Finite Group Databasebeta

← Group #10828798

Character table — Group #10828798

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order1222222222223444466666666666666644444488888888121212121212121224242424242424242424242424242424444444121212121212121212121212121212124444222444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1111111-1-1
χ911111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-1-1-11111-1-11-1
χ1011111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1111-1-1-1-111-11
χ1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111-11
χ1211111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-11-1
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1111-1-1-111-1-1-11
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1111-1-1111-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-1-1111-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-111111-1-1-11
χ172222222222222-2-2-2-2222222222222222-2-2000000000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000002222-200-200000000
χ182222222222222-2-2-2-2222222222222222-2-2000000000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000-2-2-2-2200200000000
χ19222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ21222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ22222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2322222222-2-2-2-22-2-2-2-222222-2-2-2-2-2-2-2-22222000000000000-2-2-22222-20000000000000000000000000000000000000022-2-2-200200000000
χ2422222222-2-2-2-22-2-2-2-222222-2-2-2-2-2-2-2-22222000000000000-2-2-22222-200000000000000000000000000000000000000-2-222200-200000000
χ2522222222-2-2-2-2-12222-1-1-1-1-111111111-1-1-2-222222222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-2-2-2-2-12222-1-1-1-1-111111111-1-1-2-22222-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2722222222-2-2-2-2-12222-1-1-1-1-111111111-1-1-2-2-2-2-2-22222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111122-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2822222222-2-2-2-2-12222-1-1-1-1-111111111-1-1-2-2-2-2-2-2-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-12222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2922-222-2-2-200002-222-222-2-2-2000000002-2002i2i−2i−2i000022-2-22-2-200002000000002222-2-2-2-200002i−2i2i2i−2i−2i000000002i2i−2i−2i0000000000000000
χ3022-222-2-2-200002-222-222-2-2-2000000002-2002i2i−2i−2i0000-2-2222-2-20000200000000-2-2-2-222220000−2i2i2i2i−2i−2i00000000−2i−2i2i2i0000000000000000
χ3122-222-2-2-200002-222-222-2-2-2000000002-200−2i−2i2i2i000022-2-22-2-200002000000002222-2-2-2-20000−2i2i−2i−2i2i2i00000000−2i−2i2i2i0000000000000000
χ3222-222-2-2-200002-222-222-2-2-2000000002-200−2i−2i2i2i0000-2-2222-2-20000200000000-2-2-2-2222200002i−2i−2i−2i2i2i000000002i2i−2i−2i0000000000000000
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χ3722-222-2-2-20000-1-222-2-1-1111i3i3i3i3−i3−i3−i3−i3-11002i2i−2i−2i000022-2-2-111i3i3−i3−i3-1i3i3i3i3−i3−i3−i3−i3-1-1-1-1111100002i−2i−i−iii−3−333−3−333−i−iii0000000000000000
χ3822-222-2-2-20000-1-222-2-1-1111i3i3i3i3−i3−i3−i3−i3-11002i2i−2i−2i0000-2-222-111i3i3−i3−i3-1−i3−i3−i3−i3i3i3i3i31111-1-1-1-10000−2i2i−i−iii−3−33333−3−3ii−i−i0000000000000000
χ3922-222-2-2-20000-1-222-2-1-1111i3i3i3i3−i3−i3−i3−i3-1100−2i−2i2i2i000022-2-2-111i3i3−i3−i3-1i3i3i3i3−i3−i3−i3−i3-1-1-1-111110000−2i2iii−i−i33−3−333−3−3ii−i−i0000000000000000
χ4022-222-2-2-20000-1-222-2-1-1111i3i3i3i3−i3−i3−i3−i3-1100−2i−2i2i2i0000-2-222-111i3i3−i3−i3-1−i3−i3−i3−i3i3i3i3i31111-1-1-1-100002i−2iii−i−i33−3−3−3−333−i−iii0000000000000000
χ412-222-22-2-200002-22-22-2-222-2000000002-2002i−2i2i−2i22-2-20000-22-20000222-2-222-2-200000000002i−2i002i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ422-222-22-2-200002-22-22-2-222-2000000002-2002i−2i2i−2i-2-2220000-22-200002-2-222-2-2220000000000−2i2i002i−2i2i−2i0000−2i2i−2i2i00000000000000000000
χ432-222-22-2-200002-22-22-2-222-2000000002-200−2i2i−2i2i22-2-20000-22-20000222-2-222-2-20000000000−2i2i00−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ442-222-22-2-200002-22-22-2-222-2000000002-200−2i2i−2i2i-2-2220000-22-200002-2-222-2-22200000000002i−2i00−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ452-222-22-2-20000-1-22-2211-1-11−i3−i3i3i3−i3−i3i3i3-11002i−2i2i−2i22-2-200001-11−i3i3−i3i3-1-1-111-1-111−i3−i3i3i3−i3−i3i3i3002i−2i00−ii−ii3−33−3−ii−ii3−33−30000000000000000
χ462-222-22-2-20000-1-22-2211-1-11−i3−i3i3i3−i3−i3i3i3-11002i−2i2i−2i-2-22200001-11−i3i3−i3i3-111-1-111-1-1i3i3−i3−i3i3i3−i3−i300−2i2i00−ii−ii3−33−3i−ii−i−33−330000000000000000
χ472-222-22-2-20000-1-22-2211-1-11−i3−i3i3i3−i3−i3i3i3-1100−2i2i−2i2i22-2-200001-11−i3i3−i3i3-1-1-111-1-111−i3−i3i3i3−i3−i3i3i300−2i2i00i−ii−i−33−33i−ii−i−33−330000000000000000
χ482-222-22-2-20000-1-22-2211-1-11−i3−i3i3i3−i3−i3i3i3-1100−2i2i−2i2i-2-22200001-11−i3i3−i3i3-111-1-111-1-1i3i3−i3−i3i3i3−i3−i3002i−2i00i−ii−i−33−33−ii−ii3−33−30000000000000000
χ492-222-22-2-20000-1-22-2211-1-11i3i3−i3−i3i3i3−i3−i3-11002i−2i2i−2i22-2-200001-11i3−i3i3−i3-1-1-111-1-111i3i3−i3−i3i3i3−i3−i3002i−2i00−ii−ii−33−33−ii−ii−33−330000000000000000
χ502-222-22-2-20000-1-22-2211-1-11i3i3−i3−i3i3i3−i3−i3-11002i−2i2i−2i-2-22200001-11i3−i3i3−i3-111-1-111-1-1−i3−i3i3i3−i3−i3i3i300−2i2i00−ii−ii−33−33i−ii−i3−33−30000000000000000
χ512-222-22-2-20000-1-22-2211-1-11i3i3−i3−i3i3i3−i3−i3-1100−2i2i−2i2i22-2-200001-11i3−i3i3−i3-1-1-111-1-111i3i3−i3−i3i3i3−i3−i300−2i2i00i−ii−i3−33−3i−ii−i3−33−30000000000000000
χ522-222-22-2-20000-1-22-2211-1-11i3i3−i3−i3i3i3−i3−i3-1100−2i2i−2i2i-2-22200001-11i3−i3i3−i3-111-1-111-1-1−i3−i3i3i3−i3−i3i3i3002i−2i00i−ii−i3−33−3−ii−ii−33−330000000000000000
χ532-2-22-2-22222-2-2222-2-2-2-2-2-2222-2-2-2-222222-22-2-2200000000-2-222-2-22200000000000000002-200002-2-222-2-22000000000000000000000000
χ542-2-22-2-22222-2-2222-2-2-2-2-2-2222-2-2-2-222222-2-222-200000000-2-222-2-2220000000000000000-220000-222-2-222-2000000000000000000000000
χ552-2-22-2-22222-2-22-2-222-2-2-2-2222-2-2-2-22222-2200000000000022-2-222-2-200000000000000000000000000000000000000000002-202-2000000
χ562-2-22-2-22222-2-22-2-222-2-2-2-2222-2-2-2-22222-2200000000000022-2-222-2-20000000000000000000000000000000000000000000-220-22000000
χ572-2-22-2-22222-2-2-122-2-21111-1-1-11111-1-1-1-12-22-2-220000000011-1-111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32-20000-111-1-111-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ582-2-22-2-22222-2-2-122-2-21111-1-1-11111-1-1-1-12-22-2-220000000011-1-111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32-20000-111-1-111-1i3−i3−i3i3i3−i3−i3i30000000000000000
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χ622-2-22-2-222-2-222222-2-2-2-2-2-22-2-22222-2-222-22-222-200000000-2-22-222-2200000000000000002-20000-222-22-2-22000000000000000000000000
χ632-2-22-2-222-2-2222-2-222-2-2-2-22-2-22222-2-2222-200000000000022-22-2-22-200000000000000000000000000000000000000000002-20-22000000
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χ692-2-2-2222-22-22-2200002-22-222-22-22-22-2-2-20000002−22−22−22−2000000002−22−22−22−22−22−22−22−200000000000000000000002i−2i2i−2i000000−i2i2−i2i200
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χ712-2-2-2222-22-22-2200002-22-222-22-22-22-2-2-2000000−22−22−22−2200000000−22−22−22−22−22−22−22−2200000000000000000000002i−2i2i−2i000000i2−i2i2−i200
χ722-2-2-2222-22-22-2200002-22-222-22-22-22-2-2-2000000−22−22−22−2200000000−22−22−22−22−22−22−22−220000000000000000000000−2i2i−2i2i000000−i2i2−i2i200
χ732-2-2-2222-2-22-22200002-22-22-22-22-22-22-2-20000002−22−2−22−22000000002−22−22−22−2−22−22−22−2200000000000000000000002i−2i−2i2i000000−i2i2i2−i200
χ742-2-2-2222-2-22-22200002-22-22-22-22-22-22-2-20000002−22−2−22−22000000002−22−22−22−2−22−22−22−220000000000000000000000−2i2i2i−2i000000i2−i2−i2i200
χ752-2-2-2222-2-22-22200002-22-22-22-22-22-22-2-2000000−22−222−22−200000000−22−22−22−222−22−22−22−200000000000000000000002i−2i−2i2i000000i2−i2−i2i200
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χ77444444444444-2-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-400000000000022222222000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-4-2-4-4-4-4-2-2-2-2-222222222-2-244000000000000222-2-2-2-22000000000000000000000000000000000000000000000000000000
χ79444-4-4-44-44-4-4440000-44-4444-4-44-444-4-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
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χ81444-4-4-44-44-4-44-200002-22-2-2-222-22-2-22220000000000000000000000−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000000000
χ82444-4-4-44-4-444-440000-44-444-444-44-4-44-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ83444-4-4-44-4-444-4-200002-22-2-22-2-22-222-2220000000000000000000000i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000000000
χ84444-4-4-44-4-444-4-200002-22-2-22-2-22-222-2220000000000000000000000−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000000000
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χ8744-444-4-4-40000-24-4-44-2-22222i32i32i32i3−2i3−2i3−2i3−2i3-22000000000000002-2-2−2i3−2i32i32i32000000000000000000000000000000000000000000000000000000
χ8844-4-4-44-44000040000-444-4-400000000-4400000022−22−222200000000000022−22−222222−22−22220000000000000000000000000000000000000000000000
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χ9044-4-4-44-440000-200002-2-222−2i32i32i3−2i3−2i32i32i3−2i32-200000022−22−2222000000000000−222−2−222−2−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000000000
χ9144-4-4-44-440000-200002-2-222−2i32i32i3−2i3−2i32i32i3−2i32-2000000−222222−220000000000002−2−222−2−22i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000000000
χ9244-4-4-44-440000-200002-2-2222i3−2i3−2i32i32i3−2i3−2i32i32-200000022−22−2222000000000000−222−2−222−2i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000000000
χ9344-4-4-44-440000-200002-2-2222i3−2i3−2i32i32i3−2i3−2i32i32-2000000−222222−220000000000002−2−222−2−22−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000000000
χ944-444-44-4-4000044-44-4-4-444-4000000004-4000000000000004-440000-4000000000000000000000000000000000000000000000000000000
χ954-444-44-4-40000-24-44-422-2-22−2i3−2i32i32i3−2i3−2i32i32i3-2200000000000000-22-22i3−2i32i3−2i32000000000000000000000000000000000000000000000000000000
χ964-444-44-4-40000-24-44-422-2-222i32i3−2i3−2i32i32i3−2i3−2i3-2200000000000000-22-2−2i32i3−2i32i32000000000000000000000000000000000000000000000000000000
χ974-44-44-4-440000400004-4-44-400000000-44000000000022−22−2222000000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ984-44-44-4-440000400004-4-44-400000000-440000000000−222222−220000000000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ994-44-44-4-440000-20000-222-22−2i32i3−2i32i32i3−2i32i3−2i32-2000000000022−22−222200000000−i6i6−i6i6i6−i6i6−i6−22−222−22−200000000000000000000000000000000000000
χ1004-44-44-4-440000-20000-222-22−2i32i3−2i32i32i3−2i32i3−2i32-20000000000−222222−2200000000i6−i6i6−i6−i6i6−i6i62−22−2−22−2200000000000000000000000000000000000000
χ1014-44-44-4-440000-20000-222-222i3−2i32i3−2i3−2i32i3−2i32i32-2000000000022−22−222200000000i6−i6i6−i6−i6i6−i6i6−22−222−22−200000000000000000000000000000000000000
χ1024-44-44-4-440000-20000-222-222i3−2i32i3−2i3−2i32i3−2i32i32-20000000000−222222−2200000000−i6i6−i6i6i6−i6i6−i62−22−2−22−2200000000000000000000000000000000000000
χ1034-4-44-4-44444-4-4-2-4-4442222-2-2-22222-2-2-2-2-44000000000000-2-222-2-222000000000000000000000000000000000000000000000000000000
χ1044-4-44-4-444-4-444-2-4-4442222-222-2-2-2-222-2-24-4000000000000-2-22-222-22000000000000000000000000000000000000000000000000000000
χ1054-4-4-4444-44-44-4-20000-22-22-2-22-22-22-222200000022−2222−2222−2222−2200000000−22−22−22−22−22−22−22−2200000000000000000000000000000000000000
χ1064-4-4-4444-44-44-4-20000-22-22-2-22-22-22-2222000000−2222−2222−2222−2222000000002−22−22−22−22−22−22−22−200000000000000000000000000000000000000
χ1074-4-4-4444-4-44-44-20000-22-22-22-22-22-22-22200000022−2222−22−2222−222200000000−22−22−22−222−22−22−22−200000000000000000000000000000000000000
χ1084-4-4-4444-4-44-44-20000-22-22-22-22-22-22-222000000−2222−222222−2222−22000000002−22−22−22−2−22−22−22−2200000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).