Finite Group Databasebeta

← Group #11858616

Character table — Group #11858616

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222444444444444444444444444444444449999181818181818363636363636363611112222224444444444444444444444444444444499991818181818183636363636363636
order124424888833666666121212121212121224242424242424242424242424242424224424888888888888224424888866666666121212121212121224242424242424242424242424242424224424888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ6111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111
χ7111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ911-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1111-1-1i−ii−ii−ii−i11-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1111-1-1i−ii−ii−ii−i
χ1011-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1111-1-1−ii−ii−ii−ii11-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1111-1-1−ii−ii−ii−ii
χ1111-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1111-11-1-11-1111-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1111-11-1-11-11
χ1211-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-111-11-111-11-111-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-111-11-111-11-1
χ1311-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-11-1-111i−i−iii−i−ii11-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-11-1-111i−i−iii−i−ii
χ1411-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-11-1-111−iii−i−iii−i11-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-11-1-111−iii−i−iii−i
χ1511-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111-111-1-11-1-11-111-111-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111-111-1-11-1-11-111-1
χ1611-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111-111-1-1-111-11-1-1111-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111-111-1-1-111-11-1-11
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χ182222-2-2000022-2-2-2-2222222-2-2-2-20000000000000000-2-2-2-2220000000000002222-2-2000022-2-2-2-2222222-2-2-2-20000000000000000-2-2-2-222000000000000
χ1922-2-22-2000022222222-2-2-2-2-2-2-2-2000000000000000022-2-22-200000000000022-2-22-2000022222222-2-2-2-2-2-2-2-2000000000000000022-2-22-2000000000000
χ2022-2-22-2000022222222-2-2-2-2-2-2-2-20000000000000000-2-222-2200000000000022-2-22-2000022222222-2-2-2-2-2-2-2-20000000000000000-2-222-22000000000000
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χ242-22i−2i00−i2i2−22220000-2-22i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2−2−2−2−22222-22−2i2i00i2−i22−2000000002-22i−2i00−i2i2−22220000-2-22i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2−2−2−2−22222-22−2i2i00i2−i22−200000000
χ252-2−2i2i00i2−i2−22220000-2-2−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2−2−2−2−222222-2−2i2i00i2−i2−22000000002-2−2i2i00i2−i2−22220000-2-2−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2−2−2−2−222222-2−2i2i00i2−i2−2200000000
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χ282-2−2i2i00−i2i22−2220000-2-2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i22222−2−2−2−2-222i−2i00i2−i2−22000000002-2−2i2i00−i2i22−2220000-2-2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i22222−2−2−2−2-222i−2i00i2−i2−2200000000
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χ304444444444-21-2-211-21-21-21-2-211-2-211-2-211-2-211-2-2110000000000000000004444444444-21-2-211-21-21-21-2-211-2-211-2-211-2-211-2-211000000000000000000
χ31444444-4-4-4-41-211-2-21-21-21-211-2-2-1-122-1-122-1-122-1-122000000000000000000444444-4-4-4-41-211-2-21-21-21-211-2-2-1-122-1-122-1-122-1-122000000000000000000
χ32444444-4-4-4-4-21-2-211-21-21-21-2-21122-1-122-1-122-1-122-1-1000000000000000000444444-4-4-4-4-21-2-211-21-21-21-2-21122-1-122-1-122-1-122-1-1000000000000000000
χ334444-4-400001-2-1-1221-21-21-2-1-1223i−3i003i−3i003i−3i003i−3i000000000000000000004444-4-400001-2-1-1221-21-21-2-1-1223i−3i003i−3i003i−3i003i−3i00000000000000000000
χ344444-4-400001-2-1-1221-21-21-2-1-122−3i3i00−3i3i00−3i3i00−3i3i000000000000000000004444-4-400001-2-1-1221-21-21-2-1-122−3i3i00−3i3i00−3i3i00−3i3i00000000000000000000
χ354444-4-40000-2122-1-1-21-21-2122-1-1003i−3i003i−3i003i−3i003i−3i0000000000000000004444-4-40000-2122-1-1-21-21-2122-1-1003i−3i003i−3i003i−3i003i−3i000000000000000000
χ364444-4-40000-2122-1-1-21-21-2122-1-100−3i3i00−3i3i00−3i3i00−3i3i0000000000000000004444-4-40000-2122-1-1-21-21-2122-1-100−3i3i00−3i3i00−3i3i00−3i3i000000000000000000
χ3744-4-44-400001-211-2-21-2-12-12-1-1223i−3i003i−3i00−3i3i00−3i3i0000000000000000000044-4-44-400001-211-2-21-2-12-12-1-1223i−3i003i−3i00−3i3i00−3i3i00000000000000000000
χ3844-4-44-400001-211-2-21-2-12-12-1-122−3i3i00−3i3i003i−3i003i−3i0000000000000000000044-4-44-400001-211-2-21-2-12-12-1-122−3i3i00−3i3i003i−3i003i−3i00000000000000000000
χ3944-4-44-40000-21-2-211-212-12-122-1-1003i−3i003i−3i00−3i3i00−3i3i00000000000000000044-4-44-40000-21-2-211-212-12-122-1-1003i−3i003i−3i00−3i3i00−3i3i000000000000000000
χ4044-4-44-40000-21-2-211-212-12-122-1-100−3i3i00−3i3i003i−3i003i−3i00000000000000000044-4-44-40000-21-2-211-212-12-122-1-100−3i3i00−3i3i003i−3i003i−3i000000000000000000
χ4144-4-4-4444-4-41-2-1-1221-2-12-1211-2-211-2-211-2-2-1-122-1-12200000000000000000044-4-4-4444-4-41-2-1-1221-2-12-1211-2-211-2-211-2-2-1-122-1-122000000000000000000
χ4244-4-4-4444-4-4-2122-1-1-212-12-1-2-211-2-211-2-21122-1-122-1-100000000000000000044-4-4-4444-4-4-2122-1-1-212-12-1-2-211-2-211-2-21122-1-122-1-1000000000000000000
χ4344-4-4-44-4-4441-2-1-1221-2-12-1211-2-2-1-122-1-12211-2-211-2-200000000000000000044-4-4-44-4-4441-2-1-1221-2-12-1211-2-2-1-122-1-12211-2-211-2-2000000000000000000
χ4444-4-4-44-4-444-2122-1-1-212-12-1-2-21122-1-122-1-1-2-211-2-21100000000000000000044-4-4-44-4-444-2122-1-1-212-12-1-2-21122-1-122-1-1-2-211-2-211000000000000000000
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χ464-44i−4i002i2−2i222−221-2-3300-12i−2i−i2i−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3220000000000000000004-44i−4i002i2−2i222−221-2-3300-12i−2i−i2i−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000000000000
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χ484-44i−4i002i2−2i222−22-2100-332-1−2ii2i−i00−3i3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ30000000000000000004-44i−4i002i2−2i222−22-2100-332-1−2ii2i−i00−3i3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000000000000
χ494-44i−4i00−2i22i2−22221-23-300-12i−2i−i2i3i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−20000000000000000004-44i−4i00−2i22i2−22221-23-300-12i−2i−i2i3i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000000000000
χ504-44i−4i00−2i22i2−22221-2-3300-12i−2i−i2i−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−20000000000000000004-44i−4i00−2i22i2−22221-2-3300-12i−2i−i2i−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000000000000
χ514-44i−4i00−2i22i2−2222-21003-32-1−2ii2i−i003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ30000000000000000004-44i−4i00−2i22i2−2222-21003-32-1−2ii2i−i003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000000000000
χ524-44i−4i00−2i22i2−2222-2100-332-1−2ii2i−i00−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ30000000000000000004-44i−4i00−2i22i2−2222-2100-332-1−2ii2i−i00−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000000000000
χ534-4−4i4i002i2−2i2−22221-23-300-12−i2ii−2i−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−20000000000000000004-4−4i4i002i2−2i2−22221-23-300-12−i2ii−2i−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000000000000
χ544-4−4i4i002i2−2i2−22221-2-3300-12−i2ii−2i3i−3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−20000000000000000004-4−4i4i002i2−2i2−22221-2-3300-12−i2ii−2i3i−3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000000000000
χ554-4−4i4i002i2−2i2−2222-21003-32-12i−i−2ii00−3i3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ30000000000000000004-4−4i4i002i2−2i2−2222-21003-32-12i−i−2ii00−3i3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000000000000
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χ574-4−4i4i00−2i22i222−221-23-300-12−i2ii−2i−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3220000000000000000004-4−4i4i00−2i22i222−221-23-300-12−i2ii−2i−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000000000000
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χ1154-4−4i4i002i2−2i2−2222-21003-32-12i−i−2ii00−3i3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000000000000-444i−4i00−2i22i222−222-100-33-21−2ii2i−i003i−3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000000000000
χ1164-4−4i4i002i2−2i2−2222-2100-332-12i−i−2ii003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000000000000-444i−4i00−2i22i222−222-1003-3-21−2ii2i−i00−3i3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000000000000
χ1174-4−4i4i00−2i22i222−221-23-300-12−i2ii−2i−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000000000000-444i−4i002i2−2i2−2222-12-33001-2i−2i−i2i3i−3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000000000000
χ1184-4−4i4i00−2i22i222−221-2-3300-12−i2ii−2i3i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i2−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322000000000000000000-444i−4i002i2−2i2−2222-123-3001-2i−2i−i2i−3i3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000000000000
χ1194-4−4i4i00−2i22i222−22-21003-32-12i−i−2ii00−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000000000000-444i−4i002i2−2i2−22222-100-33-21−2ii2i−i003i−3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000000000000
χ1204-4−4i4i00−2i22i222−22-2100-332-12i−i−2ii003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000000000000-444i−4i002i2−2i2−22222-1003-3-21−2ii2i−i00−3i3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000000000000

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