Finite Group Databasebeta

← Group #72213835

Character table — Group #72213835

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size1111222222333366666666666666666666666666666666666666161616161616161616161616323232323232323232323232484848486464646464646464
order1222444444222244444444444444444444444444444444444444233444666666121212121212121212121212444466121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111111111111111111111111−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ41111111111111111111111111111111111111111111111111111-111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111111111111111111111111111111111111111-1−1−i32−1+i32-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32
χ61111111111111111111111111111111111111111111111111111-1−1+i32−1−i32-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32
χ7111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-111-1-1111-1-11-1-1
χ8111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−1−i32−1+i321-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i3211-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ9111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−1+i32−1−i321-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i3211-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ10111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-1-1-111-1-1-1-1-1-111-1-1-111-111
χ11111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32-111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-1-1111+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ12111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32-111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-1-1111−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ131111-1-111-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-11-1111111-1-111-1-1-1-111-1-11-11-111-11-1-11-1
χ141111-1-111-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11−1−i32−1+i32-11-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i321-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ151111-1-111-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11−1+i32−1−i32-11-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i321-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ161111-1-111-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-11111111-1-111-1-1-1-111-1-1-11-11-1-11-111-11
χ171111-1-111-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1−1−i32−1+i321-11−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32-11-111+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ181111-1-111-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1−1+i32−1−i321-11−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32-11-111−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ191111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11111111-1-1-1-111-1-1-1-1111-1-1111-1-11-1-11
χ201111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111−1−i32−1+i32-1-11−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ211111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111−1+i32−1−i32-1-11−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ221111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1111111-1-1-1-111-1-1-1-111-111-1-1-111-111-1
χ231111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1−1−i32−1+i3211-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32-111-11+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ241111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1−1+i32−1−i3211-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32-111-11−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ2522-2-200002i−2i22-2-200002i−2i2222-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i0220002-2-22-2-200002i−2i00002i−2i000000000000
χ2622-2-200002i−2i22-2-200002i−2i2222-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i0−1−i3−1+i3000−1−i31+i31+i3−1+i31−i31−i300002ζ11−2ζ1100002ζ7−2ζ7000000000000
χ2722-2-200002i−2i22-2-200002i−2i2222-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i0−1+i3−1−i3000−1+i31−i31−i3−1−i31+i31+i300002ζ7−2ζ700002ζ11−2ζ11000000000000
χ2822-2-20000−2i2i22-2-20000−2i2i2222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i0220002-2-22-2-20000−2i2i0000−2i2i000000000000
χ2922-2-20000−2i2i22-2-20000−2i2i2222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i0−1−i3−1+i3000−1−i31+i31+i3−1+i31−i31−i30000−2ζ112ζ110000−2ζ72ζ7000000000000
χ3022-2-20000−2i2i22-2-20000−2i2i2222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i0−1+i3−1−i3000−1+i31−i31−i3−1−i31+i31+i30000−2ζ72ζ70000−2ζ112ζ11000000000000
χ312-22-2002i−2i002-22-2002i−2i0022-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i00000000022000-22-2-22-2002i−2i00002i−2i00000000000000
χ322-22-2002i−2i002-22-2002i−2i0022-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i000000000−1−i3−1+i30001+i3−1−i31+i31−i3−1+i31−i3002ζ11−2ζ1100002ζ7−2ζ700000000000000
χ332-22-2002i−2i002-22-2002i−2i0022-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i000000000−1+i3−1−i30001−i3−1+i31−i31+i3−1−i31+i3002ζ7−2ζ700002ζ11−2ζ1100000000000000
χ342-22-200−2i2i002-22-200−2i2i0022-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i00000000022000-22-2-22-200−2i2i0000−2i2i00000000000000
χ352-22-200−2i2i002-22-200−2i2i0022-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i000000000−1−i3−1+i30001+i3−1−i31+i31−i3−1+i31−i300−2ζ112ζ110000−2ζ72ζ700000000000000
χ362-22-200−2i2i002-22-200−2i2i0022-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i000000000−1+i3−1−i30001−i3−1+i31−i31+i3−1−i31+i300−2ζ72ζ70000−2ζ112ζ1100000000000000
χ372-2-222i−2i00002-2-222i−2i000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000022000-2-22-2-222i−2i00002i−2i0000000000000000
χ382-2-222i−2i00002-2-222i−2i000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000000000−1−i3−1+i30001+i31+i3−1−i31−i31−i3−1+i32ζ11−2ζ1100002ζ7−2ζ70000000000000000
χ392-2-222i−2i00002-2-222i−2i000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000000000−1+i3−1−i30001−i31−i3−1+i31+i31+i3−1−i32ζ7−2ζ700002ζ11−2ζ110000000000000000
χ402-2-22−2i2i00002-2-22−2i2i000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000022000-2-22-2-22−2i2i0000−2i2i0000000000000000
χ412-2-22−2i2i00002-2-22−2i2i000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000000−1−i3−1+i30001+i31+i3−1−i31−i31−i3−1+i3−2ζ112ζ110000−2ζ72ζ70000000000000000
χ422-2-22−2i2i00002-2-22−2i2i000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000000−1+i3−1−i30001−i31−i3−1+i31+i31+i3−1−i3−2ζ72ζ70000−2ζ112ζ110000000000000000
χ4333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1300333000000000000000000-1-1-1-100000000
χ4433333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-300-3-3-3000000000000000000111100000000
χ45333333-3-3-3-3333333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111113003-3-3000000000000000000-1-11100000000
χ46333333-3-3-3-3333333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-300-33300000000000000000011-1-100000000
χ473333-3-333-3-33333-3-333-3-3-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111300-33-3000000000000000000-11-1100000000
χ483333-3-333-3-33333-3-333-3-3-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-3003-330000000000000000001-11-100000000
χ493333-3-3-3-3333333-3-3-3-333-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1300-3-33000000000000000000-111-100000000
χ503333-3-3-3-3333333-3-3-3-333-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-30033-30000000000000000001-1-1100000000
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χ526666666666-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ53666666-6-6-6-6-2-2-2-2-2-222222i−2i2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ54666666-6-6-6-6-2-2-2-2-2-22222−2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ556666-6-666-6-6-2-2-2-222-2-2222i−2i2i−2i2i−2i2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
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χ586666-6-6-6-666-2-2-2-22222-2-2−2i2i−2i2i−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
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χ6066-6-600006i−6i-2-2220000−2i2i2i−2i2i−2i−2i2i−2i2i2−2i−2+2i2+2i−2−2i2−2i−2+2i2+2i−2−2i2+2i−2−2i2−2i−2+2i2+2i−2−2i2−2i−2+2i-2-22222-2-2000000000000000000000000000000000000
χ6166-6-600006i−6i-2-2220000−2i2i2i−2i2i−2i−2i2i−2i2i−2+2i2−2i−2−2i2+2i−2+2i2−2i−2−2i2+2i−2−2i2+2i−2+2i2−2i−2−2i2+2i−2+2i2−2i-2-22222-2-2000000000000000000000000000000000000
χ6266-6-600006i−6i-2-2220000−2i2i−2i2i−2i2i2i−2i2i−2i2+2i−2−2i2−2i−2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i−2−2i2+2i−2+2i2−2i−2−2i2+2i22-2-2-2-222000000000000000000000000000000000000
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χ696-66-6006i−6i006-66-6006i−6i00-2-222-2-22200000000−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000000000
χ706-66-6006i−6i00-22-2200−2i2i002i−2i−2i2i2i−2i−2i2i2+2i−2−2i−2+2i2−2i−2−2i2+2i2−2i−2+2i-2-22222-2-22−2i−2+2i2+2i−2−2i2−2i−2+2i2+2i−2−2i000000000000000000000000000000000000
χ716-66-6006i−6i00-22-2200−2i2i002i−2i−2i2i2i−2i−2i2i−2−2i2+2i2−2i−2+2i2+2i−2−2i−2+2i2−2i-2-22222-2-2−2+2i2−2i−2−2i2+2i−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000
χ726-66-6006i−6i00-22-2200−2i2i00−2i2i2i−2i−2i2i2i−2i2−2i−2+2i−2−2i2+2i−2+2i2−2i2+2i−2−2i22-2-2-2-222−2−2i2+2i−2+2i2−2i−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000
χ736-66-6006i−6i00-22-2200−2i2i00−2i2i2i−2i−2i2i2i−2i−2+2i2−2i2+2i−2−2i2−2i−2+2i−2−2i2+2i22-2-2-2-2222+2i−2−2i2−2i−2+2i2+2i−2−2i2−2i−2+2i000000000000000000000000000000000000
χ746-66-600−6i6i006-66-600−6i6i00-2-222-2-222000000002i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000000000
χ756-66-600−6i6i00-22-22002i−2i002i−2i−2i2i2i−2i−2i2i2+2i−2−2i−2+2i2−2i−2−2i2+2i2−2i−2+2i22-2-2-2-222−2+2i2−2i−2−2i2+2i−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000
χ766-66-600−6i6i00-22-22002i−2i002i−2i−2i2i2i−2i−2i2i−2−2i2+2i2−2i−2+2i2+2i−2−2i−2+2i2−2i22-2-2-2-2222−2i−2+2i2+2i−2−2i2−2i−2+2i2+2i−2−2i000000000000000000000000000000000000
χ776-66-600−6i6i00-22-22002i−2i00−2i2i2i−2i−2i2i2i−2i2−2i−2+2i−2−2i2+2i−2+2i2−2i2+2i−2−2i-2-22222-2-22+2i−2−2i2−2i−2+2i2+2i−2−2i2−2i−2+2i000000000000000000000000000000000000
χ786-66-600−6i6i00-22-22002i−2i00−2i2i2i−2i−2i2i2i−2i−2+2i2−2i2+2i−2−2i2−2i−2+2i−2−2i2+2i-2-22222-2-2−2−2i2+2i−2+2i2−2i−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000
χ796-6-666i−6i00006-6-666i−6i0000-2-22222-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000000000
χ806-6-666i−6i0000-222-2−2i2i00002i−2i−2i2i−2i2i2i−2i-2-22222-2-22−2i−2+2i−2−2i2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i2−2i−2+2i2+2i−2−2i−2+2i2−2i000000000000000000000000000000000000
χ816-6-666i−6i0000-222-2−2i2i00002i−2i−2i2i−2i2i2i−2i-2-22222-2-2−2+2i2−2i2+2i−2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i−2+2i2−2i−2−2i2+2i2−2i−2+2i000000000000000000000000000000000000
χ826-6-666i−6i0000-222-2−2i2i0000−2i2i2i−2i2i−2i−2i2i22-2-2-2-2222+2i−2−2i−2+2i2−2i−2−2i2+2i2−2i−2+2i2−2i−2+2i−2−2i2+2i−2+2i2−2i2+2i−2−2i000000000000000000000000000000000000
χ836-6-666i−6i0000-222-2−2i2i0000−2i2i2i−2i2i−2i−2i2i22-2-2-2-222−2−2i2+2i2−2i−2+2i2+2i−2−2i−2+2i2−2i−2+2i2−2i2+2i−2−2i2−2i−2+2i−2−2i2+2i000000000000000000000000000000000000
χ846-6-66−6i6i00006-6-66−6i6i0000-2-22222-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000000000
χ856-6-66−6i6i0000-222-22i−2i00002i−2i−2i2i−2i2i2i−2i22-2-2-2-2222−2i−2+2i−2−2i2+2i−2+2i2−2i2+2i−2−2i2+2i−2−2i−2+2i2−2i−2−2i2+2i2−2i−2+2i000000000000000000000000000000000000
χ866-6-66−6i6i0000-222-22i−2i00002i−2i−2i2i−2i2i2i−2i22-2-2-2-222−2+2i2−2i2+2i−2−2i2−2i−2+2i−2−2i2+2i−2−2i2+2i2−2i−2+2i2+2i−2−2i−2+2i2−2i000000000000000000000000000000000000
χ876-6-66−6i6i0000-222-22i−2i0000−2i2i2i−2i2i−2i−2i2i-2-22222-2-22+2i−2−2i−2+2i2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i2+2i−2−2i2−2i−2+2i−2−2i2+2i000000000000000000000000000000000000
χ886-6-66−6i6i0000-222-22i−2i0000−2i2i2i−2i2i−2i−2i2i-2-22222-2-2−2−2i2+2i2−2i−2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i−2−2i2+2i−2+2i2−2i2+2i−2−2i000000000000000000000000000000000000

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