2-2-22-222-22000000000000000000002-2-220000-2-2-2-222-2-22222-22-2-22-200000000000000000000-222-20000
χ702222-2-222-2-2-2-22-222-2200000000000000000000-222-20000-2-2-2-222-2-22222-22-2-22-2000000000000000000002-2-220000
χ712222-2-2-2-22222-2-22-2-2200002-22-200000000000000000000-2-2-2-22222-2-2-2-222-222-20000-22-2200000000000000000000
χ722222-2-2-2-22222-2-22-2-220000-22-2200000000000000000000-2-2-2-22222-2-2-2-222-222-200002-22-200000000000000000000
χ732222-2-2-2-222-2-222-222-200002-2-2200000000000000000000-2-2-2-22222-2-222-2-22-2-220000-222-200000000000000000000
χ742222-2-2-2-222-2-222-222-20000-222-200000000000000000000-2-2-2-22222-2-222-2-22-2-2200002-2-2200000000000000000000
χ7522-2-22-22-22-22-2222-2-2-22-22-2000000000000000000000000-2-222-22-22-22-22-2-2-2222-22-22000000000000000000000000
χ7622-2-22-22-22-22-2222-2-2-2-22-22000000000000000000000000-2-222-22-22-22-22-2-2-22222-22-2000000000000000000000000
χ7722-2-22-22-22-2-22-2-2-22222-2-22000000000000000000000000-2-222-22-22-222-2222-2-2-2-222-2000000000000000000000000
χ7822-2-22-22-22-2-22-2-2-2222-222-2000000000000000000000000-2-222-22-22-222-2222-2-2-22-2-22000000000000000000000000
χ7922-2-22-2-22-222-22-2-2-22200000000000000002-22-200000000-2-222-222-22-2-22-2222-2-20000000000000000-22-2200000000
χ8022-2-22-2-22-222-22-2-2-2220000000000000000-22-2200000000-2-222-222-22-2-22-2222-2-200000000000000002-22-200000000
χ8122-2-22-2-22-22-22-2222-2-200000000000000002i−2i−2i2i00000000-2-222-222-22-22-22-2-2-2220000000000000000−2i2i2i−2i00000000
χ8222-2-22-2-22-22-22-2222-2-20000000000000000−2i2i2i−2i00000000-2-222-222-22-22-22-2-2-22200000000000000002i−2i−2i2i00000000
χ8322-2-2-222-2-222-2-22-22-220000000000002-22-2000000000000-2-2222-2-222-2-222-22-22-2000000000000-22-22000000000000
χ8422-2-2-222-2-222-2-22-22-22000000000000-22-22000000000000-2-2222-2-222-2-222-22-22-20000000000002-22-2000000000000
χ8522-2-2-222-2-22-222-22-22-20000000000002i−2i−2i2i000000000000-2-2222-2-222-22-2-22-22-22000000000000−2i2i2i−2i000000000000
χ8622-2-2-222-2-22-222-22-22-2000000000000−2i2i2i−2i000000000000-2-2222-2-222-22-2-22-22-220000000000002i−2i−2i2i000000000000
χ8722-2-2-22-222-22-2-2-2222-2000000002i−2i2i−2i0000000000000000-2-2222-22-2-22-2222-2-2-2200000000−2i2i−2i2i0000000000000000
χ8822-2-2-22-222-22-2-2-2222-200000000−2i2i−2i2i0000000000000000-2-2222-22-2-22-2222-2-2-22000000002i−2i2i−2i0000000000000000
χ8922-2-2-22-222-2-2222-2-2-22000000002i−2i−2i2i0000000000000000-2-2222-22-2-222-2-2-2222-200000000−2i2i2i−2i0000000000000000
χ9022-2-2-22-222-2-2222-2-2-2200000000−2i2i2i−2i0000000000000000-2-2222-22-2-222-2-2-2222-2000000002i−2i−2i2i0000000000000000
χ918-88-8000000000000000000000000000000000000000000-88-88000000000000000000000000000000000000000000
χ928-8-88000000000000000000000000000000000000000000-888-8000000000000000000000000000000000000000000

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