Finite Group Databasebeta

← Group #11784331

Character table — Group #11784331

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222244444444444444444444888888888888888888888888999999991818181818181818181818181818181818181818363636363636363636363636
order12224444888833446666668812121212121212121212121212121212242424242424242424242424242424242222444444444444888888888888444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i-1-1ii−i−i-1-1ii−i−i
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii-1-1−i−iii-1-1−i−iii
χ511111111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i11−i−iii11−i−iii
χ811111111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii11ii−i−i11ii−i−i
χ911111111-1-1-1-11111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ1011111111-1-1-1-11111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111
χ1111111111-1-1-1-11111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii-1-1ii−i−i11−i−iii
χ1211111111-1-1-1-11111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i-1-1−i−iii11ii−i−i
χ1311111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ1411111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1
χ1511111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii11−i−iii-1-1ii−i−i
χ1611111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i11ii−i−i-1-1−i−iii
χ171111-1-1-1-1ii−i−i111-1111111i−i-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−i1-11-11-1i−ii−ii−i
χ181111-1-1-1-1ii−i−i111-1111111i−i-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111-1-111ii−i−i−i−iii−i−iii1-1-11-11i−i−ii−ii
χ191111-1-1-1-1ii−i−i111-1111111i−i-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111ii−i−i−i−iii−i−iii-1-11111-1-1-11i−i−ii−ii-111-1
χ201111-1-1-1-1ii−i−i111-1111111i−i-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i−i−iii11-1-1-1-111-11−iii−i−ii1-1-11
χ211111-1-1-1-1ii−i−i11-11111111−ii-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−i-11-11-11−ii−ii−ii
χ221111-1-1-1-1ii−i−i11-11111111−ii-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111-1-111ii−i−i−i−iii−i−iii-111-11-1−iii−ii−i
χ231111-1-1-1-1ii−i−i11-11111111−ii-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iii−i−iii-1-11111-1-11-1−iii−ii−i1-1-11
χ241111-1-1-1-1ii−i−i11-11111111−ii-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iiiii−i−i−i−iii11-1-1-1-1111-1i−i−iii−i-111-1
χ251111-1-1-1-1−i−iii111-1111111−ii-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii1-11-11-1−ii−ii−ii
χ261111-1-1-1-1−i−iii111-1111111−ii-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-111-1-111−i−iiiii−i−iii−i−i1-1-11-11−iii−ii−i
χ271111-1-1-1-1−i−iii111-1111111−ii-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iiiii−i−i11-1-1-1-111-11i−i−iii−i1-1-11
χ281111-1-1-1-1−i−iii111-1111111−ii-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111−i−iiiii−i−iii−i−i-1-11111-1-1-11−iii−ii−i-111-1
χ291111-1-1-1-1−i−iii11-11111111i−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii-11-11-11i−ii−ii−i
χ301111-1-1-1-1−i−iii11-11111111i−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iiiii−i−iii−i−i-111-11-1i−i−ii−ii
χ311111-1-1-1-1−i−iii11-11111111i−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i−i−iiiii−i−i11-1-1-1-1111-1−iii−i−ii-111-1
χ321111-1-1-1-1−i−iii11-11111111i−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−iii−i−i-1-11111-1-11-1i−i−ii−ii1-1-11
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χ3422-2-222-2-22-22-2220022-2-2-2-2002222-2-2-2-20000000022-2-222-2-200000000-2-222-2-22200000000-22-2200000000000000000000
χ3522-2-222-2-2-22-22220022-2-2-2-2002222-2-2-2-200000000-2-222-2-2220000000022-2-222-2-200000000-22-2200000000000000000000
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χ432-22-22i−2i2i−2i00002200-2-222-2-2002i2i−2i−2i2i2i−2i−2i000000000000000000000000-22-22−2i2i−2i2i0000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ000000000000
χ442-22-22i−2i2i−2i00002200-2-222-2-2002i2i−2i−2i2i2i−2i−2i000000000000000000000000-22-22−2i2i−2i2i000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ000000000000
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χ462-22-2−2i2i−2i2i00002200-2-222-2-200−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-22-2−2i2i−2i2i000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000
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χ482-22-2−2i2i−2i2i00002200-2-222-2-200−2i−2i2i2i−2i−2i2i2i000000000000000000000000-22-222i−2i2i−2i000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3000000000000
χ492-2-222i−2i−2i2i00002200-2-2-2-222002i2i−2i−2i−2i−2i2i2i0000000000000000000000002-2-222i−2i−2i2i2i−2i2-22i−2i2-2000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.