Finite Group Databasebeta

← Group #11784333

Character table — Group #11784333

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222244444444444444444444888888888888888888888888999999991818181818181818181818181818181818181818363636363636363636363636
order122222224444334444666666666666661212121212121212121212121212121212121212121212124444444444448888888888888888444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1−i−iii−i−iii
χ511111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111−i−iii−i−iii
χ811111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111ii−i−iii−i−i
χ911111111-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ1011111111-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111
χ1111111111-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii
χ1211111111-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ1311111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
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
χ1511111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ1611111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iii
χ171-1-1111-1-1ii−i−i111-1i−i1111-1-1-1-111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1-1-111ii−i−iii−i−iii−i−i11-1-111-1-11-1i−ii−ii−i1-11-1
χ181-1-1111-1-1ii−i−i111-1i−i1111-1-1-1-111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii−i−iii-1-111-1-1111-1i−i−ii−ii-11-11
χ191-1-1111-1-1ii−i−i111-1i−i1111-1-1-1-111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-11111-1-1−i−iii11-1-1-1-111−i−iiiii−i−i-11−ii1-1-11−iii−i
χ201-1-1111-1-1ii−i−i111-1i−i1111-1-1-1-111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-11111-1-1−i−iii-1-11111-1-1ii−i−i−i−iii-11−ii-111-1i−i−ii
χ211-1-1111-1-1ii−i−i11-11−ii1111-1-1-1-111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1-1-111ii−i−iii−i−iii−i−i11-1-111-1-1-11−ii−ii−ii-11-11
χ221-1-1111-1-1ii−i−i11-11−ii1111-1-1-1-111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii−i−iii-1-111-1-111-11−iii−ii−i1-11-1
χ231-1-1111-1-1ii−i−i11-11−ii1111-1-1-1-111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-11111-1-1−i−iii11-1-1-1-111−i−iiiii−i−i1-1i−i-111-1i−i−ii
χ241-1-1111-1-1ii−i−i11-11−ii1111-1-1-1-111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-11111-1-1−i−iii-1-11111-1-1ii−i−i−i−iii1-1i−i1-1-11−iii−i
χ251-1-1111-1-1−i−iii111-1−ii1111-1-1-1-111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−iii−i−i-1-111-1-1111-1−iii−ii−i-11-11
χ261-1-1111-1-1−i−iii111-1−ii1111-1-1-1-111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1-1-111−i−iii−i−iii−i−iii11-1-111-1-11-1−ii−ii−ii1-11-1
χ271-1-1111-1-1−i−iii111-1−ii1111-1-1-1-111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-11111-1-1ii−i−i11-1-1-1-111ii−i−i−i−iii-11i−i1-1-11i−i−ii
χ281-1-1111-1-1−i−iii111-1−ii1111-1-1-1-111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-11111-1-1ii−i−i-1-11111-1-1−i−iiiii−i−i-11i−i-111-1−iii−i
χ291-1-1111-1-1−i−iii11-11i−i1111-1-1-1-111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1-1-111−i−iiiii−i−iii−i−i-1-111-1-111-11i−i−ii−ii1-11-1
χ301-1-1111-1-1−i−iii11-11i−i1111-1-1-1-111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1-1-111−i−iii−i−iii−i−iii11-1-111-1-1-11i−ii−ii−i-11-11
χ311-1-1111-1-1−i−iii11-11i−i1111-1-1-1-111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-11111-1-1ii−i−i11-1-1-1-111ii−i−i−i−iii1-1−ii-111-1−iii−i
χ321-1-1111-1-1−i−iii11-11i−i1111-1-1-1-111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-11111-1-1ii−i−i-1-11111-1-1−i−iiiii−i−i1-1−ii1-1-11i−i−ii
χ33222-22-2-2-2000022000022-2-22222-2-2-2-2-2-20000000000000000000000002222-2-2-2-200002-22-22-22-200000000000000000000
χ34222-22-2-2-2000022000022-2-22222-2-2-2-2-2-20000000000000000000000002222-2-2-2-20000-22-22-22-2200000000000000000000
χ35222-22-2-2-2000022000022-2-22222-2-2-2-2-2-2000000000000000000000000-2-2-2-2222200002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ36222-22-2-2-2000022000022-2-22222-2-2-2-2-2-2000000000000000000000000-2-2-2-222220000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ3722-22-2-22-20000220000-2-2-2-222-2-22222-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000
χ3822-22-2-22-20000220000-2-2-2-222-2-22222-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000
χ3922-22-2-22-20000220000-2-2-2-222-2-22222-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000
χ4022-22-2-22-20000220000-2-2-2-222-2-22222-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000
χ4122-2-2-22-222i−2i2i−2i220000-2-22222-2-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i00000000000000002i−2i2i−2i−2i2i−2i2i2-22-20000000000000000000000000000
χ4222-2-2-22-222i−2i2i−2i220000-2-22222-2-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i−2i2i2i−2i2i−2i-22-220000000000000000000000000000
χ4322-2-2-22-22−2i2i−2i2i220000-2-22222-2-2-2-2-2-222−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i2i−2i−2i2i−2i2i-22-220000000000000000000000000000
χ4422-2-2-22-22−2i2i−2i2i220000-2-22222-2-2-2-2-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000−2i2i−2i2i2i−2i2i−2i2-22-20000000000000000000000000000
χ452-222-2-2-220000220000-2-2-2-2-2-22222-2-2220000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000
χ462-222-2-2-220000220000-2-2-2-2-2-22222-2-2220000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000
χ472-222-2-2-220000220000-2-2-2-2-2-22222-2-222000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000
χ482-222-2-2-220000220000-2-2-2-2-2-22222-2-222000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000
χ492-22-2-222-22-2-22220000-2-222-2-222-2-222-2-222-2-2-2-22200000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ502-22-2-222-22-2-22220000-2-222-2-222-2-222-2-222-2-2-2-2220000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ512-22-2-222-2-222-2220000-2-222-2-222-2-222-2-2-2-22222-2-200000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ522-22-2-222-2-222-2220000-2-222-2-222-2-222-2-2-2-22222-2-20000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ532-2-2-22-222000022000022-2-2-2-2-2-2-2-2222200000000000000000000000022-2-222-2-200002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ542-2-2-22-222000022000022-2-2-2-2-2-2-2-2222200000000000000000000000022-2-222-2-20000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ552-2-2-22-222000022000022-2-2-2-2-2-2-2-22222000000000000000000000000-2-222-2-22200002-2-22-222-200000000000000000000
χ562-2-2-22-222000022000022-2-2-2-2-2-2-2-22222000000000000000000000000-2-222-2-2220000-222-22-2-2200000000000000000000
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χ6644-4-4-44-444i−4i4i−4i1-20000-121-21-2-12-12-121-2i−2i−i2ii−2i−i2i−3i3i00−3i3i00-3300-33000000000000000000000000000000000000000000
χ6744-4-4-44-444i−4i4i−4i-2100002-1-21-212-12-12-1-21−2ii2i−i−2ii2i−i003i−3i003i−3i003-3003-30000000000000000000000000000000000000000
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χ6944-4-4-44-44−4i4i−4i4i1-20000-121-21-2-12-12-121-2−i2ii−2i−i2ii−2i3i−3i003i−3i00-3300-33000000000000000000000000000000000000000000
χ7044-4-4-44-44−4i4i−4i4i1-20000-121-21-2-12-12-121-2−i2ii−2i−i2ii−2i−3i3i00−3i3i003-3003-3000000000000000000000000000000000000000000
χ7144-4-4-44-44−4i4i−4i4i-2100002-1-21-212-12-12-1-212i−i−2ii2i−i−2ii003i−3i003i−3i00-3300-330000000000000000000000000000000000000000
χ7244-4-4-44-44−4i4i−4i4i-2100002-1-21-212-12-12-1-212i−i−2ii2i−i−2ii00−3i3i00−3i3i003-3003-30000000000000000000000000000000000000000
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χ744-44-4-444-44-4-441-20000-121-2-121-2-121-2-121-2-12-121-2−3i3i003i−3i003i−3i00−3i3i000000000000000000000000000000000000000000
χ754-44-4-444-44-4-44-2100002-1-212-1-212-1-212-1-212-12-1-21003i−3i00−3i3i00−3i3i003i−3i0000000000000000000000000000000000000000
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χ814-4-4444-4-44i4i−4i−4i1-24-44i−4i1-21-2-12-121-2-12-12i−2ii−2i−i2i−i2i11-2-2-1-122ii−2i−2i−i−i2i2i0000000000000000000000000000000000000000
χ824-4-4444-4-44i4i−4i−4i1-2-44−4i4i1-21-2-12-121-2-12-12i−2ii−2i−i2i−i2i-1-12211-2-2−i−i2i2iii−2i−2i0000000000000000000000000000000000000000
χ834-4-4444-4-44i4i−4i−4i-214-44i−4i-21-212-12-1-212-12-1−2ii−2ii2i−i2i−i-2-21122-1-1−2i−2iii2i2i−i−i0000000000000000000000000000000000000000
χ844-4-4444-4-44i4i−4i−4i-21-44−4i4i-21-212-12-1-212-12-1−2ii−2ii2i−i2i−i22-1-1-2-2112i2i−i−i−2i−2iii0000000000000000000000000000000000000000
χ854-4-4444-4-4−4i−4i4i4i1-24-4−4i4i1-21-2-12-121-2-12-12−i2i−i2ii−2ii−2i11-2-2-1-122−i−i2i2iii−2i−2i0000000000000000000000000000000000000000
χ864-4-4444-4-4−4i−4i4i4i1-2-444i−4i1-21-2-12-121-2-12-12−i2i−i2ii−2ii−2i-1-12211-2-2ii−2i−2i−i−i2i2i0000000000000000000000000000000000000000
χ874-4-4444-4-4−4i−4i4i4i-214-4−4i4i-21-212-12-1-212-12-12i−i2i−i−2ii−2ii-2-21122-1-12i2i−i−i−2i−2iii0000000000000000000000000000000000000000
χ884-4-4444-4-4−4i−4i4i4i-21-444i−4i-21-212-12-1-212-12-12i−i2i−i−2ii−2ii22-1-1-2-211−2i−2iii2i2i−i−i0000000000000000000000000000000000000000
χ89888-88-8-8-800002-400002-4-242-42-4-24-24-240000000000000000000000000000000000000000000000000000000000000000
χ90888-88-8-8-80000-420000-424-2-42-424-24-24-20000000000000000000000000000000000000000000000000000000000000000
χ9188-88-8-88-800002-40000-24-242-4-242-42-4-240000000000000000000000000000000000000000000000000000000000000000
χ9288-88-8-88-80000-4200004-24-2-424-2-42-424-20000000000000000000000000000000000000000000000000000000000000000
χ938-888-8-8-8800002-40000-24-24-242-42-4-242-40000000000000000000000000000000000000000000000000000000000000000
χ948-888-8-8-880000-4200004-24-24-2-42-424-2-420000000000000000000000000000000000000000000000000000000000000000
χ958-8-8-88-88800002-400002-4-24-24-24-242-42-40000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-88-8880000-420000-424-24-24-24-2-42-420000000000000000000000000000000000000000000000000000000000000000

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