Finite Group Databasebeta

← Group #360810

Character table — Group #360810

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222224444444444444444222222224444444444448888888888888888444444444444444444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ9111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ10111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ11111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ12111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ13111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ14111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ15111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ16111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ17111-1-1-1-11111-1-11-1-111-1-1-11111-1-1-1-111-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1i−ii−iii−i−iii−i−iii−i−iii−i−ii−ii−i
χ18111-1-1-1-11111-1-11-1-111-1-1-11111-1-1-1-111-11111-1-1-1-111-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii−ii−ii
χ19111-1-1-1-11111-1-11-1-111-1-1-11111-1-1-1-111-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii−ii−ii
χ20111-1-1-1-11111-1-11-1-111-1-1-11111-1-1-1-111-11111-1-1-1-111-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−ii−ii−i
χ21111-1-1-1-11111-1-11-1-111-1-1-11111-1-1-1-111-1-1-1-1-1111111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111i−ii−i−i−iii−i−iiiii−i−iii−i−i−ii−ii
χ22111-1-1-1-11111-1-11-1-111-1-1-11111-1-1-1-111-1-1-1-1-1111111-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111i−ii−i−i−iii−i−iii−i−iii−i−iiii−ii−i
χ23111-1-1-1-11111-1-11-1-111-1-1-11111-1-1-1-111-1-1-1-1-1111111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111−ii−iiii−i−iii−i−i−i−iii−i−iiii−ii−i
χ24111-1-1-1-11111-1-11-1-111-1-1-11111-1-1-1-111-1-1-1-1-1111111-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111−ii−iiii−i−iii−i−iii−i−iii−i−i−ii−ii
χ25111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111i−i−iiii−i−i−i−iiiii−i−i−i−iiii−i−ii
χ26111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111i−i−iiii−i−i−i−iii−i−iiiii−i−i−iii−i
χ27111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111−iii−i−i−iiiii−i−i−i−iiiii−i−i−iii−i
χ28111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111−iii−i−i−iiiii−i−iii−i−i−i−iiii−i−ii
χ29111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1i−i−ii−i−iiiii−i−iii−i−i−i−iii−iii−i
χ30111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-111ii−i−i−i−iii-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1i−i−ii−i−iiiii−i−i−i−iiiii−i−ii−i−ii
χ31111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1−iii−iii−i−i−i−iii−i−iiiii−i−ii−i−ii
χ32111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-111−i−iiiii−i−i-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1−iii−iii−i−i−i−iiiii−i−i−i−iii−iii−i
χ332222222222222222-2-2-2-2-222222222-2-2-200000000-2-2-2-2222222220000000000000000000000000000-2-2-2-200000000000000000000
χ342222222222222222-2-2-2-2-222222222-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000222200000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022222222-2-2-2-20000000000000000000000000000-2-22200000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-22222000000000000000000000000000022-2-200000000000000000000
χ37222-2-2-2-22222-2-22-2-2-2-22222222-2-2-2-2-2-2200000000-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i−2i2i00000000000000000000
χ38222-2-2-2-22222-2-22-2-2-2-22222222-2-2-2-2-2-2200000000-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002i−2i2i−2i00000000000000000000
χ39222-2-2-2-22222-2-22-2-2-2-2222-2-2-2-22222-2-220000000022-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000−2i2i2i−2i00000000000000000000
χ40222-2-2-2-22222-2-22-2-2-2-2222-2-2-2-22222-2-220000000022-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000002i−2i−2i2i00000000000000000000
χ4122-222-2-22-22-222-2-2-22-22-2-2000000002-2222-2-222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i00002i−2i2i−2i0000000000000000000000000000
χ4222-222-2-22-22-222-2-2-22-22-2-2000000002-2222-2-222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000−2i2i−2i2i0000000000000000000000000000
χ4322-222-2-22-22-222-2-2-22-22-2-2000000002-22-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i0000−2i2i−2i2i0000000000000000000000000000
χ4422-222-2-22-22-222-2-2-22-22-2-2000000002-22-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i00002i−2i2i−2i0000000000000000000000000000
χ4522-22-22-2-22-222-2-22-2000002i2i−2i−2i2i2i−2i−2i0000000000000002-22-22i−2i2i−2ii2i2−i2−i2i2i2−i2−i22−22−22−22−2000000000000000000000000i2−i2i2−i22−22−20000
χ4622-22-22-2-22-222-2-22-2000002i2i−2i−2i2i2i−2i−2i0000000000000002-22-22i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−22−22−22−22000000000000000000000000−i2i2−i2i2−22−220000
χ4722-22-22-2-22-222-2-22-2000002i2i−2i−2i2i2i−2i−2i000000000000000-22-22−2i2i−2i2ii2i2−i2−i2i2i2−i2−i22−22−22−22−2000000000000000000000000−i2i2−i2i2−22−220000
χ4822-22-22-2-22-222-2-22-2000002i2i−2i−2i2i2i−2i−2i000000000000000-22-22−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2−22−22−22−22000000000000000000000000i2−i2i2−i22−22−20000
χ4922-22-22-2-22-222-2-22-200000−2i−2i2i2i−2i−2i2i2i0000000000000002-22-2−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−22−22−22−22000000000000000000000000i2−i2i2−i2−22−220000
χ5022-22-22-2-22-222-2-22-200000−2i−2i2i2i−2i−2i2i2i0000000000000002-22-2−2i2i−2i2i−i2−i2i2i2−i2−i2i2i22−22−22−22−2000000000000000000000000−i2i2−i2i22−22−20000
χ5122-22-22-2-22-222-2-22-200000−2i−2i2i2i−2i−2i2i2i000000000000000-22-222i−2i2i−2ii2i2−i2−i2i2i2−i2−i2−22−22−22−22000000000000000000000000−i2i2−i2i22−22−20000
χ5222-22-22-2-22-222-2-22-200000−2i−2i2i2i−2i−2i2i2i000000000000000-22-222i−2i2i−2i−i2−i2i2i2−i2−i2i2i22−22−22−22−2000000000000000000000000i2−i2i2−i2−22−220000
χ5322-2-22-22-22-22-22-2-22000002i2i−2i−2i−2i−2i2i2i0000000000000002i−2i−2i2i-222-2i2i2−i2−i2−i2−i2i2i22−22−2−22−22000000000000000000000000−222−2i2−i2−i2i20000
χ5422-2-22-22-22-22-22-2-22000002i2i−2i−2i−2i−2i2i2i0000000000000002i−2i−2i2i-222-2−i2−i2i2i2i2i2−i2−i2−22−222−22−20000000000000000000000002−2−22−i2i2i2−i20000
χ5522-2-22-22-22-22-22-2-22000002i2i−2i−2i−2i−2i2i2i000000000000000−2i2i2i−2i2-2-22i2i2−i2−i2−i2−i2i2i22−22−2−22−220000000000000000000000002−2−22−i2i2i2−i20000
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χ5722-2-22-22-22-22-22-2-2200000−2i−2i2i2i2i2i−2i−2i0000000000000002i−2i−2i2i2-2-22i2i2−i2−i2−i2−i2i2i2−22−222−22−2000000000000000000000000−222−2−i2i2i2−i20000
χ5822-2-22-22-22-22-22-2-2200000−2i−2i2i2i2i2i−2i−2i0000000000000002i−2i−2i2i2-2-22−i2−i2i2i2i2i2−i2−i22−22−2−22−220000000000000000000000002−2−22i2−i2−i2i20000
χ5922-2-22-22-22-22-22-2-2200000−2i−2i2i2i2i2i−2i−2i000000000000000−2i2i2i−2i-222-2i2i2−i2−i2−i2−i2i2i2−22−222−22−20000000000000000000000002−2−22i2−i2−i2i20000
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χ6322-2-2-2222-22-2-2-2-2222-2-222000000002-2-2-2-22222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000−2i2i2i−2i0000000000000000000000000000
χ6422-2-2-2222-22-2-2-2-2222-2-222000000002-2-2-2-22222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i00002i−2i−2i2i0000000000000000000000000000
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χ722-22-2-2222-2-2222-2-2-22-2-2-2200000000-222-22-222-22-2000000000000−2i2i−2i2i2i−2i2i−2i000000002i−2i−2i2i00000000000000000000000000000000
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χ792-2-2222222-2-2-2-22-2-2-2-2-22-2-22-22-22-22222000000002-22-200000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ802-2-2222222-2-2-2-22-2-2-2-2-22-2-22-22-22-22222000000002-22-20000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ812-2-2-2-2-2-222-2-22222222-22-22-22-2-22-22-2-222-2-22-222-22-2-22000000000000000000000000000000002-2-22000000000000000000000000
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χ904444-4-44-4-4-4-44-44-4400000000000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ91444-444-4-4-4-4-4-4444-4000000000000000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ92444-444-4-4-4-4-4-4444-400000000000000000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ9344-444-4-44-44-444-4-4-4-44-44400000000-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9444-4-4-4444-44-4-4-4-444-444-4-400000000-444000000000000000000000000000000000000000000000000000000000000000000000000
χ954-4444-4-44-4-44-4-4-444-44-4-44000000004-44000000000000000000000000000000000000000000000000000000000000000000000000
χ964-444-44-4-444-4-44-4-44000004i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ974-444-44-4-444-4-44-4-4400000−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ984-44-44-44-444-44-4-44-4000004i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ994-44-44-44-444-44-4-44-400000−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-4-4444-4-4444-4-4-4-4444-4000000004-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-4-44-4-444-4444-400000000000000000000000000000000000022−22−222222−22−222200000000000000000000000000000000000000000000
χ1024-4-44-4-44-4-444-4444-4000000000000000000000000000000000000−222222−22−222222−2200000000000000000000000000000000000000000000
χ1034-4-4-444-4-4-4444-44-4400000000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ1044-4-4-444-4-4-4444-44-44000000000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000

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