Finite Group Databasebeta

← Group #13154931

Character table — Group #13154931

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112444444444888812122424242424242424242424363672721124444444448888121224242424242424242424243636727211244444444488881212242424242424242424242436367272
order1222336666666666444441212121212121212244436663366666666661212121212121212121212121261212123666336666666666121212121212121212121212126121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111-1-11111-1-1-1-111-1-11111111111111111111-1-11111-1-1-1-111-1-11111111111111111111-1-11111-1-1-1-111-1-1
χ31111111111111111-1-1-111-1-1-1-1111111-1-11111111111111111-1-1-111-1-1-1-1111111-1-11111111111111111-1-1-111-1-1-1-1111111-1-1
χ41111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111-1111111-1-11-1-1-111-1i−i11-1-1ii−i−i-11i−i111-1111111-1-11-1-1-111-1i−i11-1-1ii−i−i-11i−i111-1111111-1-11-1-1-111-1i−i11-1-1ii−i−i-11i−i
χ6111-1111111-1-11-1-1-111-1−ii11-1-1−i−iii-11−ii111-1111111-1-11-1-1-111-1−ii11-1-1−i−iii-11−ii111-1111111-1-11-1-1-111-1−ii11-1-1−i−iii-11−ii
χ7111-1111111-1-11-1-1-1-1-11i−i-1-111ii−i−i-11−ii111-1111111-1-11-1-1-1-1-11i−i-1-111ii−i−i-11−ii111-1111111-1-11-1-1-1-1-11i−i-1-111ii−i−i-11−ii
χ8111-1111111-1-11-1-1-1-1-11−ii-1-111−i−iii-11i−i111-1111111-1-11-1-1-1-1-11−ii-1-111−i−iii-11i−i111-1111111-1-11-1-1-1-1-11−ii-1-111−i−iii-11i−i
χ922222222222222220000000000000-2-20022222222222222220000000000000-2-20022222222222222220000000000000-2-200
χ10222-2222222-2-22-2-2-200000000000002-200222-2222222-2-22-2-2-200000000000002-200222-2222222-2-22-2-2-200000000000002-200
χ1144441-21-211-2-2-211-222200-1-1-1-10000000044441-21-211-2-2-211-222200-1-1-1-10000000044441-21-211-2-2-211-222200-1-1-1-100000000
χ1244441-21-211-2-2-211-2-2-2-20011110000000044441-21-211-2-2-211-2-2-2-20011110000000044441-21-211-2-2-211-2-2-2-200111100000000
χ134444-21-21-2-2111-2-21000220000-1-1-1-100004444-21-21-2-2111-2-21000220000-1-1-1-100004444-21-21-2-2111-2-21000220000-1-1-1-10000
χ144444-21-21-2-2111-2-21000-2-20000111100004444-21-21-2-2111-2-21000-2-20000111100004444-21-21-2-2111-2-21000-2-2000011110000
χ15444-41-21-21122-2-1-1222-200-1-11100000000444-41-21-21122-2-1-1222-200-1-11100000000444-41-21-21122-2-1-1222-200-1-11100000000
χ16444-41-21-21122-2-1-12-2-220011-1-100000000444-41-21-21122-2-1-12-2-220011-1-100000000444-41-21-21122-2-1-12-2-220011-1-100000000
χ17444-4-21-21-2-2-1-1122-10002i−2i0000−i−iii0000444-4-21-21-2-2-1-1122-10002i−2i0000−i−iii0000444-4-21-21-2-2-1-1122-10002i−2i0000−i−iii0000
χ18444-4-21-21-2-2-1-1122-1000−2i2i0000ii−i−i0000444-4-21-21-2-2-1-1122-1000−2i2i0000ii−i−i0000444-4-21-21-2-2-1-1122-1000−2i2i0000ii−i−i0000
χ1944-4044-444-400-40000000000000000000044-4044-444-400-40000000000000000000044-4044-444-400-400000000000000000000
χ2044-40-2121-2233-100-30000000003−33−3000044-40-2121-2233-100-30000000003−33−3000044-40-2121-2233-100-30000000003−33−30000
χ2144-40-2121-2233-100-3000000000−33−33000044-40-2121-2233-100-3000000000−33−33000044-40-2121-2233-100-3000000000−33−330000
χ2244-40-2121-22-3-3-1003000000000−i3i3i3−i3000044-40-2121-22-3-3-1003000000000−i3i3i3−i3000044-40-2121-22-3-3-1003000000000−i3i3i3−i30000
χ2344-40-2121-22-3-3-1003000000000i3−i3−i3i3000044-40-2121-22-3-3-1003000000000i3−i3−i3i3000044-40-2121-22-3-3-1003000000000i3−i3−i3i30000
χ244-4001-2-32-13−2i32i30−i3i302i−2i000i−i3−3000000004-4001-2-32-13−2i32i30−i3i302i−2i000i−i3−3000000004-4001-2-32-13−2i32i30−i3i302i−2i000i−i3−300000000
χ254-4001-2-32-13−2i32i30−i3i30−2i2i000−ii−33000000004-4001-2-32-13−2i32i30−i3i30−2i2i000−ii−33000000004-4001-2-32-13−2i32i30−i3i30−2i2i000−ii−3300000000
χ264-4001-2-32-132i3−2i30i3−i302i−2i000i−i−33000000004-4001-2-32-132i3−2i30i3−i302i−2i000i−i−33000000004-4001-2-32-132i3−2i30i3−i302i−2i000i−i−3300000000
χ274-4001-2-32-132i3−2i30i3−i30−2i2i000−ii3−3000000004-4001-2-32-132i3−2i30i3−i30−2i2i000−ii3−3000000004-4001-2-32-132i3−2i30i3−i30−2i2i000−ii3−300000000
χ284-400440-4-400000002i−2i000−2i2i00000000004-400440-4-400000002i−2i000−2i2i00000000004-400440-4-400000002i−2i000−2i2i0000000000
χ294-400440-4-40000000−2i2i0002i−2i00000000004-400440-4-40000000−2i2i0002i−2i00000000004-400440-4-40000000−2i2i0002i−2i0000000000
χ3088-802-4-2-42-20040000000000000000000088-802-4-2-42-20040000000000000000000088-802-4-2-42-200400000000000000000000
χ318-8002-464-2-6000000000000000000000008-8002-464-2-6000000000000000000000008-8002-464-2-600000000000000000000000
χ328-800-420-240−2i32i302i3−2i30000000000000000008-800-420-240−2i32i302i3−2i30000000000000000008-800-420-240−2i32i302i3−2i3000000000000000000
χ338-800-420-2402i3−2i30−2i32i30000000000000000008-800-420-2402i3−2i30−2i32i30000000000000000008-800-420-2402i3−2i30−2i32i3000000000000000000
χ34111111111111111111111111111111111−1+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+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−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ351111111111111111111-1-11111-1-1-1-111-1-1−1+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+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−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−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ361111111111111111-1-1-111-1-1-1-1111111-1-1−1+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+i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ371111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ38111-1111111-1-11-1-1-111-1i−i11-1-1ii−i−i-11i−i−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i321−i32ζ7−ζ7−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ71−i32−1+i32ζ7−ζ7−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i321+i32ζ11−ζ11−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ111+i32−1−i32ζ11−ζ11
χ39111-1111111-1-11-1-1-111-1−ii11-1-1−i−iii-11−ii−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−ζ7ζ7−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ71−i32−1+i32−ζ7ζ7−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−ζ11ζ11−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ111+i32−1−i32−ζ11ζ11
χ40111-1111111-1-11-1-1-1-1-11i−i-1-111ii−i−i-11−ii−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i321−i32−1+i32ζ7−ζ71−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ71−i32−1+i32−ζ7ζ7−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i321+i32−1−i32ζ11−ζ111+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ111+i32−1−i32−ζ11ζ11
χ41111-1111111-1-11-1-1-1-1-11−ii-1-111−i−iii-11i−i−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i321−i32−1+i32−ζ7ζ71−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ71−i32−1+i32ζ7−ζ7−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i321+i32−1−i32−ζ11ζ111+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ111+i32−1−i32ζ11−ζ11
χ4222222222222222220000000000000-2-200−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i300000000000001−i31−i300−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i300000000000001+i31+i300
χ43222-2222222-2-22-2-2-200000000000002-200−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i31−i30000000000000−1+i31−i300−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i31+i30000000000000−1−i31+i300
χ4444441-21-211-2-2-211-222200-1-1-1-100000000−2+2i3−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i31−i31−i3−1+i32−1+i321−i3−1+i3−1+i3−1+i3001−i321−i321−i321−i3200000000−2−2i3−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i31+i31+i3−1−i32−1−i321+i3−1−i3−1−i3−1−i3001+i321+i321+i321+i3200000000
χ4544441-21-211-2-2-211-2-2-2-200111100000000−2+2i3−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i31−i31−i3−1+i32−1+i321−i31−i31−i31−i300−1+i32−1+i32−1+i32−1+i3200000000−2−2i3−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i31+i31+i3−1−i32−1−i321+i31+i31+i31+i300−1−i32−1−i32−1−i32−1−i3200000000
χ464444-21-21-2-2111-2-21000220000-1-1-1-10000−2+2i3−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i32−1+i321−i31−i3−1+i32000−1+i3−1+i300001−i321−i321−i321−i320000−2−2i3−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i32−1−i321+i31+i3−1−i32000−1−i3−1−i300001+i321+i321+i321+i320000
χ474444-21-21-2-2111-2-21000-2-2000011110000−2+2i3−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i32−1+i321−i31−i3−1+i320001−i31−i30000−1+i32−1+i32−1+i32−1+i320000−2−2i3−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i32−1−i321+i31+i3−1−i320001+i31+i30000−1−i32−1−i32−1−i32−1−i320000
χ48444-41-21-21122-2-1-1222-200-1-11100000000−2+2i3−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i3−1+i32−1+i32−1+i3−1+i31−i31−i321−i32−1+i3−1+i3−1+i31−i3001−i321−i32−1+i32−1+i3200000000−2−2i3−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i3−1−i32−1−i32−1−i3−1−i31+i31+i321+i32−1−i3−1−i3−1−i31+i3001+i321+i32−1−i32−1−i3200000000
χ49444-41-21-21122-2-1-12-2-220011-1-100000000−2+2i3−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i3−1+i32−1+i32−1+i3−1+i31−i31−i321−i32−1+i31−i31−i3−1+i300−1+i32−1+i321−i321−i3200000000−2−2i3−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i3−1−i32−1−i32−1−i3−1−i31+i31+i321+i32−1−i31+i31+i3−1−i300−1−i32−1−i321+i321+i3200000000
χ50444-4-21-21-2-2-1-1122-10002i−2i0000−i−iii0000−2+2i3−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i321−i31−i31−i321−i32−1+i32−1+i3−1+i31−i320002ζ7−2ζ70000−ζ7−ζ7ζ7ζ70000−2−2i3−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i321+i31+i31+i321+i32−1−i32−1−i3−1−i31+i320002ζ11−2ζ110000−ζ11−ζ11ζ11ζ110000
χ51444-4-21-21-2-2-1-1122-1000−2i2i0000ii−i−i0000−2+2i3−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i321−i31−i31−i321−i32−1+i32−1+i3−1+i31−i32000−2ζ72ζ70000ζ7ζ7−ζ7−ζ70000−2−2i3−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i321+i31+i31+i321+i32−1−i32−1−i3−1−i31+i32000−2ζ112ζ110000ζ11ζ11−ζ11−ζ110000
χ5244-4044-444-400-400000000000000000000−2+2i3−2+2i32−2i30−2+2i3−2+2i32−2i3−2+2i3−2+2i32−2i3002−2i300000000000000000000−2−2i3−2−2i32+2i30−2−2i3−2−2i32+2i3−2−2i3−2−2i32+2i3002+2i300000000000000000000
χ5344-40-2121-2233-100-30000000003−33−30000−2+2i3−2+2i32−2i301−i3−1+i32−1+i3−1+i321−i3−1+i3−3+3i32−3+3i321−i32003−3i32000000000−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ110000−2−2i3−2−2i32+2i301+i3−1−i32−1−i3−1−i321+i3−1−i3−3−3i32−3−3i321+i32003+3i320000000002ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ110000
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χ934-4001-2-32-132i3−2i30i3−i30−2i2i000−ii3−300000000−2−2i32+2i300−1−i321+i33+3i32−1−i31+i32−3−3i323−i3−3+i303−i32−3+i320−2ζ112ζ11000−ζ11ζ112ζ7+ζ11−2ζ7−ζ1100000000−2+2i32−2i300−1+i321−i33−3i32−1+i31−i32−3+3i32−3−i33+i30−3−i323+i320−2ζ72ζ7000−ζ7ζ7−ζ7−2ζ11ζ7+2ζ1100000000
χ944-400440-4-400000002i−2i000−2i2i0000000000−2−2i32+2i300−2−2i3−2−2i302+2i32+2i300000002ζ11−2ζ11000−2ζ112ζ110000000000−2+2i32−2i300−2+2i3−2+2i302−2i32−2i300000002ζ7−2ζ7000−2ζ72ζ70000000000
χ954-400440-4-40000000−2i2i0002i−2i0000000000−2−2i32+2i300−2−2i3−2−2i302+2i32+2i30000000−2ζ112ζ110002ζ11−2ζ110000000000−2+2i32−2i300−2+2i3−2+2i302−2i32−2i30000000−2ζ72ζ70002ζ7−2ζ70000000000
χ9688-802-4-2-42-200400000000000000000000−4−4i3−4−4i34+4i30−1−i32+2i31+i32+2i3−1−i31+i300−2−2i300000000000000000000−4+4i3−4+4i34−4i30−1+i32−2i31−i32−2i3−1+i31−i300−2+2i300000000000000000000
χ978-8002-464-2-600000000000000000000000−4−4i34+4i300−1−i32+2i3−3−3i3−2−2i31+i33+3i300000000000000000000000−4+4i34−4i300−1+i32−2i3−3+3i3−2+2i31−i33−3i300000000000000000000000
χ988-800-420-240−2i32i302i3−2i3000000000000000000−4−4i34+4i3002+2i3−1−i301+i3−2−2i30−3+i33−i303−i3−3+i3000000000000000000−4+4i34−4i3002−2i3−1+i301−i3−2+2i303+i3−3−i30−3−i33+i3000000000000000000
χ998-800-420-2402i3−2i30−2i32i3000000000000000000−4−4i34+4i3002+2i3−1−i301+i3−2−2i303−i3−3+i30−3+i33−i3000000000000000000−4+4i34−4i3002−2i3−1+i301−i3−2+2i30−3−i33+i303+i3−3−i3000000000000000000

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