Finite Group Databasebeta

← Group #72342838

Character table — Group #72342838

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size1111222222444444444444888888888888888888888888888888881616161616161616161616161616161616161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232646464646464
order12442224442222224444442222224444448888888888888888888822222444444444444488888888888888888888884444444444888888888888444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1111-1-1111-1-11111-1-1-1-11111-1-1111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ911111111111111111111111-1-11111111-1-111111111111111111111-11111-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ1011111111111111111111111-1-11111111-1-11111111111111111-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ1111111111111111111111111-1-11111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1-1-111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1211111111111111111111111-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1
χ1311111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-111-1-111
χ1411111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-1
χ1511111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ1611111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ1711-1-1111-1-1-1111111-1-1-1-1-1-1-11111-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i11-11-1-11-11-111-1-111-1-1ii−i−ii−iii−i−iii−i−iii−i−iii−i−i1-111-1-111-1-1ii−i−iii−i−iii−i−i1-11-1i−i
χ1811-1-1111-1-1-1111111-1-1-1-1-1-1-11111-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii11-1-11-11-1-1111-1-1-1-111ii−i−i−iiii−i−iii−i−iii−i−i−i−iii1-111-1-1-1-111ii−i−i−i−iii−i−iii-11-11−ii
χ1911-1-1111-1-1-1111111-1-1-1-1-1-1-11111-111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i1-111-1-1-111-111-1-111-1-1−i−iiii−iii−i−i−i−iii−i−iiiii−i−i-11-1-111-1-111ii−i−iii−i−i−i−iii1-1-11−ii
χ2011-1-1111-1-1-1111111-1-1-1-1-1-1-11111-111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iii1-11-11-1-11-1111-1-1-1-111−i−iii−iiii−i−i−i−iii−i−iii−i−iii-11-1-11111-1-1ii−i−i−i−iiiii−i−i-111-1i−i
χ2111-1-1111-1-1-1111111-1-1-1-1-1-1-11111-111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i1-11-11-1-11-1111-1-1-1-111ii−i−ii−i−i−iiiii−i−iii−i−iii−i−i-11-1-11111-1-1−i−iiiii−i−i−i−iii-111-1−ii
χ2211-1-1111-1-1-1111111-1-1-1-1-1-1-11111-111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii1-111-1-1-111-111-1-111-1-1ii−i−i−ii−i−iiiii−i−iii−i−i−i−iii-11-1-111-1-111−i−iii−i−iiiii−i−i1-1-11i−i
χ2311-1-1111-1-1-1111111-1-1-1-1-1-1-11111-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i11-1-11-11-1-1111-1-1-1-111−i−iiii−i−i−iii−i−iii−i−iiiii−i−i1-111-1-1-1-111−i−iiiii−i−iii−i−i-11-11i−i
χ2411-1-1111-1-1-1111111-1-1-1-1-1-1-11111-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii11-11-1-11-11-111-1-111-1-1−i−iii−ii−i−iii−i−iii−i−iii−i−iii1-111-1-111-1-1−i−iii−i−iii−i−iii1-11-1−ii
χ2511-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-111-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−i-11-11-111-11-1-1-11111-1-1−i−iiii−iii−i−iii−i−i−i−iiiii−i−i1-1-1-11111-1-1−i−iii−i−iiiii−i−i-11-11−ii
χ2611-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-111-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii-11-1-1111-1-11-1-111-1-111−i−iii−iiii−i−iii−i−i−i−iii−i−iii1-1-1-111-1-111−i−iiiii−i−i−i−iii1-11-1i−i
χ2711-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-111-111-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i-1-111-11-111-1-1-11111-1-1ii−i−ii−iii−i−i−i−iiiii−i−iii−i−i-1111-1-1-1-111−i−iii−i−iii−i−iii-111-1i−i
χ2811-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-111-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iii-1-11-111-11-11-1-111-1-111ii−i−i−iiii−i−i−i−iiiii−i−i−i−iii-1111-1-111-1-1−i−iiiii−i−iii−i−i1-1-11−ii
χ2911-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-111-111-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-11-111-11-11-1-111-1-111−i−iiii−i−i−iiiii−i−i−i−iiiii−i−i-1111-1-111-1-1ii−i−i−i−iii−i−iii1-1-11i−i
χ3011-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-111-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iii-1-111-11-111-1-1-11111-1-1−i−iii−ii−i−iiiii−i−i−i−iii−i−iii-1111-1-1-1-111ii−i−iii−i−iii−i−i-111-1−ii
χ3111-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-111-111-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−i-11-1-1111-1-11-1-111-1-111ii−i−ii−i−i−iii−i−iiiii−i−iii−i−i1-1-1-111-1-111ii−i−i−i−iiiii−i−i1-11-1−ii
χ3211-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-111-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii-11-11-111-11-1-1-11111-1-1ii−i−i−ii−i−iii−i−iiiii−i−i−i−iii1-1-1-11111-1-1ii−i−iii−i−i−i−iii-11-11i−i
χ3322222222222222-2-22222-2-2-2002-2-2-2-22-2000000000022-2-222-2-2222200000000000000000000002200002-22-20000-2-2-2-20000002-22-2000000000000000000
χ3422222222222222-2-22222-2-2-2002-2-2-2-22-2000000000022-2-222-2-2-2-2-2-20000000000000000000000-2-200002-22-200002222000000-22-22000000000000000000
χ3522222222222222-2-22222-2-2-2002-2-2-2-22-20000000000-2-222-2-22222220000000000000000000000220000-22-220000-2-2-2-2000000-22-22000000000000000000
χ3622222222222222-2-22222-2-2-2002-2-2-2-22-20000000000-2-222-2-222-2-2-2-20000000000000000000000-2-20000-22-22000022220000002-22-2000000000000000000
χ37222222222222-2-22222-2-222-222-22-2-2-2-222222-2-222-2-20000000000002000020000-2-2-2-200000000002-22-200000000000000000000002-22-200000000000000
χ38222222222222-2-22222-2-222-222-22-2-2-2-2222-2-222-2-2220000000000002000020000-2-2-2-20000000000-22-220000000000000000000000-22-2200000000000000
χ39222222222222-2-22222-2-222-2-2-2-22-2-2-2-22-2-222-2-222-2-2000000000000-20000-20000222200000000002-22-20000000000000000000000-22-2200000000000000
χ40222222222222-2-22222-2-222-2-2-2-22-2-2-2-22-2-2-2-222-2-222000000000000-20000-2000022220000000000-22-2200000000000000000000002-22-200000000000000
χ412222222222-2-22222-2-22222200-2-2-22-2-2-20022222222222222220000022000220000000000000000-2-2-2-2-2-2-2-200000000-2-200000000000000000000000000
χ422222222222-2-22222-2-22222200-2-2-22-2-2-20022222222-2-2-2-2-2-2-2-200000-2-2000-2-20000000000000000-2-2-2-22222000000002200000000000000000000000000
χ432222222222-2-22222-2-22222200-2-2-22-2-2-200-2-2-2-2-2-2-2-22222222200000-2-2000-2-200000000000000002222-2-2-2-2000000002200000000000000000000000000
χ442222222222-2-22222-2-22222200-2-2-22-2-2-200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000220002200000000000000002222222200000000-2-200000000000000000000000000
χ452222222222-2-222-2-2-2-222-2-2-200-222-22-22000000000022-2-222-2-2000000022000220000-2-2-2-20000000000-22-22000000000000000000000000002-22-2000000
χ462222222222-2-222-2-2-2-222-2-2-200-222-22-22000000000022-2-222-2-20000000-2-2000-2-2000022220000000000-22-2200000000000000000000000000-22-22000000
χ472222222222-2-222-2-2-2-222-2-2-200-222-22-220000000000-2-222-2-222000000022000220000-2-2-2-200000000002-22-200000000000000000000000000-22-22000000
χ482222222222-2-222-2-2-2-222-2-2-200-222-22-220000000000-2-222-2-2220000000-2-2000-2-20000222200000000002-22-2000000000000000000000000002-22-2000000
χ492222222222-2-2-2-222-2-2-2-222-2002-22-222-20022-2-222-2-2000000000000000000000000000000222200-22-220000-2-2-2-20000002-22-20000000000000000000000
χ502222222222-2-2-2-222-2-2-2-222-2002-22-222-20022-2-222-2-2000000000000000000000000000000-2-2-2-200-22-2200002222000000-22-220000000000000000000000
χ512222222222-2-2-2-222-2-2-2-222-2002-22-222-200-2-222-2-2220000000000000000000000000000002222002-22-20000-2-2-2-2000000-22-220000000000000000000000
χ522222222222-2-2-2-222-2-2-2-222-2002-22-222-200-2-222-2-222000000000000000000000000000000-2-2-2-2002-22-2000022220000002-22-20000000000000000000000
χ5322-2-2222-2-2-22222-2-2-2-2-2-2222002-22-2-2-2200000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000002i−2i00002i−2i−2i2i0000−2i−2i2i2i0000002-2-22000000000000000000
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χ5622-2-2222-2-2-22222-2-2-2-2-2-2222002-22-2-2-220000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000−2i2i0000−2i2i2i−2i00002i2i−2i−2i0000002-2-22000000000000000000
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χ5822-2-2222-2-2-222-2-222-2-222-2-2222-222-2-22-2-2-2−2i−2i2i2i2i2i−2i−2i00000000000020000-20000-2-2220000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i00000000000000
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χ6122-2-2222-2-2-2-2-2222222-2-2-2-2-200-2-222-222002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000002-20002-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000-2200000000000000000000000000
χ6222-2-2222-2-2-2-2-2222222-2-2-2-2-200-2-222-222002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000-22000-220000000000000000−2i−2i2i2i2i2i−2i−2i000000002-200000000000000000000000000
χ6322-2-2222-2-2-2-2-2222222-2-2-2-2-200-2-222-22200−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000-22000-2200000000000000002i2i−2i−2i−2i−2i2i2i000000002-200000000000000000000000000
χ6422-2-2222-2-2-2-2-2222222-2-2-2-2-200-2-222-22200−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000002-20002-200000000000000002i2i−2i−2i2i2i−2i−2i00000000-2200000000000000000000000000
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χ6722-2-2222-2-2-2-2-222-2-222-2-222200-22-2-222-20000000000−2i−2i2i2i2i2i−2i−2i00000002-20002-20000-2-22200000000002i−2i−2i2i00000000000000000000000000−2i2i2i−2i000000
χ6822-2-2222-2-2-2-2-222-2-222-2-222200-22-2-222-20000000000−2i−2i2i2i2i2i−2i−2i0000000-22000-22000022-2-200000000002i−2i−2i2i000000000000000000000000002i−2i−2i2i000000
χ6922-2-2222-2-2-2-2-2-2-2222222-2-22002-2-2-22-22002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000002i2i−2i−2i00−2i2i2i−2i0000−2i−2i2i2i0000002-2-220000000000000000000000
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χ7122-2-2222-2-2-2-2-2-2-2222222-2-22002-2-2-22-2200−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000002i2i−2i−2i002i−2i−2i2i0000−2i−2i2i2i000000-222-20000000000000000000000
χ7222-2-2222-2-2-2-2-2-2-2222222-2-22002-2-2-22-2200−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000−2i−2i2i2i002i−2i−2i2i00002i2i−2i−2i0000002-2-220000000000000000000000
χ73444444444444-4-4-4-444-4-4-4-4400-4-4444-4-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ7544444-4-4-44-400004-400004-4000000000000004-4004-40000000022220002-2000-2200002-22-20000-2-20000000000002-22-20000000000000000000000000000
χ7644444-4-4-44-400004-400004-4000000000000004-4004-400000000-2-2-2-2000-220002-20000-22-22000022000000000000-22-220000000000000000000000000000
χ7744444-4-4-44-400004-400004-400000000000000-4400-44000000002222000-220002-20000-22-220000-2-20000000000002-22-20000000000000000000000000000
χ7844444-4-4-44-400004-400004-400000000000000-4400-4400000000-2-2-2-20002-2000-2200002-22-2000022000000000000-22-220000000000000000000000000000
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χ1198-8−8i8i0000004-40000−4i4i00000-4400000004i−4i00000000000000004ζ3−4ζ34ζ−4ζ000000000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000000000
χ1208-8−8i8i0000004-40000−4i4i00000-4400000004i−4i0000000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000000000
χ12116-1616i−16i000000-880000−8i8i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12216-16−16i16i000000-8800008i−8i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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