Finite Group Databasebeta

← Group #218331

Character table — Group #218331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444444444448888888888888888888888888888444444444444448888888888888844888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ9111111111111111111111111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ10111111111111111111111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ11111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-111
χ12111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111
χ14111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-111-1-1-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ1711111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-11-111-1-111-1-1i−iii−i−i11-1-1ii−i−i1-1i−ii−ii−i
χ1811111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-1-1111-1-1-111-1-111i−i−i−iii11-1-1ii−i−i-11−ii−ii−ii
χ1911111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii11-1-11-111-1-1-1-111i−i−i−iii-1-111−i−iii-11i−ii−i−ii
χ2011111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-1111-1-1-11111-1-1i−iii−i−i-1-111−i−iii1-1−ii−iii−i
χ2111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-11-111-1-111-1-1−ii−i−iii11-1-1−i−iii1-1−ii−ii−ii
χ2211111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii-1-1111-1-1-111-1-111−iiii−i−i11-1-1−i−iii-11i−ii−ii−i
χ2311111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i11-1-11-111-1-1-1-111−iiii−i−i-1-111ii−i−i-11−ii−iii−i
χ2411111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-1-1111-1-1-11111-1-1−ii−i−iii-1-111ii−i−i1-1i−ii−i−ii
χ2511111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111ii−i−i−i−iiiii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1-11-1-111-1-111−iiii−i−i-1-111−i−iii1-1i−i−ii−ii
χ2611111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111ii−i−i−i−iiiii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1111-1-111-1-1−ii−i−iii-1-111−i−iii-11−iii−ii−i
χ2711111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111ii−i−i−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiii11-1-1-11-1-11111-1-1−ii−i−iii11-1-1ii−i−i-11i−i−iii−i
χ2811111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111ii−i−i−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiii-1-111-1111-1-1-1-111−iiii−i−i11-1-1ii−i−i1-1−iii−i−ii
χ2911111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−iiiii−i−i−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1-11-1-111-1-111i−i−i−iii-1-111ii−i−i1-1−iii−ii−i
χ3011111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−iiiii−i−i−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111-1111-1-111-1-1i−iii−i−i-1-111ii−i−i-11i−i−ii−ii
χ3111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−iiiii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i11-1-1-11-1-11111-1-1i−iii−i−i11-1-1−i−iii-11−iii−i−ii
χ3211111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−iiiii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i-1-111-1111-1-1-1-111i−i−i−iii11-1-1−i−iii1-1i−i−iii−i
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χ342222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222222200000000000000000000-2-200000000-2-200000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000002200000000-2-200000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000022000000002200000000000000000000
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χ4222-2-2-2-22222-2-2-2-222000000002i−2i2i−2i00002i−2i2i−2i2-22-2−2−222−2−222−2−222−2−22200000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ4322-2-2-2-22222-2-2-2-222000000002i−2i2i−2i0000−2i2i−2i2i-22-2222−2−222−2−2−2−222−2−22200000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ4422-2-2-2-22222-2-2-2-222000000002i−2i2i−2i0000−2i2i−2i2i-22-22−2−222−2−22222−2−222−2−200000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ4522-2-2-2-22222-2-2-2-22200000000−2i2i−2i2i00002i−2i2i−2i-22-2222−2−222−2−2−2−222−2−22200000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ4622-2-2-2-22222-2-2-2-22200000000−2i2i−2i2i00002i−2i2i−2i-22-22−2−222−2−22222−2−222−2−200000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ4722-2-2-2-22222-2-2-2-22200000000−2i2i−2i2i0000−2i2i−2i2i2-22-222−2−222−2−222−2−222−2−200000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ4822-2-2-2-22222-2-2-2-22200000000−2i2i−2i2i0000−2i2i−2i2i2-22-2−2−222−2−222−2−222−2−22200000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ4922-2-2-2-222-2-22222-2-2000000002i−2i−2i2i00002-2-22−2i2i2i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i22−2−2200000000
χ5022-2-2-2-222-2-22222-2-2000000002i−2i−2i2i00002-2-22−2i2i2i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i2−222−200000000
χ5122-2-2-2-222-2-22222-2-2000000002i−2i−2i2i0000-222-22i−2i−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i2−222−200000000
χ5222-2-2-2-222-2-22222-2-2000000002i−2i−2i2i0000-222-22i−2i−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i22−2−2200000000
χ5322-2-2-2-222-2-22222-2-200000000−2i2i2i−2i00002-2-222i−2i−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i22−2−2200000000
χ5422-2-2-2-222-2-22222-2-200000000−2i2i2i−2i00002-2-222i−2i−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i2−222−200000000
χ5522-2-2-2-222-2-22222-2-200000000−2i2i2i−2i0000-222-2−2i2i2i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i2−222−200000000
χ5622-2-2-2-222-2-22222-2-200000000−2i2i2i−2i0000-222-2−2i2i2i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i22−2−2200000000
χ572-222-2-22-22i−2i2i2i−2i−2i2i−2i2-22i−2i2-22i−2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32-22i−2i0000000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ582-222-2-22-22i−2i2i2i−2i−2i2i−2i2-22i−2i2-22i−2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3-22−2i2i000000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ592-222-2-22-22i−2i2i2i−2i−2i2i−2i2-22i−2i2-22i−2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32-22i−2i000000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ602-222-2-22-22i−2i2i2i−2i−2i2i−2i2-22i−2i2-22i−2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3-22−2i2i0000000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ612-222-2-22-2−2i2i−2i−2i2i2i−2i2i2-2−2i2i2-2−2i2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2-2−2i2i0000000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ622-222-2-22-2−2i2i−2i−2i2i2i−2i2i2-2−2i2i2-2−2i2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ-222i−2i000000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ632-222-2-22-2−2i2i−2i−2i2i2i−2i2i2-2−2i2i2-2−2i2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2-2−2i2i000000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ642-222-2-22-2−2i2i−2i−2i2i2i−2i2i2-2−2i2i2-2−2i2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ-222i−2i0000000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ652-22-22-2-222i−2i2i−2i2i−2i−2i2i2-2−2i2i-222i−2i00000000000000002i−2i2i−2i2-22-2000000000000002i−2i2-22-22i−2i0000000000000000000000
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χ672-22-22-2-222i−2i2i−2i2i−2i−2i2i2-2−2i2i-222i−2i0000000000000000−2i2i−2i2i-22-22000000000000002i−2i2-2-22−2i2i0000000000000000000000
χ682-22-22-2-222i−2i2i−2i2i−2i−2i2i2-2−2i2i-222i−2i0000000000000000−2i2i−2i2i-22-2200000000000000−2i2i-222-22i−2i0000000000000000000000
χ692-22-22-2-22−2i2i−2i2i−2i2i2i−2i2-22i−2i-22−2i2i00000000000000002i−2i2i−2i-22-22000000000000002i−2i-222-2−2i2i0000000000000000000000
χ702-22-22-2-22−2i2i−2i2i−2i2i2i−2i2-22i−2i-22−2i2i00000000000000002i−2i2i−2i-22-2200000000000000−2i2i2-2-222i−2i0000000000000000000000
χ712-22-22-2-22−2i2i−2i2i−2i2i2i−2i2-22i−2i-22−2i2i0000000000000000−2i2i−2i2i2-22-2000000000000002i−2i-22-222i−2i0000000000000000000000
χ722-22-22-2-22−2i2i−2i2i−2i2i2i−2i2-22i−2i-22−2i2i0000000000000000−2i2i−2i2i2-22-200000000000000−2i2i2-22-2−2i2i0000000000000000000000
χ73444-4-44-4-4444-4-44-4-444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ74444-4-44-4-4444-4-44-4-4-4-44444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ75444-4-44-4-4-4-4-444-4444444-4-4-4-400000000000000000000000000000000000000000000000000000000000000000000
χ76444-4-44-4-4-4-4-444-444-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000000000
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χ7844-444-4-4-444-444-4-4-4000000000000-44-44000000000000000000000000000000000000000000000000000000000000
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χ814-444-4-44-44i−4i4i4i−4i−4i4i−4i-44−4i4i-44−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ824-444-4-44-4−4i4i−4i−4i4i4i−4i4i-444i−4i-444i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ834-44-44-4-444i−4i4i−4i4i−4i−4i4i-444i−4i4-4−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ844-44-44-4-44−4i4i−4i4i−4i4i4i−4i-44−4i4i4-44i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ854-4-44-44-444i−4i−4i4i−4i4i−4i4i0000000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000000000000
χ864-4-44-44-444i−4i−4i4i−4i4i−4i4i000000000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000000000000
χ874-4-44-44-44−4i4i4i−4i4i−4i4i−4i0000000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000000000000
χ884-4-44-44-44−4i4i4i−4i4i−4i4i−4i000000000000000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000000000000
χ894-4-4-4444-44i−4i−4i−4i4i4i4i−4i000000000000000000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000
χ904-4-4-4444-44i−4i−4i−4i4i4i4i−4i00000000000000000000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000
χ914-4-4-4444-4−4i4i4i4i−4i−4i−4i4i000000000000000000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000
χ924-4-4-4444-4−4i4i4i4i−4i−4i−4i4i00000000000000000000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.