Finite Group Databasebeta

← Group #376151

Character table — Group #376151

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222224444444444444444444444444444444444448888888888888888222222444444444444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1711111-1-1-1-111-1-1-1-11iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11-111-1-111-1-1i−iii−i−iii−i−i11-1-111-1-1ii−i−ii−i1-1
χ1811111-1-1-1-111-1-1-1-11iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−iii−i−i11-1-1−i−i−i−iiiii-1-1-1-111111-1-1-11111-1-1i−iii−i−i−i−iii11-1-1-1-111−i−iii−ii-11
χ1911111-1-1-1-111-1-1-1-11iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i−i−iii-1-111iiii−i−i−i−i1111-1-1-1-1-1111-1-111-1-1−ii−i−iiiii−i−i-1-111-1-111−i−iii−ii-11
χ2011111-1-1-1-111-1-1-1-11iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111-11-1-11111-1-1−ii−i−iii−i−iii-1-11111-1-1ii−i−ii−i1-1
χ2111111-1-1-1-111-1-1-1-11iiii−i−i−i−i11-1-111-1-1ii−i−i−i−i−i−iiiiiii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11-1-1-111-1-111i−i−i−iii−i−iii-1-11111-1-1ii−i−i−ii-11
χ2211111-1-1-1-111-1-1-1-11iiii−i−i−i−i11-1-111-1-1ii−i−i−i−i−i−iiiiiii−i−i11-1-1−i−i−i−iiiii-1-1-1-111111-111-1-1-1-111i−i−i−iiiii−i−i-1-111-1-111−i−iiii−i1-1
χ2311111-1-1-1-111-1-1-1-11iiii−i−i−i−i11-1-111-1-1ii−i−i−i−i−i−iiiii−i−iii-1-111iiii−i−i−i−i1111-1-1-1-1-11-1-111-1-111−iiii−i−i−i−iii11-1-1-1-111−i−iiii−i1-1
χ2411111-1-1-1-111-1-1-1-11iiii−i−i−i−i11-1-111-1-1ii−i−i−i−i−i−iiiii−i−iii-1-111−i−i−i−iiiii-1-1-1-11111-1111-1-1-1-111−iiii−i−iii−i−i11-1-111-1-1ii−i−i−ii-11
χ2511111-1-1-1-111-1-1-1-11−i−i−i−iiiii11-1-111-1-1−i−iiiiiii−i−i−i−iii−i−i-1-111iiii−i−i−i−i-1-1-1-11111-1111-1-1-1-111i−i−i−iii−i−iii11-1-111-1-1−i−iiii−i-11
χ2611111-1-1-1-111-1-1-1-11−i−i−i−iiiii11-1-111-1-1−i−iiiiiii−i−i−i−iii−i−i-1-111−i−i−i−iiiii1111-1-1-1-1-11-1-111-1-111i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−ii1-1
χ2711111-1-1-1-111-1-1-1-11−i−i−i−iiiii11-1-111-1-1−i−iiiiiii−i−i−i−i−i−iii11-1-1iiii−i−i−i−i-1-1-1-111111-111-1-1-1-111−iiii−i−i−i−iii-1-111-1-111ii−i−i−ii1-1
χ2811111-1-1-1-111-1-1-1-11−i−i−i−iiiii11-1-111-1-1−i−iiiiiii−i−i−i−i−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11-1-1-111-1-111−iiii−i−iii−i−i-1-11111-1-1−i−iiii−i-11
χ2911111-1-1-1-111-1-1-1-11−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111-11-1-11111-1-1i−iii−i−iii−i−i-1-11111-1-1−i−iii−ii1-1
χ3011111-1-1-1-111-1-1-1-11−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiiiii−i−i-1-111−i−i−i−iiiii1111-1-1-1-1-1111-1-111-1-1i−iii−i−i−i−iii-1-111-1-111ii−i−ii−i-11
χ3111111-1-1-1-111-1-1-1-11−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii−i−iii11-1-1iiii−i−i−i−i-1-1-1-111111-1-1-11111-1-1−ii−i−iiiii−i−i11-1-1-1-111ii−i−ii−i-11
χ3211111-1-1-1-111-1-1-1-11−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11-111-1-111-1-1−ii−i−iii−i−iii11-1-111-1-1−i−iii−ii1-1
χ33222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222220000000000000000-2-200000000-2-2000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000220000000022000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000002222-2-2-2-200000000000000002200000000-2-2000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-222220000000000000000-2-20000000022000000000000000000000000
χ3722222-2-2-2-222-2-2-2-222i2i2i2i−2i−2i−2i−2i-2-222-2-222−2i−2i2i2i000000002i2i−2i−2i22-2-20000000000000000-2200000000−2i2i000000000000000000000000
χ3822222-2-2-2-222-2-2-2-222i2i2i2i−2i−2i−2i−2i-2-222-2-222−2i−2i2i2i00000000−2i−2i2i2i-2-22200000000000000002-2000000002i−2i000000000000000000000000
χ3922222-2-2-2-222-2-2-2-22−2i−2i−2i−2i2i2i2i2i-2-222-2-2222i2i−2i−2i000000002i2i−2i−2i-2-22200000000000000002-200000000−2i2i000000000000000000000000
χ4022222-2-2-2-222-2-2-2-22−2i−2i−2i−2i2i2i2i2i-2-222-2-2222i2i−2i−2i00000000−2i−2i2i2i22-2-20000000000000000-22000000002i−2i000000000000000000000000
χ41222-2-222-2-22-2-222-2-222-2-222-2-2000000000000000000002i−2i2i−2i2i−2i2i−2i22−2−222−2−222−2−222−2−2000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
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χ43222-2-222-2-22-2-222-2-222-2-222-2-200000000000000000000−2i2i−2i2i−2i2i−2i2i22−2−222−2−222−2−222−2−2000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ44222-2-222-2-22-2-222-2-222-2-222-2-200000000000000000000−2i2i−2i2i−2i2i−2i2i−2−222−2−222−2−222−2−222000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ45222-2-222-2-22-2-222-2-2-2-222-2-222000000000000000000002i−2i2i−2i−2i2i−2i2i22−2−222−2−2−2−222−2−222000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ46222-2-222-2-22-2-222-2-2-2-222-2-222000000000000000000002i−2i2i−2i−2i2i−2i2i−2−222−2−22222−2−222−2−2000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ47222-2-222-2-22-2-222-2-2-2-222-2-22200000000000000000000−2i2i−2i2i2i−2i2i−2i22−2−222−2−2−2−222−2−222000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ48222-2-222-2-22-2-222-2-2-2-222-2-22200000000000000000000−2i2i−2i2i2i−2i2i−2i−2−222−2−22222−2−222−2−2000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ49222-2-2-2-2222-22-2-22-22i2i−2i−2i−2i−2i2i2i000000000000000000002-2-22−2i2i2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000000000000000−i2i2i2−i22−2−220000
χ50222-2-2-2-2222-22-2-22-22i2i−2i−2i−2i−2i2i2i000000000000000000002-2-22−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000000000000000i2−i2−i2i2−222−20000
χ51222-2-2-2-2222-22-2-22-22i2i−2i−2i−2i−2i2i2i00000000000000000000-222-22i−2i−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000000000000000i2−i2−i2i2−222−20000
χ52222-2-2-2-2222-22-2-22-22i2i−2i−2i−2i−2i2i2i00000000000000000000-222-22i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000000000000000−i2i2i2−i22−2−220000
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χ5722-22-22-22-2-2-2-22-22200000000222-2-2-22-2000022-2-222-2-200000000000000002i−2i2i−2i2i−2i2i−2i00000000000000002i−2i2i−2i0000000000000000
χ5822-22-22-22-2-2-2-22-22200000000222-2-2-22-2000022-2-222-2-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i0000000000000000
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χ732-2-2-22222-22-22-2-2-222i−2i2i−2i2i−2i2i−2i2-22-2-22-222i−2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000002-22-200000000000000000000000000
χ742-2-2-22222-22-22-2-2-222i−2i2i−2i2i−2i2i−2i2-22-2-22-222i−2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000-22-2200000000000000000000000000
χ752-2-2-22222-22-22-2-2-222i−2i2i−2i2i−2i2i−2i-22-222-22-2−2i2i−2i2i000000000000000000000000000000000000000000002i−2i2i−2i00002-22-2000000000000
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χ772-2-2-22222-22-22-2-2-22−2i2i−2i2i−2i2i−2i2i2-22-2-22-22−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000-22-2200000000000000000000000000
χ782-2-2-22222-22-22-2-2-22−2i2i−2i2i−2i2i−2i2i2-22-2-22-22−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000002-22-200000000000000000000000000
χ792-2-2-22222-22-22-2-2-22−2i2i−2i2i−2i2i−2i2i-22-222-22-22i−2i2i−2i000000000000000000000000000000000000000000002i−2i2i−2i0000-22-22000000000000
χ802-2-2-22222-22-22-2-2-22−2i2i−2i2i−2i2i−2i2i-22-222-22-22i−2i2i−2i00000000000000000000000000000000000000000000−2i2i−2i2i00002-22-2000000000000
χ812-2-2-22-2-2-222-2-222222-22-2-22-222-2-22-222-22-2-222-2-22-222-20000000000000000000000000000002-2-2200000000000000000000000000
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χ872-2-2-22-2-2-222-2-22222-22-222-22-2-222-22-2-222-2-22000000000000000000000000000000000000000000002-2-220000-222-2000000000000
χ882-2-2-22-2-2-222-2-22222-22-222-22-2-222-22-2-222-2-2200000000000000000000000000000000000000000000-222-200002-2-22000000000000
χ8944-44-44-44-4-4-4-44-44400000000-4-4-4444-44000000000000000000000000000000000000000000000000000000000000000000000000
χ9044-44-4-44-44-4-44-44-4400000000-4-44-4444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-444-4-44-4444-4-4-4000000000000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ9244-4-444-4-44-4444-4-4-400000000000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ9344-4-44-444-4-44-4-444-4000000000000000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ9444-4-44-444-4-44-4-444-400000000000000000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ954-44444-4-4-4-4-44-444-40000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ964-44444-4-4-4-4-44-444-4000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ974-4444-4444-4-4-44-4-4-400000000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ984-4444-4444-4-4-44-4-4-4000000000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ994-44-4-44-444-44-4-44-4400000000-44-4-4-4444000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-4-4-44-4-4-4444-44400000000-4444-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-444-4444-4-4-44-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-44-444-4444-4-4-44-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-4-4-44-444444-4-44-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-4-4-44-444444-4-4-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000

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