Finite Group Databasebeta

← Group #11783236

Character table — Group #11783236

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222444444444444444444444444444444449999181818181818363636363636363611112222224444444444444444444444444444444499991818181818183636363636363636
order122244888833666666121212121212121224242424242424242424242424242424222244888844444444222244888866666666121212121212121224242424242424242424242424242424222244888844444444
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
χ91-1-111-1ii−i−i11-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-11-1ii−i−i1-1i−i1-1i−i1-1-111-1ii−i−i11-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-11-1ii−i−i1-1i−i1-1i−i
χ101-1-111-1ii−i−i11-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-11-1ii−i−i-11−ii-11−ii1-1-111-1ii−i−i11-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-11-1ii−i−i-11−ii-11−ii
χ111-1-111-1ii−i−i11-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-11−i−iiii−i-11−ii1-11-1-111-1ii−i−i11-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-11−i−iiii−i-11−ii1-1
χ121-1-111-1ii−i−i11-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-11−i−iii−ii1-1i−i-111-1-111-1ii−i−i11-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-11−i−iii−ii1-1i−i-11
χ131-1-111-1−i−iii11-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-11-1−i−iii1-1−ii1-1−ii1-1-111-1−i−iii11-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-11-1−i−iii1-1−ii1-1−ii
χ141-1-111-1−i−iii11-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-11-1−i−iii-11i−i-11i−i1-1-111-1−i−iii11-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-11-1−i−iii-11i−i-11i−i
χ151-1-111-1−i−iii11-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-11ii−i−ii−i1-1−ii-111-1-111-1−i−iii11-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-11ii−i−ii−i1-1−ii-11
χ161-1-111-1−i−iii11-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-11ii−i−i−ii-11i−i1-11-1-111-1−i−iii11-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-11ii−i−i−ii-11i−i1-1
χ172222-2-2000022222222-2-2-2-2-2-2-2-200000000000000002222-2-20000000000002222-2-2000022222222-2-2-2-2-2-2-2-200000000000000002222-2-2000000000000
χ182222-2-2000022222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2220000000000002222-2-2000022222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-222000000000000
χ1922-2-200i2−i2i2−i22222-2-2-2-200000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22-2-2200i2−i2i2−i20000000022-2-200i2−i2i2−i22222-2-2-2-200000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22-2-2200i2−i2i2−i200000000
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χ2222-2-200−i2i2−i2i22222-2-2-2-200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2-222-200i2−i2i2−i20000000022-2-200−i2i2−i2i22222-2-2-2-200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2-222-200i2−i2i2−i200000000
χ232-22-2002−2−2222-2-222-2-2000000002222−2−2−2−2−2−2−2−2222222-2-2002−2−22000000002-22-2002−2−2222-2-222-2-2000000002222−2−2−2−2−2−2−2−2222222-2-2002−2−2200000000
χ242-22-2002−2−2222-2-222-2-2000000002222−2−2−2−2−2−2−2−22222-2-22200−222−2000000002-22-2002−2−2222-2-222-2-2000000002222−2−2−2−2−2−2−2−22222-2-22200−222−200000000
χ252-22-200−222−222-2-222-2-200000000−2−2−2−222222222−2−2−2−222-2-200−222−2000000002-22-200−222−222-2-222-2-200000000−2−2−2−222222222−2−2−2−222-2-200−222−200000000
χ262-22-200−222−222-2-222-2-200000000−2−2−2−222222222−2−2−2−2-2-222002−2−22000000002-22-200−222−222-2-222-2-200000000−2−2−2−222222222−2−2−2−2-2-222002−2−2200000000
χ272-2-22-22000022-2-2-2-222-2-2-2-2222200000000000000002-22-2-220000000000002-2-22-22000022-2-2-2-222-2-2-2-2222200000000000000002-22-2-22000000000000
χ282-2-22-22000022-2-2-2-222-2-2-2-222220000000000000000-22-222-20000000000002-2-22-22000022-2-2-2-222-2-2-2-222220000000000000000-22-222-2000000000000
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χ304444444444-21-21-21-21-2-211-2-211-2-211-2-211-2-211-2-2110000000000000000004444444444-21-21-21-21-2-211-2-211-2-211-2-211-2-211-2-211000000000000000000
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χ344444-4-400001-21-21-21-2-1-122-1-122−3i3i00−3i3i00−3i3i00−3i3i000000000000000000004444-4-400001-21-21-21-2-1-122-1-122−3i3i00−3i3i00−3i3i00−3i3i00000000000000000000
χ354444-4-40000-21-21-21-2122-1-122-1-1003i−3i003i−3i003i−3i003i−3i0000000000000000004444-4-40000-21-21-21-2122-1-122-1-1003i−3i003i−3i003i−3i003i−3i000000000000000000
χ364444-4-40000-21-21-21-2122-1-122-1-100−3i3i00−3i3i00−3i3i00−3i3i0000000000000000004444-4-40000-21-21-21-2122-1-122-1-100−3i3i00−3i3i00−3i3i00−3i3i000000000000000000
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χ3844-4-4002i2−2i22i2−2i21-21-2-12-12−3i3i00−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i200000000000000000044-4-4002i2−2i22i2−2i21-21-2-12-12−3i3i00−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2000000000000000000
χ3944-4-4002i2−2i22i2−2i2-21-212-12-1003i−3i003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ300000000000000000044-4-4002i2−2i22i2−2i2-21-212-12-1003i−3i003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ3000000000000000000
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χ4144-4-400−2i22i2−2i22i21-21-2-12-123i−3i003i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i200000000000000000044-4-400−2i22i2−2i22i21-21-2-12-123i−3i003i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i2000000000000000000
χ4244-4-400−2i22i2−2i22i21-21-2-12-12−3i3i00−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i200000000000000000044-4-400−2i22i2−2i22i21-21-2-12-12−3i3i00−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2000000000000000000
χ4344-4-400−2i22i2−2i22i2-21-212-12-1003i−3i003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ300000000000000000044-4-400−2i22i2−2i22i2-21-212-12-1003i−3i003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3000000000000000000
χ4444-4-400−2i22i2−2i22i2-21-212-12-100−3i3i00−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ300000000000000000044-4-400−2i22i2−2i22i2-21-212-12-100−3i3i00−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3000000000000000000
χ454-44-40022−22−22221-2-121-2-123i−3i00−3i3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−20000000000000000004-44-40022−22−22221-2-121-2-123i−3i00−3i3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000000000000
χ464-44-40022−22−22221-2-121-2-12−3i3i003i−3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−20000000000000000004-44-40022−22−22221-2-121-2-12−3i3i003i−3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000000000000
χ474-44-40022−22−2222-212-1-212-1003i−3i00−3i3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ30000000000000000004-44-40022−22−2222-212-1-212-1003i−3i00−3i3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000000000000
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χ504-44-400−222222−221-2-121-2-12−3i3i003i−3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3220000000000000000004-44-400−222222−221-2-121-2-12−3i3i003i−3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000000000000
χ514-44-400−222222−22-212-1-212-1003i−3i00−3i3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ30000000000000000004-44-400−222222−22-212-1-212-1003i−3i00−3i3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000000000000
χ524-44-400−222222−22-212-1-212-100−3i3i003i−3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ30000000000000000004-44-400−222222−22-212-1-212-100−3i3i003i−3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000000000000
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χ544-4-444-44i4i−4i−4i-212-12-1-21-2-21122-1-1−2i−2iii−2i−2iii2i2i−i−i2i2i−i−i0000000000000000004-4-444-44i4i−4i−4i-212-12-1-21-2-21122-1-1−2i−2iii−2i−2iii2i2i−i−i2i2i−i−i000000000000000000
χ554-4-444-4−4i−4i4i4i1-2-12-121-211-2-2-1-122−i−i2i2i−i−i2i2iii−2i−2iii−2i−2i0000000000000000004-4-444-4−4i−4i4i4i1-2-12-121-211-2-2-1-122−i−i2i2i−i−i2i2iii−2i−2iii−2i−2i000000000000000000
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χ1194-4-44-440000-212-12-1-2122-1-1-2-211003-3003-300-3300-33000000000000000000-444-44-400002-1-21-212-1-2-21122-1-100-3300-33003-3003-3000000000000000000
χ1204-4-44-440000-212-12-1-2122-1-1-2-21100-3300-33003-3003-3000000000000000000-444-44-400002-1-21-212-1-2-21122-1-1003-3003-300-3300-33000000000000000000

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