Finite Group Databasebeta

← Group #13166672

Character table — Group #13166672

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112444444488888121212121818181824242424242448487272112444444488888121212121818181824242424242448487272112444444488888121212121818181824242424242448487272
order12433668121212242424242488248822612242466883612336624121212242424246122424612242466612242466242436123366241212122424242461224246122424666122424662424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-11111-1-1-1-111111111111111111111111-1-11111-1-1-1-111111111111111111111111-1-11111-1-1-1-1
χ3111111111111111-1-1-1-1111111-1-1-1-111-1-1111111111111111-1-1-1-1111111-1-1-1-111-1-1111111111111111-1-1-1-1111111-1-1-1-111-1-1
χ4111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111-1111-1-1-1-111-1-111-1-11-111-1-11-11-11111111-1111-1-1-1-111-1-111-1-11-111-1-11-11-11111111-1111-1-1-1-111-1-111-1-11-111-1-11-11-1
χ61111111-1111-1-1-1-111-1-111-1-1-1111-1-1-11-111111111-1111-1-1-1-111-1-111-1-1-1111-1-1-11-111111111-1111-1-1-1-111-1-111-1-1-1111-1-1-11-11
χ71111111-1111-1-1-1-1-1-11111-1-11-1-1-1111-1-111111111-1111-1-1-1-1-1-11111-1-11-1-1-1111-1-111111111-1111-1-1-1-1-1-11111-1-11-1-1-1111-1-11
χ81111111-1111-1-1-1-1-1-11111-1-1-11-1-111-111-11111111-1111-1-1-1-1-1-11111-1-1-11-1-111-111-11111111-1111-1-1-1-1-1-11111-1-1-11-1-111-111-1
χ92222222222222220000-2-2-2-200000000002222222222222220000-2-2-2-200000000002222222222222220000-2-2-2-20000000000
χ102222222-2222-2-2-2-20000-2-22200000000002222222-2222-2-2-2-20000-2-22200000000002222222-2222-2-2-2-20000-2-2220000000000
χ1122-222220-2-2-20000002i−2i2-20000002i−2i000022-222220-2-2-20000002i−2i2-20000002i−2i000022-222220-2-2-20000002i−2i2-20000002i−2i0000
χ1222-222220-2-2-2000000−2i2i2-2000000−2i2i000022-222220-2-2-2000000−2i2i2-2000000−2i2i000022-222220-2-2-2000000−2i2i2-2000000−2i2i0000
χ1322-222220-2-2-200002-200-2200002-200000022-222220-2-2-200002-200-2200002-200000022-222220-2-2-200002-200-2200002-2000000
χ1422-222220-2-2-20000-2200-220000-2200000022-222220-2-2-20000-2200-220000-2200000022-222220-2-2-20000-2200-220000-22000000
χ154441-2-21411-211-2-22222000000-1-1-1-100004441-2-21411-211-2-22222000000-1-1-1-100004441-2-21411-211-2-22222000000-1-1-1-10000
χ164441-2-21411-211-2-2-2-2-2-2000000111100004441-2-21411-211-2-2-2-2-2-2000000111100004441-2-21411-211-2-2-2-2-2-200000011110000
χ174441-2-21-411-2-1-12222-2-2000000-1-11100004441-2-21-411-2-1-12222-2-2000000-1-11100004441-2-21-411-2-1-12222-2-2000000-1-1110000
χ184441-2-21-411-2-1-122-2-22200000011-1-100004441-2-21-411-2-1-122-2-22200000011-1-100004441-2-21-411-2-1-122-2-22200000011-1-10000
χ19444-211-24-2-21-2-21100000000220000-1-100444-211-24-2-21-2-21100000000220000-1-100444-211-24-2-21-2-21100000000220000-1-100
χ20444-211-24-2-21-2-21100000000-2-200001100444-211-24-2-21-2-21100000000-2-200001100444-211-24-2-21-2-21100000000-2-200001100
χ21444-211-2-4-2-2122-1-1000000002-20000-1100444-211-2-4-2-2122-1-1000000002-20000-1100444-211-2-4-2-2122-1-1000000002-20000-1100
χ22444-211-2-4-2-2122-1-100000000-2200001-100444-211-2-4-2-2122-1-100000000-2200001-100444-211-2-4-2-2122-1-100000000-2200001-100
χ2344-41-2-210-1-123i−3i002-22i−2i000000-11−ii000044-41-2-210-1-123i−3i002-22i−2i000000-11−ii000044-41-2-210-1-123i−3i002-22i−2i000000-11−ii0000
χ2444-41-2-210-1-123i−3i00-22−2i2i0000001-1i−i000044-41-2-210-1-123i−3i00-22−2i2i0000001-1i−i000044-41-2-210-1-123i−3i00-22−2i2i0000001-1i−i0000
χ2544-41-2-210-1-12−3i3i002-2−2i2i000000-11i−i000044-41-2-210-1-12−3i3i002-2−2i2i000000-11i−i000044-41-2-210-1-12−3i3i002-2−2i2i000000-11i−i0000
χ2644-41-2-210-1-12−3i3i00-222i−2i0000001-1−ii000044-41-2-210-1-12−3i3i00-222i−2i0000001-1−ii000044-41-2-210-1-12−3i3i00-222i−2i0000001-1−ii0000
χ274-4044-4-40000000000000022−2200000000004-4044-4-40000000000000022−2200000000004-4044-4-40000000000000022−220000000000
χ284-4044-4-400000000000000−222200000000004-4044-4-400000000000000−222200000000004-4044-4-400000000000000−22220000000000
χ2988-8-422-4044-2000000000000000000000088-8-422-4044-2000000000000000000000088-8-422-4044-20000000000000000000000
χ308-802-44-206i−6i000000000000000000000008-802-44-206i−6i000000000000000000000008-802-44-206i−6i00000000000000000000000
χ318-802-44-20−6i6i000000000000000000000008-802-44-20−6i6i000000000000000000000008-802-44-20−6i6i00000000000000000000000
χ328-80-42-2400000032−320000000000000000008-80-42-2400000032−320000000000000000008-80-42-2400000032−32000000000000000000
χ338-80-42-24000000−32320000000000000000008-80-42-24000000−32320000000000000000008-80-42-24000000−3232000000000000000000
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
χ3511111111111111111111111-1-11111-1-1-1-1−1+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+i321−i321−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ36111111111111111-1-1-1-1111111-1-1-1-111-1-1−1+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+i321−i321−i321−i321−i32−1+i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ37111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111−1+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ381111111-1111-1-1-1-111-1-111-1-11-111-1-11-11-1−1+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+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−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−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32
χ391111111-1111-1-1-1-111-1-111-1-1-1111-1-1-11-11−1+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+i321−i321−i32−1+i32−1+i321−i321−i321−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−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32
χ401111111-1111-1-1-1-1-1-11111-1-11-1-1-1111-1-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+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−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ411111111-1111-1-1-1-1-1-11111-1-1-11-1-111-111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+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+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ422222222222222220000-2-2-2-20000000000−1+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+i300001−i31−i31−i31−i30000000000−1−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−i300001+i31+i31+i31+i30000000000
χ432222222-2222-2-2-2-20000-2-2220000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i31−i31−i31−i31−i300001−i31−i3−1+i3−1+i30000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i31+i31+i31+i31+i300001+i31+i3−1−i3−1−i30000000000
χ4422-222220-2-2-20000002i−2i2-20000002i−2i0000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i301−i31−i31−i30000002ζ14−2ζ14−1+i31−i30000002ζ14−2ζ140000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i301+i31+i31+i30000002ζ22−2ζ22−1−i31+i30000002ζ22−2ζ220000
χ4522-222220-2-2-2000000−2i2i2-2000000−2i2i0000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i301−i31−i31−i3000000−2ζ142ζ14−1+i31−i3000000−2ζ142ζ140000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i301+i31+i31+i3000000−2ζ222ζ22−1−i31+i3000000−2ζ222ζ220000
χ4622-222220-2-2-200002-200-2200002-2000000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i301−i31−i31−i30000−1+i31−i3001−i3−1+i30000−1+i31−i3000000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i301+i31+i31+i30000−1−i31+i3001+i3−1−i30000−1−i31+i3000000
χ4722-222220-2-2-20000-2200-220000-22000000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i301−i31−i31−i300001−i3−1+i3001−i3−1+i300001−i3−1+i3000000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i301+i31+i31+i300001+i3−1−i3001+i3−1−i300001+i3−1−i3000000
χ484441-2-21411-211-2-22222000000-1-1-1-10000−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i32−2+2i3−1+i32−1+i321−i3−1+i32−1+i321−i31−i3−1+i3−1+i3−1+i3−1+i30000001−i321−i321−i321−i320000−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i32−2−2i3−1−i32−1−i321+i3−1−i32−1−i321+i31+i3−1−i3−1−i3−1−i3−1−i30000001+i321+i321+i321+i320000
χ494441-2-21411-211-2-2-2-2-2-200000011110000−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i32−2+2i3−1+i32−1+i321−i3−1+i32−1+i321−i31−i31−i31−i31−i31−i3000000−1+i32−1+i32−1+i32−1+i320000−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i32−2−2i3−1−i32−1−i321+i3−1−i32−1−i321+i31+i31+i31+i31+i31+i3000000−1−i32−1−i32−1−i32−1−i320000
χ504441-2-21-411-2-1-12222-2-2000000-1-1110000−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i322−2i3−1+i32−1+i321−i31−i321−i32−1+i3−1+i3−1+i3−1+i31−i31−i30000001−i321−i32−1+i32−1+i320000−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i322+2i3−1−i32−1−i321+i31+i321+i32−1−i3−1−i3−1−i3−1−i31+i31+i30000001+i321+i32−1−i32−1−i320000
χ514441-2-21-411-2-1-122-2-22200000011-1-10000−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i322−2i3−1+i32−1+i321−i31−i321−i32−1+i3−1+i31−i31−i3−1+i3−1+i3000000−1+i32−1+i321−i321−i320000−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i322+2i3−1−i32−1−i321+i31+i321+i32−1−i3−1−i31+i31+i3−1−i3−1−i3000000−1−i32−1−i321+i321+i320000
χ52444-211-24-2-21-2-21100000000220000-1-100−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i3−2+2i31−i31−i3−1+i321−i31−i3−1+i32−1+i3200000000−1+i3−1+i300001−i321−i3200−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i3−2−2i31+i31+i3−1−i321+i31+i3−1−i32−1−i3200000000−1−i3−1−i300001+i321+i3200
χ53444-211-24-2-21-2-21100000000-2-200001100−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i3−2+2i31−i31−i3−1+i321−i31−i3−1+i32−1+i32000000001−i31−i30000−1+i32−1+i3200−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i3−2−2i31+i31+i3−1−i321+i31+i3−1−i32−1−i32000000001+i31+i30000−1−i32−1−i3200
χ54444-211-2-4-2-2122-1-1000000002-20000-1100−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i32−2i31−i31−i3−1+i32−1+i3−1+i31−i321−i3200000000−1+i31−i300001−i32−1+i3200−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i32+2i31+i31+i3−1−i32−1−i3−1−i31+i321+i3200000000−1−i31+i300001+i32−1−i3200
χ55444-211-2-4-2-2122-1-100000000-2200001-100−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i32−2i31−i31−i3−1+i32−1+i3−1+i31−i321−i32000000001−i3−1+i30000−1+i321−i3200−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i32+2i31+i31+i3−1−i32−1−i3−1−i31+i321+i32000000001+i3−1−i30000−1−i321+i3200
χ5644-41-2-210-1-123i−3i002-22i−2i000000-11−ii0000−2+2i3−2+2i32−2i3−1+i321−i31−i3−1+i3201−i321−i32−1+i33ζ14−3ζ1400−1+i31−i32ζ14−2ζ140000001−i32−1+i32−ζ14ζ140000−2−2i3−2−2i32+2i3−1−i321+i31+i3−1−i3201+i321+i32−1−i33ζ22−3ζ2200−1−i31+i32ζ22−2ζ220000001+i32−1−i32−ζ22ζ220000
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χ944-4044-4-400000000000000−22220000000000−2−2i32+2i30−2−2i3−2−2i32+2i32+2i3000000000000002ζ7−2ζ13−2ζ7+2ζ130000000000−2+2i32−2i30−2+2i3−2+2i32−2i32−2i300000000000000−2ζ5+2ζ232ζ5−2ζ230000000000
χ9588-8-422-4044-20000000000000000000000−4−4i3−4−4i34+4i32+2i3−1−i3−1−i32+2i30−2−2i3−2−2i31+i30000000000000000000000−4+4i3−4+4i34−4i32−2i3−1+i3−1+i32−2i30−2+2i3−2+2i31−i30000000000000000000000
χ968-802-44-206i−6i00000000000000000000000−4−4i34+4i30−1−i32+2i3−2−2i31+i306ζ22−6ζ2200000000000000000000000−4+4i34−4i30−1+i32−2i3−2+2i31−i306ζ14−6ζ1400000000000000000000000
χ978-802-44-20−6i6i00000000000000000000000−4−4i34+4i30−1−i32+2i3−2−2i31+i30−6ζ226ζ2200000000000000000000000−4+4i34−4i30−1+i32−2i3−2+2i31−i30−6ζ146ζ1400000000000000000000000
χ988-80-42-2400000032−32000000000000000000−4−4i34+4i302+2i3−1−i31+i3−2−2i3000000−3ζ7+3ζ133ζ7−3ζ13000000000000000000−4+4i34−4i302−2i3−1+i31−i3−2+2i30000003ζ5−3ζ23−3ζ5+3ζ23000000000000000000
χ998-80-42-24000000−3232000000000000000000−4−4i34+4i302+2i3−1−i31+i3−2−2i30000003ζ7−3ζ13−3ζ7+3ζ13000000000000000000−4+4i34−4i302−2i3−1+i31−i3−2+2i3000000−3ζ5+3ζ233ζ5−3ζ23000000000000000000

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