Finite Group Databasebeta

← Group #10833372

Character table — Group #10833372

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222444444444444444444444444444444444444448888888888888888888888242424242424242448484848
order1222222234444446666666121212121212121222244444444444666612121212121212121212121212121212121212122466668888121212122424242424242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-11-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111
χ61111111111111111111111111111111-1-11-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1
χ71111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111-1-11-1-111-1-1
χ81111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-111-1-111
χ911111-1-1111-1-111111-1-1-1-1111-1-1-1-111-111-1111111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11-1-1-1-11111-11-1
χ1011111-1-1111-1-111111-1-1-1-1111-1-1-1-111-111-1111111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-11111-1-1-1-11-11
χ1111111-1-1111-1-111111-1-1-1-1111-1-1-1-111-111-111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1111-11-11
χ1211111-1-1111-1-111111-1-1-1-1111-1-1-1-111-111-111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-11111-1-1-11-11-1
χ1311111-1-1111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111111-1-1111-1-1-111-1
χ1411111-1-1111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11111-111-1-1-1111-1-11
χ1511111-1-1111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111111-1-1-1-11-1-1111-1-11-1-11
χ1611111-1-1111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-111-111-1
χ17222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2200-200000000002222-2-2-2-2000000000000000000000000000000000000000002-202-20000
χ18222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2200-200000000002222-2-2-2-200000000000000000000000000000000000000000-220-220000
χ1922222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2022222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000
χ2122222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-22-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2-2-2111111111111000000000000
χ2222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-22-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2111122221111-1-1-1-1-1-1-1-1000000000000
χ2322222-2-222-222-2-2-222-2-2-2-22-2-22222-2-2-200200000000002-2-22-2-222000000000000000000000000000000000000000002-20-220000
χ2422222-2-222-222-2-2-222-2-2-2-22-2-22222-2-2-200200000000002-2-22-2-22200000000000000000000000000000000000000000-2202-20000
χ2522222-2-22-12-2-2222-1-11111-1-1-11111-1-1-222-2222222-2-2-2-2-111-1-1-111-1-1-1-1-1-1-1-111111111-2-2-1-11122-2-2-1-111-1-1-1-11111000000000000
χ2622222-2-22-12-2-2222-1-11111-1-1-11111-1-1-222-222-2-2-2-22222-111-1-1-11111111111-1-1-1-1-1-1-1-1-2-2-1-111-2-222-1-1111111-1-1-1-1000000000000
χ2722222-2-22-12-2-2222-1-11111-1-1-11111-1-1-2-2-2-2-2-22222-2-2-2-2-111-1-1-111-1-1-1-1-1-1-1-1111111112211-1-1-2-22211-1-11111-1-1-1-1000000000000
χ2822222-2-22-12-2-2222-1-11111-1-1-11111-1-1-2-2-2-2-2-2-2-2-2-22222-111-1-1-11111111111-1-1-1-1-1-1-1-12211-1-122-2-211-1-1-1-1-1-11111000000000000
χ292222-222-222222-2-2222222222222222-200-20000000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000022-200-2000000
χ302222-222-222222-2-2222222222222222-200-20000000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000-2-22002000000
χ312222-222-22-2-2-2-2222222222-2-2-2-2-2-2-2-2-2222-2-200000000-2-2-2-2222200000000000000002-222220000-2-2-2-200000000000000000000
χ322222-222-22-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-222200000000-2-2-2-222220000000000000000-22-2-2-2-20000222200000000000000000000
χ332222-222-2-1-2-2-2-222-1-1-1-1-1-1-111111111-2222-2-2000000001111-1-1-1-13333−3−3−3−33333−3−3−3−32-2-1-1-1-10000111133−3−333−3−3000000000000
χ342222-222-2-1-2-2-2-222-1-1-1-1-1-1-111111111-2222-2-2000000001111-1-1-1-1−3−3−3−33333−3−3−3−333332-2-1-1-1-100001111−3−333−3−333000000000000
χ352222-222-2-1-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2222000000001111-1-1-1-13333−3−3−3−33333−3−3−3−3-2211110000-1-1-1-1−3−333−3−333000000000000
χ362222-222-2-1-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2222000000001111-1-1-1-1−3−3−3−33333−3−3−3−33333-2211110000-1-1-1-133−3−333−3−3000000000000
χ372222-2-2-2-222-2-22-2-222-2-2-2-2222-2-2-2-22220020000000000-222-2-2-222000000000000000000000000000000000000002-2200-2000000
χ382222-2-2-2-222-2-22-2-222-2-2-2-2222-2-2-2-22220020000000000-222-2-2-22200000000000000000000000000000000000000-22-2002000000
χ392222-2-2-2-22-222-22222-2-2-2-22-2-22222-2-2222-2-2-200000000-222-222-2-20000000000000000-2222-2-20000-2-22200000000000000000000
χ402222-2-2-2-22-222-22222-2-2-2-22-2-22222-2-22-2-2-22200000000-222-222-2-200000000000000002-2-2-222000022-2-200000000000000000000
χ412222-2-2-2-2-1-222-222-1-11111-111-1-1-1-111222-2-2-2000000001-1-11-1-1113333−3−3−3−3−3−3−3−33333-22-1-111000011-1-133−3−3−3−333000000000000
χ422222-2-2-2-2-1-222-222-1-11111-111-1-1-1-111222-2-2-2000000001-1-11-1-111−3−3−3−333333333−3−3−3−3-22-1-111000011-1-1−3−33333−3−3000000000000
χ432222-2-2-2-2-1-222-222-1-11111-111-1-1-1-1112-2-2-222000000001-1-11-1-1113333−3−3−3−3−3−3−3−333332-211-1-10000-1-111−3−33333−3−3000000000000
χ442222-2-2-2-2-1-222-222-1-11111-111-1-1-1-1112-2-2-222000000001-1-11-1-111−3−3−3−333333333−3−3−3−32-211-1-10000-1-11133−3−3−3−333000000000000
χ452-2-22200-22200-22-2-2-200002220000-2-202-202-22i2i−2i−2i0000200-22-2002i2i−2i−2i2i2i−2i−2i00000000002-2002i−2i002-2002i−2i2i−2i0000000000000000
χ462-2-22200-22200-22-2-2-200002220000-2-202-202-2−2i−2i2i2i0000200-22-200−2i−2i2i2i−2i−2i2i2i00000000002-200−2i2i002-200−2i2i−2i2i0000000000000000
χ472-2-22200-22200-22-2-2-200002220000-2-20-220-222i2i−2i−2i0000200-22-2002i2i−2i−2i2i2i−2i−2i0000000000-2200−2i2i00-2200−2i2i−2i2i0000000000000000
χ482-2-22200-22200-22-2-2-200002220000-2-20-220-22−2i−2i2i2i0000200-22-200−2i−2i2i2i−2i−2i2i2i0000000000-22002i−2i00-22002i−2i2i−2i0000000000000000
χ492-2-22200-2-1200-22-211−i3−i3i3i3-1-1-1−i3−i3i3i31102-202-22i2i−2i−2i0000-1−i3i31-11−i3i3−i−iii−i−iii33−3−333−3−300-11−i3i32i−2i00-11−i3i3−ii−ii3−33−3000000000000
χ502-2-22200-2-1200-22-211−i3−i3i3i3-1-1-1−i3−i3i3i31102-202-2−2i−2i2i2i0000-1−i3i31-11−i3i3ii−i−iii−i−i−3−333−3−33300-11−i3i3−2i2i00-11−i3i3i−ii−i−33−33000000000000
χ512-2-22200-2-1200-22-211−i3−i3i3i3-1-1-1−i3−i3i3i3110-220-222i2i−2i−2i0000-1−i3i31-11−i3i3−i−iii−i−iii33−3−333−3−3001-1i3−i3−2i2i001-1i3−i3i−ii−i−33−33000000000000
χ522-2-22200-2-1200-22-211−i3−i3i3i3-1-1-1−i3−i3i3i3110-220-22−2i−2i2i2i0000-1−i3i31-11−i3i3ii−i−iii−i−i−3−333−3−333001-1i3−i32i−2i001-1i3−i3−ii−ii3−33−3000000000000
χ532-2-22200-2-1200-22-211i3i3−i3−i3-1-1-1i3i3−i3−i31102-202-22i2i−2i−2i0000-1i3−i31-11i3−i3−i−iii−i−iii−3−333−3−33300-11i3−i32i−2i00-11i3−i3−ii−ii−33−33000000000000
χ542-2-22200-2-1200-22-211i3i3−i3−i3-1-1-1i3i3−i3−i31102-202-2−2i−2i2i2i0000-1i3−i31-11i3−i3ii−i−iii−i−i33−3−333−3−300-11i3−i3−2i2i00-11i3−i3i−ii−i3−33−3000000000000
χ552-2-22200-2-1200-22-211i3i3−i3−i3-1-1-1i3i3−i3−i3110-220-222i2i−2i−2i0000-1i3−i31-11i3−i3−i−iii−i−iii−3−333−3−333001-1−i3i3−2i2i001-1−i3i3i−ii−i3−33−3000000000000
χ562-2-22200-2-1200-22-211i3i3−i3−i3-1-1-1i3i3−i3−i3110-220-22−2i−2i2i2i0000-1i3−i31-11i3−i3ii−i−iii−i−i33−3−333−3−3001-1−i3i32i−2i001-1−i3i3−ii−ii−33−33000000000000
χ572-2-22-20022-20022-2-2-200002-2-200002202-20-22000022-2-2-20022-2000000000022-2-2-2-222002-200002-2-220000002-2-22000000000000
χ582-2-22-20022-20022-2-2-200002-2-200002202-20-220000-2-222-20022-20000000000-2-22222-2-2002-20000-22-22000000-222-2000000000000
χ592-2-22-20022-20022-2-2-200002-2-20000220-2202-2000022-2-2-20022-2000000000022-2-2-2-22200-220000-222-2000000-222-2000000000000
χ602-2-22-20022-20022-2-2-200002-2-20000220-2202-20000-2-222-20022-20000000000-2-22222-2-200-2200002-22-20000002-2-22000000000000
χ612-2-22-2002-1-20022-211−i3−i3i3i3-111i3i3−i3−i3-1-102-20-22000022-2-21i3−i3-1-11−i3i3−i3−i3i3i3i3i3−i3−i3-1-11111-1-100-11−i3i3002-21-1i3−i3−i3i3i3−i3-111-1000000000000
χ622-2-22-2002-1-20022-211−i3−i3i3i3-111i3i3−i3−i3-1-102-20-220000-2-2221i3−i3-1-11−i3i3i3i3−i3−i3−i3−i3i3i311-1-1-1-11100-11−i3i300-221-1i3−i3i3−i3−i3i31-1-11000000000000
χ632-2-22-2002-1-20022-211−i3−i3i3i3-111i3i3−i3−i3-1-10-2202-2000022-2-21i3−i3-1-11−i3i3−i3−i3i3i3i3i3−i3−i3-1-11111-1-1001-1i3−i300-22-11−i3i3i3−i3−i3i31-1-11000000000000
χ642-2-22-2002-1-20022-211−i3−i3i3i3-111i3i3−i3−i3-1-10-2202-20000-2-2221i3−i3-1-11−i3i3i3i3−i3−i3−i3−i3i3i311-1-1-1-111001-1i3−i3002-2-11−i3i3−i3i3i3−i3-111-1000000000000
χ652-2-22-2002-1-20022-211i3i3−i3−i3-111−i3−i3i3i3-1-102-20-22000022-2-21−i3i3-1-11i3−i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-100-11i3−i3002-21-1−i3i3i3−i3−i3i3-111-1000000000000
χ662-2-22-2002-1-20022-211i3i3−i3−i3-111−i3−i3i3i3-1-102-20-220000-2-2221−i3i3-1-11i3−i3−i3−i3i3i3i3i3−i3−i311-1-1-1-11100-11i3−i300-221-1−i3i3−i3i3i3−i31-1-11000000000000
χ672-2-22-2002-1-20022-211i3i3−i3−i3-111−i3−i3i3i3-1-10-2202-2000022-2-21−i3i3-1-11i3−i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-1001-1−i3i300-22-11i3−i3−i3i3i3−i31-1-11000000000000
χ682-2-22-2002-1-20022-211i3i3−i3−i3-111−i3−i3i3i3-1-10-2202-20000-2-2221−i3i3-1-11i3−i3−i3−i3i3i3i3i3−i3−i311-1-1-1-111001-1−i3i3002-2-11i3−i3i3−i3−i3i3-111-1000000000000
χ6944444444-2-4-4-4-4-4-4-2-2-2-2-2-2-222222222400-40000000000-2-2-2-2222200000000000000000000000000000000000000000000000000
χ7044444-4-44-2-444-4-4-4-2-22222-222-2-2-2-222-40040000000000-222-222-2-200000000000000000000000000000000000000000000000000
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χ7644-4-404-40-2000000-22-22-22223−2323−2323−2323−23000000-22-22-22-22000000001−3−1+31−3−1+31+3−1−31+3−1−31−3−1+31−3−1+31+3−1−31+3−1−30000000000000000000000000000000000
χ7744-4-404-40-2000000-22-22-222−2323−2323−2323−23230000002-22-22-22-200000000−1−31+3−1−31+3−1+31−3−1+31−3−1−31+3−1−31+3−1+31−3−1+31−30000000000000000000000000000000000
χ7844-4-404-40-2000000-22-22-222−2323−2323−2323−2323000000-22-22-22-22000000001+3−1−31+3−1−31−3−1+31−3−1+31+3−1−31+3−1−31−3−1+31−3−1+30000000000000000000000000000000000
χ7944-4-40-44040000004-4-44-44-4000000000000002-22-2-22-22000000002-22-22-22-2-22-22-22-220000000000000000000000000000000000
χ8044-4-40-44040000004-4-44-44-400000000000000-22-222-22-200000000-22-22-22-222-22-22-22-20000000000000000000000000000000000
χ8144-4-40-440-2000000-222-22-2223−23−2323−232323−230000002-22-2-22-2200000000−1+31−3−1+31−3−1−31+3−1−31+31−3−1+31−3−1+31+3−1−31+3−1−30000000000000000000000000000000000
χ8244-4-40-440-2000000-222-22-2223−23−2323−232323−23000000-22-222-22-2000000001−3−1+31−3−1+31+3−1−31+3−1−3−1+31−3−1+31−3−1−31+3−1−31+30000000000000000000000000000000000
χ8344-4-40-440-2000000-222-22-22−232323−2323−23−23230000002-22-2-22-2200000000−1−31+3−1−31+3−1+31−3−1+31−31+3−1−31+3−1−31−3−1+31−3−1+30000000000000000000000000000000000
χ8444-4-40-440-2000000-222-22-22−232323−2323−23−2323000000-22-222-22-2000000001+3−1−31+3−1−31−3−1+31−3−1+3−1−31+3−1−31+3−1+31−3−1+31−30000000000000000000000000000000000
χ854-44-40000404i−4i000-440000-4004i−4i−4i4i000000002i−2i−2i2i-222-2000000002i−2i−2i2i2i−2i−2i2i-222-22-2-220000000000000000000000000000000000
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χ1024-4-44-4004-2400-4-44222i32i3−2i3−2i3-2-2-22i32i3−2i3−2i322000000000000002−2i32i3-22-2−2i32i300000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.