Finite Group Databasebeta

← Group #13166658

Character table — Group #13166658

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112444444488888991212121218242424242424364848727211244444448888899121212121824242424242436484872721124444444888889912121212182424242424243648487272
order1243366812121224242424222488444612242481212443612336624121212242424246661224241212126122424241212121236123366241212122424242466612242412121261224242412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-111111-1-1-1-11111111111111111111111-1-111111-1-1-1-11111111111111111111111-1-111111-1-1-1-1
χ311111111111111111-1-1-1-1111-1-1-1-1111-1-111111111111111111-1-1-1-1111-1-1-1-1111-1-111111111111111111-1-1-1-1111-1-1-1-1111-1-1
χ411111111111111111-1-1-1-11-1-1-1-1-1-11-1-11111111111111111111-1-1-1-11-1-1-1-1-1-11-1-11111111111111111111-1-1-1-11-1-1-1-1-1-11-1-111
χ51111111-1111-1-1-1-11111-1-111-111-1-1-11-11-11111111-1111-1-1-1-11111-1-111-111-1-1-11-11-11111111-1111-1-1-1-11111-1-111-111-1-1-11-11-1
χ61111111-1111-1-1-1-11111-1-11-1111-1-1-1-11-111111111-1111-1-1-1-11111-1-11-1111-1-1-1-11-111111111-1111-1-1-1-11111-1-11-1111-1-1-1-11-11
χ71111111-1111-1-1-1-111-1-11111-1-1-111-11-1-111111111-1111-1-1-1-111-1-11111-1-1-111-11-1-111111111-1111-1-1-1-111-1-11111-1-1-111-11-1-11
χ81111111-1111-1-1-1-111-1-1111-11-1-111-1-111-11111111-1111-1-1-1-111-1-1111-11-1-111-1-111-11111111-1111-1-1-1-111-1-1111-11-1-111-1-111-1
χ9222222222222222-2-20000-2000000-20000222222222222222-2-20000-2000000-20000222222222222222-2-20000-2000000-20000
χ102222222-2222-2-2-2-2-2-20000-2000000200002222222-2222-2-2-2-2-2-20000-2000000200002222222-2222-2-2-2-2-2-20000-200000020000
χ1122-222220-2-2-20000222-200-2002-2000000022-222220-2-2-20000222-200-2002-2000000022-222220-2-2-20000222-200-2002-20000000
χ1222-222220-2-2-2000022-2200-200-22000000022-222220-2-2-2000022-2200-200-22000000022-222220-2-2-2000022-2200-200-220000000
χ1322-222220-2-2-20000-2-2002i−2i200002i−2i0000022-222220-2-2-20000-2-2002i−2i200002i−2i0000022-222220-2-2-20000-2-2002i−2i200002i−2i00000
χ1422-222220-2-2-20000-2-200−2i2i20000−2i2i0000022-222220-2-2-20000-2-200−2i2i20000−2i2i0000022-222220-2-2-20000-2-200−2i2i20000−2i2i00000
χ154441-2-214-2-21-2-21100000002200000-1-1004441-2-214-2-21-2-21100000002200000-1-1004441-2-214-2-21-2-21100000002200000-1-100
χ164441-2-214-2-21-2-2110000000-2-20000011004441-2-214-2-21-2-2110000000-2-20000011004441-2-214-2-21-2-2110000000-2-2000001100
χ174441-2-21-4-2-2122-1-100000002-200000-11004441-2-21-4-2-2122-1-100000002-200000-11004441-2-21-4-2-2122-1-100000002-200000-1100
χ184441-2-21-4-2-2122-1-10000000-22000001-1004441-2-21-4-2-2122-1-10000000-22000001-1004441-2-21-4-2-2122-1-10000000-22000001-100
χ19444-211-2411-211-2-2002222000-1-1-1-100000444-211-2411-211-2-2002222000-1-1-1-100000444-211-2411-211-2-2002222000-1-1-1-100000
χ20444-211-2411-211-2-200-2-2-2-2000111100000444-211-2411-211-2-200-2-2-2-2000111100000444-211-2411-211-2-200-2-2-2-2000111100000
χ21444-211-2-411-2-1-1220022-2-2000-1-11100000444-211-2-411-2-1-1220022-2-2000-1-11100000444-211-2-411-2-1-1220022-2-2000-1-11100000
χ22444-211-2-411-2-1-12200-2-22200011-1-100000444-211-2-411-2-1-12200-2-22200011-1-100000444-211-2-411-2-1-12200-2-22200011-1-100000
χ2344-4-211-20-1-123i−3i00002-22i−2i000-11−ii0000044-4-211-20-1-123i−3i00002-22i−2i000-11−ii0000044-4-211-20-1-123i−3i00002-22i−2i000-11−ii00000
χ2444-4-211-20-1-123i−3i0000-22−2i2i0001-1i−i0000044-4-211-20-1-123i−3i0000-22−2i2i0001-1i−i0000044-4-211-20-1-123i−3i0000-22−2i2i0001-1i−i00000
χ2544-4-211-20-1-12−3i3i00002-2−2i2i000-11i−i0000044-4-211-20-1-12−3i3i00002-2−2i2i000-11i−i0000044-4-211-20-1-12−3i3i00002-2−2i2i000-11i−i00000
χ2644-4-211-20-1-12−3i3i0000-222i−2i0001-1−ii0000044-4-211-20-1-12−3i3i0000-222i−2i0001-1−ii0000044-4-211-20-1-12−3i3i0000-222i−2i0001-1−ii00000
χ274-4044-4-4000000004-400000000000000004-4044-4-4000000004-400000000000000004-4044-4-4000000004-40000000000000000
χ284-4044-4-400000000-4400000000000000004-4044-4-400000000-4400000000000000004-4044-4-400000000-440000000000000000
χ2988-82-4-42044-2000000000000000000000088-82-4-42044-2000000000000000000000088-82-4-42044-20000000000000000000000
χ308-802-44-200000032−320000000000000000008-802-44-200000032−320000000000000000008-802-44-200000032−32000000000000000000
χ318-802-44-2000000−32320000000000000000008-802-44-2000000−32320000000000000000008-802-44-2000000−3232000000000000000000
χ328-80-42-2406i−6i000000000000000000000008-80-42-2406i−6i000000000000000000000008-80-42-2406i−6i00000000000000000000000
χ338-80-42-240−6i6i000000000000000000000008-80-42-240−6i6i000000000000000000000008-80-42-240−6i6i00000000000000000000000
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
χ351111111111111111111111-1-111111-1-1-1-1−1+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+i321−i321−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ3611111111111111111-1-1-1-1111-1-1-1-1111-1-1−1+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−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−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32
χ3711111111111111111-1-1-1-11-1-1-1-1-1-11-1-111−1+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+i321−i321−i321−i321−i321−i321−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+i321+i321+i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32
χ381111111-1111-1-1-1-11111-1-111-111-1-1-11-11-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32
χ391111111-1111-1-1-1-11111-1-11-1111-1-1-1-11-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32
χ401111111-1111-1-1-1-111-1-11111-1-1-111-11-1-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32
χ411111111-1111-1-1-1-111-1-1111-11-1-111-1-111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32
χ42222222222222222-2-20000-2000000-20000−1+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+i31−i31−i300001−i30000001−i30000−1−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−i31+i31+i300001+i30000001+i30000
χ432222222-2222-2-2-2-2-2-20000-200000020000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i300001−i3000000−1+i30000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i300001+i3000000−1−i30000
χ4422-222220-2-2-20000222-200-2002-20000000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i301−i31−i31−i30000−1+i3−1+i3−1+i31−i3001−i300−1+i31−i30000000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i301+i31+i31+i30000−1−i3−1−i3−1−i31+i3001+i300−1−i31+i30000000
χ4522-222220-2-2-2000022-2200-200-220000000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i301−i31−i31−i30000−1+i3−1+i31−i3−1+i3001−i3001−i3−1+i30000000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i301+i31+i31+i30000−1−i3−1−i31+i3−1−i3001+i3001+i3−1−i30000000
χ4622-222220-2-2-20000-2-2002i−2i200002i−2i00000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i301−i31−i31−i300001−i31−i3002ζ14−2ζ14−1+i300002ζ14−2ζ1400000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i301+i31+i31+i300001+i31+i3002ζ22−2ζ22−1−i300002ζ22−2ζ2200000
χ4722-222220-2-2-20000-2-200−2i2i20000−2i2i00000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i301−i31−i31−i300001−i31−i300−2ζ142ζ14−1+i30000−2ζ142ζ1400000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i301+i31+i31+i300001+i31+i300−2ζ222ζ22−1−i30000−2ζ222ζ2200000
χ484441-2-214-2-21-2-21100000002200000-1-100−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i32−2+2i31−i31−i3−1+i321−i31−i3−1+i32−1+i320000000−1+i3−1+i3000001−i321−i3200−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i32−2−2i31+i31+i3−1−i321+i31+i3−1−i32−1−i320000000−1−i3−1−i3000001+i321+i3200
χ494441-2-214-2-21-2-2110000000-2-2000001100−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i32−2+2i31−i31−i3−1+i321−i31−i3−1+i32−1+i3200000001−i31−i300000−1+i32−1+i3200−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i32−2−2i31+i31+i3−1−i321+i31+i3−1−i32−1−i3200000001+i31+i300000−1−i32−1−i3200
χ504441-2-21-4-2-2122-1-100000002-200000-1100−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i322−2i31−i31−i3−1+i32−1+i3−1+i31−i321−i320000000−1+i31−i3000001−i32−1+i3200−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i322+2i31+i31+i3−1−i32−1−i3−1−i31+i321+i320000000−1−i31+i3000001+i32−1−i3200
χ514441-2-21-4-2-2122-1-10000000-22000001-100−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i322−2i31−i31−i3−1+i32−1+i3−1+i31−i321−i3200000001−i3−1+i300000−1+i321−i3200−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i322+2i31+i31+i3−1−i32−1−i3−1−i31+i321+i3200000001+i3−1−i300000−1−i321+i3200
χ52444-211-2411-211-2-2002222000-1-1-1-100000−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i3−2+2i3−1+i32−1+i321−i3−1+i32−1+i321−i31−i300−1+i3−1+i3−1+i3−1+i30001−i321−i321−i321−i3200000−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i3−2−2i3−1−i32−1−i321+i3−1−i32−1−i321+i31+i300−1−i3−1−i3−1−i3−1−i30001+i321+i321+i321+i3200000
χ53444-211-2411-211-2-200-2-2-2-2000111100000−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i3−2+2i3−1+i32−1+i321−i3−1+i32−1+i321−i31−i3001−i31−i31−i31−i3000−1+i32−1+i32−1+i32−1+i3200000−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i3−2−2i3−1−i32−1−i321+i3−1−i32−1−i321+i31+i3001+i31+i31+i31+i3000−1−i32−1−i32−1−i32−1−i3200000
χ54444-211-2-411-2-1-1220022-2-2000-1-11100000−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i32−2i3−1+i32−1+i321−i31−i321−i32−1+i3−1+i300−1+i3−1+i31−i31−i30001−i321−i32−1+i32−1+i3200000−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i32+2i3−1−i32−1−i321+i31+i321+i32−1−i3−1−i300−1−i3−1−i31+i31+i30001+i321+i32−1−i32−1−i3200000
χ55444-211-2-411-2-1-12200-2-22200011-1-100000−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i32−2i3−1+i32−1+i321−i31−i321−i32−1+i3−1+i3001−i31−i3−1+i3−1+i3000−1+i32−1+i321−i321−i3200000−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i32+2i3−1−i32−1−i321+i31+i321+i32−1−i3−1−i3001+i31+i3−1−i3−1−i3000−1−i32−1−i321+i321+i3200000
χ5644-4-211-20-1-123i−3i00002-22i−2i000-11−ii00000−2+2i3−2+2i32−2i31−i3−1+i32−1+i321−i301−i321−i32−1+i33ζ14−3ζ140000−1+i31−i32ζ14−2ζ140001−i32−1+i32−ζ14ζ1400000−2−2i3−2−2i32+2i31+i3−1−i32−1−i321+i301+i321+i32−1−i33ζ22−3ζ220000−1−i31+i32ζ22−2ζ220001+i32−1−i32−ζ22ζ2200000
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χ944-4044-4-400000000-440000000000000000−2−2i32+2i30−2−2i3−2−2i32+2i32+2i3000000002+2i3−2−2i30000000000000000−2+2i32−2i30−2+2i3−2+2i32−2i32−2i3000000002−2i3−2+2i30000000000000000
χ9588-82-4-42044-20000000000000000000000−4−4i3−4−4i34+4i3−1−i32+2i32+2i3−1−i30−2−2i3−2−2i31+i30000000000000000000000−4+4i3−4+4i34−4i3−1+i32−2i32−2i3−1+i30−2+2i3−2+2i31−i30000000000000000000000
χ968-802-44-200000032−32000000000000000000−4−4i34+4i30−1−i32+2i3−2−2i31+i3000000−3ζ7+3ζ133ζ7−3ζ13000000000000000000−4+4i34−4i30−1+i32−2i3−2+2i31−i30000003ζ5−3ζ23−3ζ5+3ζ23000000000000000000
χ978-802-44-2000000−3232000000000000000000−4−4i34+4i30−1−i32+2i3−2−2i31+i30000003ζ7−3ζ13−3ζ7+3ζ13000000000000000000−4+4i34−4i30−1+i32−2i3−2+2i31−i3000000−3ζ5+3ζ233ζ5−3ζ23000000000000000000
χ988-80-42-2406i−6i00000000000000000000000−4−4i34+4i302+2i3−1−i31+i3−2−2i306ζ22−6ζ2200000000000000000000000−4+4i34−4i302−2i3−1+i31−i3−2+2i306ζ14−6ζ1400000000000000000000000
χ998-80-42-240−6i6i00000000000000000000000−4−4i34+4i302+2i3−1−i31+i3−2−2i30−6ζ226ζ2200000000000000000000000−4+4i34−4i302−2i3−1+i31−i3−2+2i30−6ζ146ζ1400000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.