Finite Group Databasebeta

← Group #11784224

Character table — Group #11784224

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
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1−i−i−i−iiiii
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
χ711111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111−i−i−i−iiiii
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−i−i−i−i−iiiiiiiii1111iiii−i−i−i−i
χ911111111-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
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
χ1311111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ1411111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
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
χ1711-1-111-1-1ii−i−i111-1i−i1111-1-1-1-111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ1811-1-111-1-1ii−i−i111-1i−i1111-1-1-1-111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i-1-111−i−iii-1-111−i−iii1-1i−i-11−ii-11−ii
χ1911-1-111-1-1ii−i−i111-1i−i1111-1-1-1-111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−iiiii−i−i-1-111−i−iii11-1-1-11−iii−i-11−ii1-1
χ2011-1-111-1-1ii−i−i111-1i−i1111-1-1-1-111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−iii−i−iii11-1-1ii−i−i-1-111-11−ii−ii1-1i−i-11
χ2111-1-111-1-1ii−i−i11-11−ii1111-1-1-1-111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11−ii
χ2211-1-111-1-1ii−i−i11-11−ii1111-1-1-1-111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-111-1-1ii−i−i-1-111−i−iii-1-111−i−iii-11−ii1-1i−i1-1i−i
χ2311-1-111-1-1ii−i−i11-11−ii1111-1-1-1-111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i-1-111−i−iii11-1-11-1i−i−ii1-1i−i-11
χ2411-1-111-1-1ii−i−i11-11−ii1111-1-1-1-111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111-1-111−i−iii−i−iii11-1-1ii−i−i-1-1111-1i−ii−i-11−ii1-1
χ2511-1-111-1-1−i−iii111-1−ii1111-1-1-1-111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ2611-1-111-1-1−i−iii111-1−ii1111-1-1-1-111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii-1-111ii−i−i-1-111ii−i−i1-1−ii-11i−i-11i−i
χ2711-1-111-1-1−i−iii111-1−ii1111-1-1-1-111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i11-1-1−i−iii-1-111-11i−ii−i1-1−ii-11
χ2811-1-111-1-1−i−iii111-1−ii1111-1-1-1-111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111ii−i−i−i−iii-1-111ii−i−i11-1-1-11i−i−ii-11i−i1-1
χ2911-1-111-1-1−i−iii11-11i−i1111-1-1-1-111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-111-1-1−i−iii11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11i−i
χ3011-1-111-1-1−i−iii11-11i−i1111-1-1-1-111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-111-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-11i−i1-1−ii1-1−ii
χ3111-1-111-1-1−i−iii11-11i−i1111-1-1-1-111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111-1-111ii−i−iii−i−i11-1-1−i−iii-1-1111-1−ii−ii-11i−i1-1
χ3211-1-111-1-1−i−iii11-11i−i1111-1-1-1-111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111-1-111ii−i−i−i−iii-1-111ii−i−i11-1-11-1−iii−i1-1−ii-11
χ33222-2-2-22-20000220000-2-2-2-222-2-22222-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i000000002ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ3000000000000
χ34222-2-2-22-20000220000-2-2-2-222-2-22222-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000−2ζ2ζ−2ζ2ζ0000−2ζ32ζ3−2ζ32ζ3000000000000
χ35222-2-2-22-20000220000-2-2-2-222-2-22222-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ000000000000
χ36222-2-2-22-20000220000-2-2-2-222-2-22222-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ000000000000
χ3722-22-2-2-220000220000-2-2-2-2-2-22222-2-2220000000000000000000000002i−2i−2i2i2i−2i−2i2i000000002ζ3−2ζ3−2ζ32ζ30000−2ζ2ζ2ζ−2ζ000000000000
χ3822-22-2-2-220000220000-2-2-2-2-2-22222-2-2220000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000−2ζ32ζ32ζ3−2ζ300002ζ−2ζ−2ζ2ζ000000000000
χ3922-22-2-2-220000220000-2-2-2-2-2-22222-2-222000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000002ζ−2ζ−2ζ2ζ0000−2ζ32ζ32ζ3−2ζ3000000000000
χ4022-22-2-2-220000220000-2-2-2-2-2-22222-2-222000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000−2ζ2ζ2ζ−2ζ00002ζ3−2ζ3−2ζ32ζ3000000000000
χ412-2222-2-2-2000022000022-2-2-2-2-2-2-2-222220000000000000000000000002i−2i2i−2i−2i2i−2i2i00002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ0000000000000000
χ422-2222-2-2-2000022000022-2-2-2-2-2-2-2-222220000000000000000000000002i−2i2i−2i−2i2i−2i2i0000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ0000000000000000
χ432-2222-2-2-2000022000022-2-2-2-2-2-2-2-22222000000000000000000000000−2i2i−2i2i2i−2i2i−2i00002ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ30000000000000000
χ442-2222-2-2-2000022000022-2-2-2-2-2-2-2-22222000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000−2ζ2ζ−2ζ2ζ0000−2ζ32ζ3−2ζ32ζ30000000000000000
χ452-22-2-22-222-22-2220000-2-222-2-222-2-222-2-222-2-222-2-200000000000000002222-2-2-2-22-22-20000000000000000000000000000
χ462-22-2-22-222-22-2220000-2-222-2-222-2-222-2-222-2-222-2-20000000000000000-2-2-2-22222-22-220000000000000000000000000000
χ472-22-2-22-22-22-22220000-2-222-2-222-2-222-2-2-2-222-2-22200000000000000002222-2-2-2-2-22-220000000000000000000000000000
χ482-22-2-22-22-22-22220000-2-222-2-222-2-222-2-2-2-222-2-2220000000000000000-2-2-2-222222-22-20000000000000000000000000000
χ492-2-22-222-22i−2i−2i2i220000-2-22222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000022-2-2-2-2222i−2i−2i2i0000000000000000000000000000
χ502-2-22-222-22i−2i−2i2i220000-2-22222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000-2-22222-2-2−2i2i2i−2i0000000000000000000000000000
χ512-2-22-222-2−2i2i2i−2i220000-2-22222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000022-2-2-2-222−2i2i2i−2i0000000000000000000000000000
χ522-2-22-222-2−2i2i2i−2i220000-2-22222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000-2-22222-2-22i−2i−2i2i0000000000000000000000000000
χ532-2-2-22-222000022000022-2-22222-2-2-2-2-2-20000000000000000000000002i−2i−2i2i−2i2i2i−2i00002ζ3−2ζ3−2ζ32ζ300002ζ−2ζ−2ζ2ζ0000000000000000
χ542-2-2-22-222000022000022-2-22222-2-2-2-2-2-20000000000000000000000002i−2i−2i2i−2i2i2i−2i0000−2ζ32ζ32ζ3−2ζ30000−2ζ2ζ2ζ−2ζ0000000000000000
χ552-2-2-22-222000022000022-2-22222-2-2-2-2-2-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i00002ζ−2ζ−2ζ2ζ00002ζ3−2ζ3−2ζ32ζ30000000000000000
χ562-2-2-22-222000022000022-2-22222-2-2-2-2-2-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000−2ζ2ζ2ζ−2ζ0000−2ζ32ζ32ζ3−2ζ30000000000000000
χ574444444444441-244441-21-21-21-21-21-21-21-21-21-21-211-2-211-2-211-2-211-2-20000000000000000000000000000000000000000
χ584444444444441-2-4-4-4-41-21-21-21-21-21-21-21-21-21-21-2-1-122-1-122-1-122-1-1220000000000000000000000000000000000000000
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χ60444444444444-21-4-4-4-4-21-21-21-21-21-21-21-21-21-21-2122-1-122-1-122-1-122-1-10000000000000000000000000000000000000000
χ6144444444-4-4-4-41-244-4-41-21-21-21-21-21-21-2-12-12-12-1211-2-211-2-2-1-122-1-1220000000000000000000000000000000000000000
χ6244444444-4-4-4-41-2-4-4441-21-21-21-21-21-21-2-12-12-12-12-1-122-1-12211-2-211-2-20000000000000000000000000000000000000000
χ6344444444-4-4-4-4-2144-4-4-21-21-21-21-21-21-212-12-12-12-1-2-211-2-21122-1-122-1-10000000000000000000000000000000000000000
χ6444444444-4-4-4-4-21-4-444-21-21-21-21-21-21-212-12-12-12-122-1-122-1-1-2-211-2-2110000000000000000000000000000000000000000
χ6544-4-444-4-44i4i−4i−4i1-24-44i−4i1-21-2-12-121-2-12-12i−2ii−2i−i2i−i2i11-2-2-1-122ii−2i−2i−i−i2i2i0000000000000000000000000000000000000000
χ6644-4-444-4-44i4i−4i−4i1-2-44−4i4i1-21-2-12-121-2-12-12i−2ii−2i−i2i−i2i-1-12211-2-2−i−i2i2iii−2i−2i0000000000000000000000000000000000000000
χ6744-4-444-4-44i4i−4i−4i-214-44i−4i-21-212-12-1-212-12-1−2ii−2ii2i−i2i−i-2-21122-1-1−2i−2iii2i2i−i−i0000000000000000000000000000000000000000
χ6844-4-444-4-44i4i−4i−4i-21-44−4i4i-21-212-12-1-212-12-1−2ii−2ii2i−i2i−i22-1-1-2-2112i2i−i−i−2i−2iii0000000000000000000000000000000000000000
χ6944-4-444-4-4−4i−4i4i4i1-24-4−4i4i1-21-2-12-121-2-12-12−i2i−i2ii−2ii−2i11-2-2-1-122−i−i2i2iii−2i−2i0000000000000000000000000000000000000000
χ7044-4-444-4-4−4i−4i4i4i1-2-444i−4i1-21-2-12-121-2-12-12−i2i−i2ii−2ii−2i-1-12211-2-2ii−2i−2i−i−i2i2i0000000000000000000000000000000000000000
χ7144-4-444-4-4−4i−4i4i4i-214-4−4i4i-21-212-12-1-212-12-12i−i2i−i−2ii−2ii-2-21122-1-12i2i−i−i−2i−2iii0000000000000000000000000000000000000000
χ7244-4-444-4-4−4i−4i4i4i-21-444i−4i-21-212-12-1-212-12-12i−i2i−i−2ii−2ii22-1-1-2-211−2i−2iii2i2i−i−i0000000000000000000000000000000000000000
χ734-44-4-44-444-44-41-20000-121-2-121-2-121-2-121-2-121-2-123i−3i003i−3i003i−3i003i−3i000000000000000000000000000000000000000000
χ744-44-4-44-444-44-41-20000-121-2-121-2-121-2-121-2-121-2-12−3i3i00−3i3i00−3i3i00−3i3i000000000000000000000000000000000000000000
χ754-44-4-44-444-44-4-2100002-1-212-1-212-1-212-1-212-1-212-1003i−3i003i−3i003i−3i003i−3i0000000000000000000000000000000000000000
χ764-44-4-44-444-44-4-2100002-1-212-1-212-1-212-1-212-1-212-100−3i3i00−3i3i00−3i3i00−3i3i0000000000000000000000000000000000000000
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χ784-44-4-44-44-44-441-20000-121-2-121-2-121-2-12-121-2-121-2−3i3i00−3i3i003i−3i003i−3i000000000000000000000000000000000000000000
χ794-44-4-44-44-44-44-2100002-1-212-1-212-1-212-12-1-212-1-21003i−3i003i−3i00−3i3i00−3i3i0000000000000000000000000000000000000000
χ804-44-4-44-44-44-44-2100002-1-212-1-212-1-212-12-1-212-1-2100−3i3i00−3i3i003i−3i003i−3i0000000000000000000000000000000000000000
χ814-4-44-444-44i−4i−4i4i1-20000-121-21-2-12-12-121-2i−2i−i2i−i2ii−2i3i−3i00−3i3i00-33003-3000000000000000000000000000000000000000000
χ824-4-44-444-44i−4i−4i4i1-20000-121-21-2-12-12-121-2i−2i−i2i−i2ii−2i−3i3i003i−3i003-300-33000000000000000000000000000000000000000000
χ834-4-44-444-44i−4i−4i4i-2100002-1-21-212-12-12-1-21−2ii2i−i2i−i−2ii003i−3i00−3i3i00-33003-30000000000000000000000000000000000000000
χ844-4-44-444-44i−4i−4i4i-2100002-1-21-212-12-12-1-21−2ii2i−i2i−i−2ii00−3i3i003i−3i003-300-330000000000000000000000000000000000000000
χ854-4-44-444-4−4i4i4i−4i1-20000-121-21-2-12-12-121-2−i2ii−2ii−2i−i2i3i−3i00−3i3i003-300-33000000000000000000000000000000000000000000
χ864-4-44-444-4−4i4i4i−4i1-20000-121-21-2-12-12-121-2−i2ii−2ii−2i−i2i−3i3i003i−3i00-33003-3000000000000000000000000000000000000000000
χ874-4-44-444-4−4i4i4i−4i-2100002-1-21-212-12-12-1-212i−i−2ii−2ii2i−i003i−3i00−3i3i003-300-330000000000000000000000000000000000000000
χ884-4-44-444-4−4i4i4i−4i-2100002-1-21-212-12-12-1-212i−i−2ii−2ii2i−i00−3i3i003i−3i00-33003-30000000000000000000000000000000000000000
χ89888-8-8-88-800002-40000-24-242-4-242-42-4-240000000000000000000000000000000000000000000000000000000000000000
χ90888-8-8-88-80000-4200004-24-2-424-2-42-424-20000000000000000000000000000000000000000000000000000000000000000
χ9188-88-8-8-8800002-40000-24-24-242-42-4-242-40000000000000000000000000000000000000000000000000000000000000000
χ9288-88-8-8-880000-4200004-24-24-2-42-424-2-420000000000000000000000000000000000000000000000000000000000000000
χ938-8888-8-8-800002-400002-4-24-24-24-242-42-40000000000000000000000000000000000000000000000000000000000000000
χ948-8888-8-8-80000-420000-424-24-24-24-2-42-420000000000000000000000000000000000000000000000000000000000000000
χ958-8-8-88-88800002-400002-4-242-42-4-24-24-240000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-88-8880000-420000-424-2-42-424-24-24-20000000000000000000000000000000000000000000000000000000000000000

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