Finite Group Databasebeta

← Group #481529

Character table — Group #481529

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222244444444888888888888888888888888881111111122224444444488888888888888888888888888
order12224444224422444444222444444488888888888888882222444422442244444422244444448888888888888888
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
χ3111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-11-1-11-1-11111iiii−i−i−i−i−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-11-1-11-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-11-1-11-1-11111−i−i−i−iiiiiiiii−i−i−i−i111111111111-1-1-1-1-1-1-1-11-1-11-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-111-1-11111-1-1-1-1-1111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i1111-1-1-1-111-1-11111-1-1-1-1-1111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111-1-11111-1-1-1-1-1111-1-111-1-1−i−iii−i−iii−i−iii−i−iii1111-1-1-1-111-1-11111-1-1-1-1-1111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111-1-11111-1-1-1-1-1-1-1111-1-111ii−i−iii−i−i−i−iii−i−iii1111-1-1-1-111-1-11111-1-1-1-1-1-1-1111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-111-1-11111-1-1-1-1-1-1-1111-1-111−i−iii−i−iiiii−i−iii−i−i1111-1-1-1-111-1-11111-1-1-1-1-1-1-1111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-111-1-1-1-1-1-11111-1111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111-1-1-1-111-1-1-1-1-1-11111-1111-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-111-1-1-1-1-1-11111-1-1-111111-1-111-1-1-1-111-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-111111-1-111-1-1-1-111-1-11111-1-1
χ161111-1-1-1-111-1-1-1-1-1-11111-1-1-111111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-111111-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222-2-2-2-222-200-2000000000000000000000022222222222222-2-2-2-222-200-20000000000000000000000
χ18222222222222-2-22222-2-2-200-20000000000000000000000222222222222-2-22222-2-2-200-20000000000000000000000
χ192222-2-2-2-222-2-222-2-222-2-2200-200000000000000000000002222-2-2-2-222-2-222-2-222-2-2200-20000000000000000000000
χ202222-2-2-2-222-2-2-2-222-2-222200-200000000000000000000002222-2-2-2-222-2-2-2-222-2-222200-20000000000000000000000
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χ2222-2-22i2i−2i−2i2-22i−2i002i−2i2-2000000000000−i2i2−22−22−i2i20000000022-2-22i2i−2i−2i2-22i−2i002i−2i2-2000000000000−i2i2−22−22−i2i200000000
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χ2922-2-2−2i−2i2i2i2-2−2i2i002i−2i-220000000000002−2i2−i2−i2i2−220000000022-2-2−2i−2i2i2i2-2−2i2i002i−2i-220000000000002−2i2−i2−i2i2−2200000000
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χ3122-2-2−2i−2i2i2i2-2−2i2i00−2i2i2-2000000000000i2−i2−22−22i2−i20000000022-2-2−2i−2i2i2i2-2−2i2i00−2i2i2-2000000000000i2−i2−22−22i2−i200000000
χ3222-2-2−2i−2i2i2i2-2−2i2i00−2i2i2-2000000000000−i2i22−22−2−i2i20000000022-2-2−2i−2i2i2i2-2−2i2i00−2i2i2-2000000000000−i2i22−22−2−i2i200000000
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χ3422-2-2−2i−2i2i2i-222i−2i2-20000−2i2i000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i22-2-2−2i−2i2i2i-222i−2i2-20000−2i2i000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ3522-2-2−2i−2i2i2i-222i−2i-2200002i−2i0000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i22-2-2−2i−2i2i2i-222i−2i-2200002i−2i0000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ3622-2-2−2i−2i2i2i-222i−2i-2200002i−2i000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i22-2-2−2i−2i2i2i-222i−2i-2200002i−2i000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ3744444444-4-4-4-4000000000000000000000000000000000044444444-4-4-4-40000000000000000000000000000000000
χ384444-4-4-4-4-4-44400000000000000000000000000000000004444-4-4-4-4-4-4440000000000000000000000000000000000
χ394-44-44i−4i4i−4i0000000000000000002-22i−2i00000000000000004-44-44i−4i4i−4i0000000000000000002-22i−2i0000000000000000
χ404-44-44i−4i4i−4i000000000000000000-22−2i2i00000000000000004-44-44i−4i4i−4i000000000000000000-22−2i2i0000000000000000
χ414-44-4−4i4i−4i4i0000000000000000002-2−2i2i00000000000000004-44-4−4i4i−4i4i0000000000000000002-2−2i2i0000000000000000
χ424-44-4−4i4i−4i4i000000000000000000-222i−2i00000000000000004-44-4−4i4i−4i4i000000000000000000-222i−2i0000000000000000
χ434-4-444-4-4400000000000002-202-2000000000000000000004-4-444-4-4400000000000002-202-200000000000000000000
χ444-4-444-4-440000000000000-220-22000000000000000000004-4-444-4-440000000000000-220-2200000000000000000000
χ454-4-44-444-400000000000002-20-22000000000000000000004-4-44-444-400000000000002-20-2200000000000000000000
χ464-4-44-444-40000000000000-2202-2000000000000000000004-4-44-444-40000000000000-2202-200000000000000000000
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
χ49111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-111111111
χ50111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111111111-1-1-1-1-1-1-1-1
χ51111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii
χ52111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i
χ53111111111111-1-1-1-1-1-1-1-11-1-11-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i
χ54111111111111-1-1-1-1-1-1-1-11-1-11-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii
χ551111-1-1-1-111-1-11111-1-1-1-1-1111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-11111-1-111-1-1-1-111111-1-1-111-1-111−i−iii−i−iii−i−iii−i−iii
χ561111-1-1-1-111-1-11111-1-1-1-1-1111-1-111-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-11111-1-111-1-1-1-111111-1-1-111-1-111ii−i−iii−i−iii−i−iii−i−i
χ571111-1-1-1-111-1-11111-1-1-1-1-1-1-1111-1-111ii−i−iii−i−i−i−iii−i−iii-1-1-1-11111-1-111-1-1-1-11111111-1-1-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ581111-1-1-1-111-1-11111-1-1-1-1-1-1-1111-1-111−i−iii−i−iiiii−i−iii−i−i-1-1-1-11111-1-111-1-1-1-11111111-1-1-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ591111-1-1-1-111-1-1-1-1-1-11111-1111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ601111-1-1-1-111-1-1-1-1-1-11111-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-11-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ611111-1-1-1-111-1-1-1-1-1-11111-1-1-111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1111-1-1-1-1-111-1-11111-1-111-1-1-1-111
χ621111-1-1-1-111-1-1-1-1-1-11111-1-1-111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1111-1-1-1-1-11111-1-1-1-111-1-11111-1-1
χ6322222222222222-2-2-2-222-200-20000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-220020000000000000000000000
χ64222222222222-2-22222-2-2-200-20000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22220020000000000000000000000
χ652222-2-2-2-222-2-222-2-222-2-2200-20000000000000000000000-2-2-2-22222-2-222-2-222-2-222-20020000000000000000000000
χ662222-2-2-2-222-2-2-2-222-2-222200-20000000000000000000000-2-2-2-22222-2-22222-2-222-2-2-20020000000000000000000000
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χ6822-2-22i2i−2i−2i2-22i−2i002i−2i2-2000000000000−i2i2−22−22−i2i200000000-2-222−2i−2i2i2i-22−2i2i00−2i2i-22000000000000i2−i22−22−2i2−i200000000
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χ8344444444-4-4-4-40000000000000000000000000000000000-4-4-4-4-4-4-4-444440000000000000000000000000000000000
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χ904-4-444-4-440000000000000-220-2200000000000000000000-444-4-444-400000000000002-202-200000000000000000000
χ914-4-44-444-400000000000002-20-2200000000000000000000-444-44-4-440000000000000-2202-200000000000000000000
χ924-4-44-444-40000000000000-2202-200000000000000000000-444-44-4-4400000000000002-20-2200000000000000000000

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