Finite Group Databasebeta

← Group #211166

Character table — Group #211166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444444444444444448888888888888888444444444444444444448888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ1711-11-1-1-11ii−i−iii−i−iii−i−i1-11-11-11-11111-1-1-1-1iiii−i−i−i−i1-1i−iiiii−i−i−i−i11-1-111-1-111-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1i−ii−i1-11-11-1i−i1-1i−i
χ1811-11-1-1-11ii−i−iii−i−iii−i−i1-11-11-11-11111-1-1-1-1iiii−i−i−i−i1-1i−iiiii−i−i−i−i11-1-111-1-111-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1−ii−ii-11-11-11−ii-11−ii
χ1911-11-1-1-11ii−i−iii−i−iii−i−i1-11-11-11-11111-1-1-1-1iiii−i−i−i−i1-1i−i−i−i−i−iiiii-1-111-1-11111-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111i−ii−i1-11-1-11−ii-11−ii
χ2011-11-1-1-11ii−i−iii−i−iii−i−i1-11-11-11-11111-1-1-1-1iiii−i−i−i−i1-1i−i−i−i−i−iiiii-1-111-1-11111-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111−ii−ii-11-111-1i−i1-1i−i
χ2111-11-1-1-11ii−i−iii−i−iii−i−i1-11-11-11-1-1-1-1-11111−i−i−i−iiiii1-1i−iiiii−i−i−i−i11-1-111-1-1-1-111−i−iii−i−i−i−iiiii-1-1-1-11111i−i−ii1-1-111-1i−i-11−ii
χ2211-11-1-1-11ii−i−iii−i−iii−i−i1-11-11-11-1-1-1-1-11111−i−i−i−iiiii1-1i−iiiii−i−i−i−i11-1-111-1-1-1-111−i−iii−i−i−i−iiiii-1-1-1-11111−iii−i-111-1-11−ii1-1i−i
χ2311-11-1-1-11ii−i−iii−i−iii−i−i1-11-11-11-1-1-1-1-11111−i−i−i−iiiii1-1i−i−i−i−i−iiiii-1-111-1-111-1-111−i−iiiiiii−i−i−i−i1111-1-1-1-1i−i−ii1-1-11-11−ii1-1i−i
χ2411-11-1-1-11ii−i−iii−i−iii−i−i1-11-11-11-1-1-1-1-11111−i−i−i−iiiii1-1i−i−i−i−i−iiiii-1-111-1-111-1-111−i−iiiiiii−i−i−i−i1111-1-1-1-1−iii−i-111-11-1i−i-11−ii
χ2511-11-1-1-11−i−iii−i−iii−i−iii1-11-11-11-11111-1-1-1-1−i−i−i−iiiii1-1−iiiiii−i−i−i−i-1-111-1-11111-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111i−ii−i-11-111-1−ii1-1−ii
χ2611-11-1-1-11−i−iii−i−iii−i−iii1-11-11-11-11111-1-1-1-1−i−i−i−iiiii1-1−iiiiii−i−i−i−i-1-111-1-11111-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111−ii−ii1-11-1-11i−i-11i−i
χ2711-11-1-1-11−i−iii−i−iii−i−iii1-11-11-11-11111-1-1-1-1−i−i−i−iiiii1-1−ii−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1i−ii−i-11-11-11i−i-11i−i
χ2811-11-1-1-11−i−iii−i−iii−i−iii1-11-11-11-11111-1-1-1-1−i−i−i−iiiii1-1−ii−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−ii−ii1-11-11-1−ii1-1−ii
χ2911-11-1-1-11−i−iii−i−iii−i−iii1-11-11-11-1-1-1-1-11111iiii−i−i−i−i1-1−iiiiii−i−i−i−i-1-111-1-111-1-111ii−i−i−i−i−i−iiiii1111-1-1-1-1i−i−ii-111-11-1−ii-11i−i
χ3011-11-1-1-11−i−iii−i−iii−i−iii1-11-11-11-1-1-1-1-11111iiii−i−i−i−i1-1−iiiiii−i−i−i−i-1-111-1-111-1-111ii−i−i−i−i−i−iiiii1111-1-1-1-1−iii−i1-1-11-11i−i1-1−ii
χ3111-11-1-1-11−i−iii−i−iii−i−iii1-11-11-11-1-1-1-1-11111iiii−i−i−i−i1-1−ii−i−i−i−iiiii11-1-111-1-1-1-111ii−i−iiiii−i−i−i−i-1-1-1-11111i−i−ii-111-1-11i−i1-1−ii
χ3211-11-1-1-11−i−iii−i−iii−i−iii1-11-11-11-1-1-1-1-11111iiii−i−i−i−i1-1−ii−i−i−i−iiiii11-1-111-1-1-1-111ii−i−iiiii−i−i−i−i-1-1-1-11111−iii−i1-1-111-1−ii-11i−i
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χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ35222222222222-2-2-2-22222-2-22222-2-22222222222222222-2-2-2-20000000000000000-2-2-2-2-2-2-2-200000000000000000000000000000000
χ36222222222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222222200000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-222-2-2-2-2220000000000000000-2-22222-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-222-2-2-2-2220000000000000000-2-222-2-222-2-222-2-2-2-222220000000000000000000000000000000000000000
χ3922222222-2-2-2-22222222222-2-2-2-2220000000000000000-2-2-2-222-2-222-2-2-2-2-2-222220000000000000000000000000000000000000000
χ4022222222-2-2-2-22222222222-2-2-2-2220000000000000000-2-2-2-2-2-222-2-2222222-2-2-2-20000000000000000000000000000000000000000
χ4122222222-2-2-2-22222-2-2-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-2-2-2220000000000000000-2-2-2-2222200000000000000000000000000000000
χ4222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-222222222-2-22200000000000000002222-2-2-2-200000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022220000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000002222000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ4522-22-2-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-22-22-22-2200000000000000002-2−2i2i00000000000000000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000
χ4622-22-2-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-22-22-22-2200000000000000002-2−2i2i000000000000000000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000
χ4722-22-2-2-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-222-22-2-222222-2-2-2-22i2i2i2i−2i−2i−2i−2i-22−2i2i0000000000000000-2-222−2i−2i2i2i00000000000000000000000000000000
χ4822-22-2-2-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-222-22-2-22-2-2-2-22222−2i−2i−2i−2i2i2i2i2i-22−2i2i000000000000000022-2-22i2i−2i−2i00000000000000000000000000000000
χ4922-22-2-2-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-2-22-222-20000000000000000-222i−2i2i2i−2i−2i−2i−2i2i2i22-2-2-2-2220000000000000000000000000000000000000000
χ5022-22-2-2-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-2-22-222-20000000000000000-222i−2i−2i−2i2i2i2i2i−2i−2i-2-22222-2-20000000000000000000000000000000000000000
χ5122-22-2-2-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2-2-22-222-20000000000000000-22−2i2i2i2i−2i−2i−2i−2i2i2i-2-22222-2-20000000000000000000000000000000000000000
χ5222-22-2-2-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2-2-22-222-20000000000000000-22−2i2i−2i−2i2i2i2i2i−2i−2i22-2-2-2-2220000000000000000000000000000000000000000
χ5322-22-2-2-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-222-22-2-222222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-222i−2i0000000000000000-2-2222i2i−2i−2i00000000000000000000000000000000
χ5422-22-2-2-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-222-22-2-22-2-2-2-222222i2i2i2i−2i−2i−2i−2i-222i−2i000000000000000022-2-2−2i−2i2i2i00000000000000000000000000000000
χ5522-22-2-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-22-22-22-2200000000000000002-22i−2i00000000000000000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000
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χ582-22-22-2-2200002i−2i2i−2i2i−2i2i−2i2-20000-2222−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000-2200-22−2i2i−2i2i00002−22−2i2−i2i2−i2−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
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χ662-22-22-2-220000−2i2i−2i2i2i−2i2i−2i-2200002-222−2−222−2−2i2i2−i2−i2i2i2−i2−i20000−2i2i00−2i2i0000002-22-2−22−22−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000000000
χ672-22-22-2-220000−2i2i−2i2i2i−2i2i−2i-2200002-2−2−222−2−222−i2−i2i2i2−i2−i2i2i200002i−2i002i−2i000000-22-222−22−2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000000000
χ682-22-22-2-220000−2i2i−2i2i2i−2i2i−2i-2200002-2−2−222−2−222−i2−i2i2i2−i2−i2i2i20000−2i2i00−2i2i0000002-22-22−22−2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000000000
χ692-22-22-2-220000−2i2i−2i2i−2i2i−2i2i2-20000-2222−2−222−2−2−i2−i2i2i2−i2−i2i2i20000002-2002-2−2i2i−2i2i00002−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ702-22-22-2-220000−2i2i−2i2i−2i2i−2i2i2-20000-2222−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000-2200-222i−2i2i−2i00002−22−2−i2i2−i2i2−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ712-22-22-2-220000−2i2i−2i2i−2i2i−2i2i2-20000-22−2−222−2−222i2i2−i2−i2i2i2−i2−i20000002-2002-2−2i2i−2i2i0000−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ722-22-22-2-220000−2i2i−2i2i−2i2i−2i2i2-20000-22−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000-2200-222i−2i2i−2i0000−22−22i2−i2i2−i22−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ732-2-2-2-222200002-2-222-2-22220000-2-222−2−2−2−22222−2−2−2−2220000002i−2i00−2i2i−2i2i2i−2i00002−2−222−2−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ742-2-2-2-222200002-2-222-2-22220000-2-222−2−2−2−22222−2−2−2−222000000−2i2i002i−2i2i−2i−2i2i00002−2−222−2−22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ752-2-2-2-222200002-2-222-2-22220000-2-2−2−22222−2−2−2−22222−2−20000002i−2i00−2i2i−2i2i2i−2i0000−222−2−222−2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ762-2-2-2-222200002-2-222-2-22220000-2-2−2−22222−2−2−2−22222−2−2000000−2i2i002i−2i2i−2i−2i2i0000−222−2−222−2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ772-2-2-2-222200002-2-22-222-2-2-200002222−2−2−2−222−2−22222−2−200002-200-220000002-2-22−222−22−2−222−2−22−222−2−222−22−2−220000000000000000
χ782-2-2-2-222200002-2-22-222-2-2-200002222−2−2−2−222−2−22222−2−20000-22002-2000000-222-2−222−22−2−22−222−22−2−222−2−22−222−20000000000000000
χ792-2-2-2-222200002-2-22-222-2-2-2000022−2−22222−2−222−2−2−2−22200002-200-220000002-2-222−2−22−222−2−222−22−2−222−2−22−222−20000000000000000
χ802-2-2-2-222200002-2-22-222-2-2-2000022−2−22222−2−222−2−2−2−2220000-22002-2000000-222-22−2−22−222−22−2−22−222−2−222−22−2−220000000000000000
χ812-2-2-2-22220000-222-22-2-22-2-200002222−2−2−2−22222−2−2−2−22200002-200-22000000-222-2−222−2−222−22−2−22−222−22−2−22−222−20000000000000000
χ822-2-2-2-22220000-222-22-2-22-2-200002222−2−2−2−22222−2−2−2−2220000-22002-20000002-2-22−222−2−222−2−222−22−2−22−222−22−2−220000000000000000
χ832-2-2-2-22220000-222-22-2-22-2-2000022−2−22222−2−2−2−22222−2−200002-200-22000000-222-22−2−222−2−22−222−22−2−22−222−22−2−220000000000000000
χ842-2-2-2-22220000-222-22-2-22-2-2000022−2−22222−2−2−2−22222−2−20000-22002-20000002-2-222−2−222−2−222−2−22−222−22−2−22−222−20000000000000000
χ852-2-2-2-22220000-222-2-222-2220000-2-222−2−2−2−222−2−22222−2−20000002i−2i00−2i2i2i−2i−2i2i00002−2−22−222−2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ862-2-2-2-22220000-222-2-222-2220000-2-222−2−2−2−222−2−22222−2−2000000−2i2i002i−2i−2i2i2i−2i00002−2−22−222−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ872-2-2-2-22220000-222-2-222-2220000-2-2−2−22222−2−222−2−2−2−2220000002i−2i00−2i2i2i−2i−2i2i0000−222−22−2−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ882-2-2-2-22220000-222-2-222-2220000-2-2−2−22222−2−222−2−2−2−222000000−2i2i002i−2i−2i2i2i−2i0000−222−22−2−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ89444-4-4-44-40000000000000044-4-4004-44-44-44-400000000000000000000000000000000000000000000000000000000000000000000
χ90444-4-4-44-40000000000000044-4-400-44-44-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ91444-4-4-44-400000000000000-4-44400000000004i−4i4i−4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ92444-4-4-44-400000000000000-4-4440000000000−4i4i−4i4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ9344-4-444-4-4000000000000004-4-44004-44-4-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ9444-4-444-4-4000000000000004-4-4400-44-444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-444-4-400000000000000-444-400000000004-44-4-44-44000000000000000000000000000000000000000000000000000000000000
χ9644-4-444-4-400000000000000-444-40000000000-44-444-44-4000000000000000000000000000000000000000000000000000000000000
χ974-444-44-4-44-44-4000000000000000022−22−222222−22−222222−22−222222−22−2222000000000000000000000000000000000000000000000000000000000000
χ984-444-44-4-44-44-40000000000000000−222222−22−222222−22−222222−22−222222−22000000000000000000000000000000000000000000000000000000000000
χ994-444-44-4-4-44-44000000000000000022−22−222222−22−2222−222222−22−222222−22000000000000000000000000000000000000000000000000000000000000
χ1004-444-44-4-4-44-440000000000000000−222222−22−222222−2222−22−222222−22−2222000000000000000000000000000000000000000000000000000000000000
χ1014-4-444-44-44i−4i−4i4i000000000000000022−22−2222−222222−222i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ1024-4-444-44-44i−4i−4i4i0000000000000000−222222−2222−22−2222−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ1034-4-444-44-4−4i4i4i−4i000000000000000022−22−2222−222222−22−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ1044-4-444-44-4−4i4i4i−4i0000000000000000−222222−2222−22−22222i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000

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