Finite Group Databasebeta

← Group #13157136

Character table — Group #13157136

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112444444444888888888888836363636727272721124444444448888888888888363636367272727211244444444488888888888883636363672727272
order12233466666626666666612121212224444443663312666666666666666121212126612121212121236633126666666666666661212121266121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-111111111111111111111111111111-1-1-1-111111111111111111111111111111-1-1-1-1
χ31111111111111111111111111-1-1-1-1ii−i−i1111111111111111111111111-1-1-1-1ii−i−i1111111111111111111111111-1-1-1-1ii−i−i
χ41111111111111111111111111-1-1-1-1−i−iii1111111111111111111111111-1-1-1-1−i−iii1111111111111111111111111-1-1-1-1−i−iii
χ5111111111111-1-1-1-1-1-1-1-1-1111111-1-11-11-1111111111111-1-1-1-1-1-1-1-1-1111111-1-11-11-1111111111111-1-1-1-1-1-1-1-1-1111111-1-11-11-1
χ6111111111111-1-1-1-1-1-1-1-1-1111111-1-1-11-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-11-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-11-11
χ7111111111111-1-1-1-1-1-1-1-1-11111-1-111i−i−ii111111111111-1-1-1-1-1-1-1-1-11111-1-111i−i−ii111111111111-1-1-1-1-1-1-1-1-11111-1-111i−i−ii
χ8111111111111-1-1-1-1-1-1-1-1-11111-1-111−iii−i111111111111-1-1-1-1-1-1-1-1-11111-1-111−iii−i111111111111-1-1-1-1-1-1-1-1-11111-1-111−iii−i
χ922222-2222222000000000-2-2-2-22-200000022222-2222222000000000-2-2-2-22-200000022222-2222222000000000-2-2-2-22-2000000
χ1022222-2222222000000000-2-2-2-2-2200000022222-2222222000000000-2-2-2-2-2200000022222-2222222000000000-2-2-2-2-22000000
χ114441-2411-2-21-241111-2-2-2-211-2-2000000004441-2411-2-21-241111-2-2-2-211-2-2000000004441-2411-2-21-241111-2-2-2-211-2-200000000
χ124441-2411-2-21-2-4-1-1-1-1222211-2-2000000004441-2411-2-21-2-4-1-1-1-1222211-2-2000000004441-2411-2-21-2-4-1-1-1-1222211-2-200000000
χ134441-2-411-2-21-2033-3-30000-1-122000000004441-2-411-2-21-2033-3-30000-1-122000000004441-2-411-2-21-2033-3-30000-1-12200000000
χ144441-2-411-2-21-20-3-3330000-1-122000000004441-2-411-2-21-20-3-3330000-1-122000000004441-2-411-2-21-20-3-3330000-1-12200000000
χ15444-214-2-211-214-2-2-2-21111-2-21100000000444-214-2-211-214-2-2-2-21111-2-21100000000444-214-2-211-214-2-2-2-21111-2-21100000000
χ16444-214-2-211-21-42222-1-1-1-1-2-21100000000444-214-2-211-21-42222-1-1-1-1-2-21100000000444-214-2-211-21-42222-1-1-1-1-2-21100000000
χ17444-21-4-2-211-210000033-3-322-1-100000000444-21-4-2-211-210000033-3-322-1-100000000444-21-4-2-211-210000033-3-322-1-100000000
χ18444-21-4-2-211-2100000-3-33322-1-100000000444-21-4-2-211-2100000-3-33322-1-100000000444-21-4-2-211-2100000-3-33322-1-100000000
χ1944-41-20-1-1221-20−i3i3−i3i300−2i32i33-3000000000044-41-20-1-1221-20−i3i3−i3i300−2i32i33-3000000000044-41-20-1-1221-20−i3i3−i3i300−2i32i33-30000000000
χ2044-41-20-1-1221-20−i3i3i3−i3−2i32i300-33000000000044-41-20-1-1221-20−i3i3i3−i3−2i32i300-33000000000044-41-20-1-1221-20−i3i3i3−i3−2i32i300-330000000000
χ2144-41-20-1-1221-20i3−i3−i3i32i3−2i300-33000000000044-41-20-1-1221-20i3−i3−i3i32i3−2i300-33000000000044-41-20-1-1221-20i3−i3−i3i32i3−2i300-330000000000
χ2244-41-20-1-1221-20i3−i3i3−i3002i3−2i33-3000000000044-41-20-1-1221-20i3−i3i3−i3002i3−2i33-3000000000044-41-20-1-1221-20i3−i3i3−i3002i3−2i33-30000000000
χ2344-4440-4-4-4-44400000000000000000000044-4440-4-4-4-44400000000000000000000044-4440-4-4-4-444000000000000000000000
χ2444-4-21022-1-1-21000−2i32i3−i3i3i3−i3003-30000000044-4-21022-1-1-21000−2i32i3−i3i3i3−i3003-30000000044-4-21022-1-1-21000−2i32i3−i3i3i3−i3003-300000000
χ2544-4-21022-1-1-210002i3−2i3i3−i3−i3i3003-30000000044-4-21022-1-1-210002i3−2i3i3−i3−i3i3003-30000000044-4-21022-1-1-210002i3−2i3i3−i3−i3i3003-300000000
χ2644-4-21022-1-1-210−2i32i300i3−i3i3−i300-330000000044-4-21022-1-1-210−2i32i300i3−i3i3−i300-330000000044-4-21022-1-1-210−2i32i300i3−i3i3−i300-3300000000
χ2744-4-21022-1-1-2102i3−2i300−i3i3−i3i300-330000000044-4-21022-1-1-2102i3−2i300−i3i3−i3i300-330000000044-4-21022-1-1-2102i3−2i300−i3i3−i3i300-3300000000
χ284-404400000-4-40000000000000002-200004-404400000-4-40000000000000002-200004-404400000-4-40000000000000002-20000
χ294-404400000-4-4000000000000000-2200004-404400000-4-4000000000000000-2200004-404400000-4-4000000000000000-220000
χ308-802-406-600-240000000000000000000008-802-406-600-240000000000000000000008-802-406-600-24000000000000000000000
χ318-802-40-6600-240000000000000000000008-802-40-6600-240000000000000000000008-802-40-6600-24000000000000000000000
χ328-80-420006-64-20000000000000000000008-80-420006-64-20000000000000000000008-80-420006-64-2000000000000000000000
χ338-80-42000-664-20000000000000000000008-80-42000-664-20000000000000000000008-80-42000-664-2000000000000000000000
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
χ3511111111111111111111111111111-1-1-1-1−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ361111111111111111111111111-1-1-1-1ii−i−i−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+i321−i321−i321−i321−i32ζ7ζ7−ζ7−ζ7−1−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−i321+i321+i321+i321+i32ζ11ζ11−ζ11−ζ11
χ371111111111111111111111111-1-1-1-1−i−iii−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+i321−i321−i321−i321−i32−ζ7−ζ7ζ7ζ7−1−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−i321+i321+i321+i321+i32−ζ11−ζ11ζ11ζ11
χ38111111111111-1-1-1-1-1-1-1-1-1111111-1-11-11-1−1+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−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32
χ39111111111111-1-1-1-1-1-1-1-1-1111111-1-1-11-11−1+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−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32
χ40111111111111-1-1-1-1-1-1-1-1-11111-1-111i−i−ii−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−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32ζ7−ζ7−ζ7ζ7−1−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+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32ζ11−ζ11−ζ11ζ11
χ41111111111111-1-1-1-1-1-1-1-1-11111-1-111−iii−i−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−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−ζ7ζ7ζ7−ζ7−1−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+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−ζ11ζ11ζ11−ζ11
χ4222222-2222222000000000-2-2-2-22-2000000−1+i3−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i30000000001−i31−i31−i31−i3−1+i31−i3000000−1−i3−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i30000000001+i31+i31+i31+i3−1−i31+i3000000
χ4322222-2222222000000000-2-2-2-2-22000000−1+i3−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i30000000001−i31−i31−i31−i31−i3−1+i3000000−1−i3−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i30000000001+i31+i31+i31+i31+i3−1−i3000000
χ444441-2411-2-21-241111-2-2-2-211-2-200000000−2+2i3−2+2i3−2+2i3−1+i321−i3−2+2i3−1+i32−1+i321−i31−i3−1+i321−i3−2+2i3−1+i32−1+i32−1+i32−1+i321−i31−i31−i31−i3−1+i32−1+i321−i31−i300000000−2−2i3−2−2i3−2−2i3−1−i321+i3−2−2i3−1−i32−1−i321+i31+i3−1−i321+i3−2−2i3−1−i32−1−i32−1−i32−1−i321+i31+i31+i31+i3−1−i32−1−i321+i31+i300000000
χ454441-2411-2-21-2-4-1-1-1-1222211-2-200000000−2+2i3−2+2i3−2+2i3−1+i321−i3−2+2i3−1+i32−1+i321−i31−i3−1+i321−i32−2i31−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i3−1+i32−1+i321−i31−i300000000−2−2i3−2−2i3−2−2i3−1−i321+i3−2−2i3−1−i32−1−i321+i31+i3−1−i321+i32+2i31+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i3−1−i32−1−i321+i31+i300000000
χ464441-2-411-2-21-2033-3-30000-1-12200000000−2+2i3−2+2i3−2+2i3−1+i321−i32−2i3−1+i32−1+i321−i31−i3−1+i321−i30−3+3i32−3+3i323−3i323−3i3200001−i321−i32−1+i3−1+i300000000−2−2i3−2−2i3−2−2i3−1−i321+i32+2i3−1−i32−1−i321+i31+i3−1−i321+i30−3−3i32−3−3i323+3i323+3i3200001+i321+i32−1−i3−1−i300000000
χ474441-2-411-2-21-20-3-3330000-1-12200000000−2+2i3−2+2i3−2+2i3−1+i321−i32−2i3−1+i32−1+i321−i31−i3−1+i321−i303−3i323−3i32−3+3i32−3+3i3200001−i321−i32−1+i3−1+i300000000−2−2i3−2−2i3−2−2i3−1−i321+i32+2i3−1−i32−1−i321+i31+i3−1−i321+i303+3i323+3i32−3−3i32−3−3i3200001+i321+i32−1−i3−1−i300000000
χ48444-214-2-211-214-2-2-2-21111-2-21100000000−2+2i3−2+2i3−2+2i31−i3−1+i32−2+2i31−i31−i3−1+i32−1+i321−i3−1+i32−2+2i31−i31−i31−i31−i3−1+i32−1+i32−1+i32−1+i321−i31−i3−1+i32−1+i3200000000−2−2i3−2−2i3−2−2i31+i3−1−i32−2−2i31+i31+i3−1−i32−1−i321+i3−1−i32−2−2i31+i31+i31+i31+i3−1−i32−1−i32−1−i32−1−i321+i31+i3−1−i32−1−i3200000000
χ49444-214-2-211-21-42222-1-1-1-1-2-21100000000−2+2i3−2+2i3−2+2i31−i3−1+i32−2+2i31−i31−i3−1+i32−1+i321−i3−1+i322−2i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i31−i3−1+i32−1+i3200000000−2−2i3−2−2i3−2−2i31+i3−1−i32−2−2i31+i31+i3−1−i32−1−i321+i3−1−i322+2i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i31+i3−1−i32−1−i3200000000
χ50444-21-4-2-211-210000033-3-322-1-100000000−2+2i3−2+2i3−2+2i31−i3−1+i322−2i31−i31−i3−1+i32−1+i321−i3−1+i3200000−3+3i32−3+3i323−3i323−3i32−1+i3−1+i31−i321−i3200000000−2−2i3−2−2i3−2−2i31+i3−1−i322+2i31+i31+i3−1−i32−1−i321+i3−1−i3200000−3−3i32−3−3i323+3i323+3i32−1−i3−1−i31+i321+i3200000000
χ51444-21-4-2-211-2100000-3-33322-1-100000000−2+2i3−2+2i3−2+2i31−i3−1+i322−2i31−i31−i3−1+i32−1+i321−i3−1+i32000003−3i323−3i32−3+3i32−3+3i32−1+i3−1+i31−i321−i3200000000−2−2i3−2−2i3−2−2i31+i3−1−i322+2i31+i31+i3−1−i32−1−i321+i3−1−i32000003+3i323+3i32−3−3i32−3−3i32−1−i3−1−i31+i321+i3200000000
χ5244-41-20-1-1221-20−i3i3−i3i300−2i32i33-30000000000−2+2i3−2+2i32−2i3−1+i321−i301−i321−i32−1+i3−1+i3−1+i321−i303+i32−3−i323+i32−3−i32003+i3−3−i3−3+3i323−3i320000000000−2−2i3−2−2i32+2i3−1−i321+i301+i321+i32−1−i3−1−i3−1−i321+i30−3+i323−i32−3+i323−i3200−3+i33−i3−3−3i323+3i320000000000
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χ9144-4-21022-1-1-210002i3−2i3i3−i3−i3i3003-300000000−2−2i3−2−2i32+2i31+i3−1−i320−1−i3−1−i31+i321+i321+i3−1−i320003−i3−3+i33−i32−3+i32−3+i323−i3200−3−3i323+3i3200000000−2+2i3−2+2i32−2i31−i3−1+i320−1+i3−1+i31−i321−i321−i3−1+i32000−3−i33+i3−3−i323+i323+i32−3−i3200−3+3i323−3i3200000000
χ9244-4-21022-1-1-210−2i32i300i3−i3i3−i300-3300000000−2−2i3−2−2i32+2i31+i3−1−i320−1−i3−1−i31+i321+i321+i3−1−i320−3+i33−i3003−i32−3+i323−i32−3+i32003+3i32−3−3i3200000000−2+2i3−2+2i32−2i31−i3−1+i320−1+i3−1+i31−i321−i321−i3−1+i3203+i3−3−i300−3−i323+i32−3−i323+i32003−3i32−3+3i3200000000
χ9344-4-21022-1-1-2102i3−2i300−i3i3−i3i300-3300000000−2−2i3−2−2i32+2i31+i3−1−i320−1−i3−1−i31+i321+i321+i3−1−i3203−i3−3+i300−3+i323−i32−3+i323−i32003+3i32−3−3i3200000000−2+2i3−2+2i32−2i31−i3−1+i320−1+i3−1+i31−i321−i321−i3−1+i320−3−i33+i3003+i32−3−i323+i32−3−i32003−3i32−3+3i3200000000
χ944-404400000-4-40000000000000002-20000−2−2i32+2i30−2−2i3−2−2i3000002+2i32+2i3000000000000000−1−i31+i30000−2+2i32−2i30−2+2i3−2+2i3000002−2i32−2i3000000000000000−1+i31−i30000
χ954-404400000-4-4000000000000000-220000−2−2i32+2i30−2−2i3−2−2i3000002+2i32+2i30000000000000001+i3−1−i30000−2+2i32−2i30−2+2i3−2+2i3000002−2i32−2i30000000000000001−i3−1+i30000
χ968-802-406-600-24000000000000000000000−4−4i34+4i30−1−i32+2i30−3−3i33+3i3001+i3−2−2i3000000000000000000000−4+4i34−4i30−1+i32−2i30−3+3i33−3i3001−i3−2+2i3000000000000000000000
χ978-802-40-6600-24000000000000000000000−4−4i34+4i30−1−i32+2i303+3i3−3−3i3001+i3−2−2i3000000000000000000000−4+4i34−4i30−1+i32−2i303−3i3−3+3i3001−i3−2+2i3000000000000000000000
χ988-80-420006-64-2000000000000000000000−4−4i34+4i302+2i3−1−i3000−3−3i33+3i3−2−2i31+i3000000000000000000000−4+4i34−4i302−2i3−1+i3000−3+3i33−3i3−2+2i31−i3000000000000000000000
χ998-80-42000-664-2000000000000000000000−4−4i34+4i302+2i3−1−i30003+3i3−3−3i3−2−2i31+i3000000000000000000000−4+4i34−4i302−2i3−1+i30003−3i3−3+3i3−2+2i31−i3000000000000000000000

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