Finite Group Databasebeta

← Group #13172167

Character table — Group #13172167

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122233366666666623336666666666644443666666666666666444412121212121212121212121212121212226666121212121212121212121212121212122244466661212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111111111-1-111-1-11111111-1-1111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-1111111-1-1-1-111-1-111-1-1-1-1-1-1-11111111-1-1-1-11111-1-11-11-1-1-1-1111-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1111
χ51111111111111111111111111111111-1-111111111111111111111-11-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-111111111-11-11-111-1-1-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-1111-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-11111-1-111-1-11111-1-1111111-11-1-111-1-111-1-111-1-1-1-1-111-1-1-1-111-111-1
χ101111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-11111-1-111-1-1-1-11111111111-1-11-111-1-111-1-1-1-111-111-1-111-1-1-1-11-1-11
χ111111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-11111111-1-1-11
χ121111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-11-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-11-111-1-1-1-111-1-1111-111-1-1-111-1-1111-1
χ131111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-11-1-11111-1-111-1-11-111-1-1-111-1-111-11
χ141111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111111-1-11-1
χ151111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-111-1-1-1-111-1-11111-1-1-1-111111111-11-1-111-1-11111-1-1-111-1-111-1-1-1-11-11-1
χ161111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-1111111111-111-1-111-1-111-1-111-1-1-111-1-1-1-111-11-11
χ17222222-1-1222-1-122222-1-1-1-12-1-122-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1-1-1002222-1-1-1-1-1-1-1-100220022-1-1-1-12002-1-1-1-1-1-1-1-100002000000-1-1000000
χ18222222-1-1222-1-122222-1-1-1-12-1-122-1-1-1-122-2-2-12222-1-1-1-1-1-1-1-1-1-1-1002-222-1-1-1-1111100-2-200-2-21111-2002-1-1-1-111110000-200000011000000
χ19222222-1-1222-1-122222-1-1-1-12-1-122-1-1-1-1-2-222-12222-1-1-1-1-1-1-1-1-1-1-100-22-2-21111-1-1-1-1002200-2-21111200-21111-1-1-1-10000-200000011000000
χ20222222-1-1222-1-122222-1-1-1-12-1-122-1-1-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-100-2-2-2-21111111100-2-20022-1-1-1-1-200-21111111100002000000-1-1000000
χ21222222-1-1222-1-1222-22-1-1112-1-122-1-1-1-12222-1-2-2-2-21111-1-1-1111100-2-222-1-111-1-11100220022-1-1-1-1-200-2-1-111-1-1110000-200000011000000
χ22222222-1-1222-1-1222-22-1-1112-1-122-1-1-1-122-2-2-1-2-2-2-21111-1-1-1111100-2222-1-11111-1-100-2-200-2-21111200-2-1-11111-1-100002000000-1-1000000
χ23222222-1-1222-1-1222-22-1-1112-1-122-1-1-1-1-2-222-1-2-2-2-21111-1-1-11111002-2-2-211-1-1-1-111002200-2-21111-200211-1-1-1-11100002000000-1-1000000
χ24222222-1-1222-1-1222-22-1-1112-1-122-1-1-1-1-2-2-2-2-1-2-2-2-21111-1-1-111110022-2-211-1-111-1-100-2-20022-1-1-1-1200211-1-111-1-10000-200000011000000
χ2522222-122-1-122222-12-12-122-12-1-1-122-1-10022-12-1-1-122-1-1-1-1-1-1-1-1-12202000000222222-1-1-1-1000000-1-1200000-1-1-1-1-1-1-1-102020-1-100000-100
χ2622222-122-1-122222-12-12-122-12-1-1-122-1-10022-12-1-1-122-1-1-1-1-1-1-1-1-1-2-2020000002222-2-2-1-111000000-11-200000-1-1-1-111110-20-201100000100
χ2722222-122-1-122222-12-12-122-12-1-1-122-1-100-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1220-2000000-2-2-2-22211-1-10000001-12000001111-1-1-1-10-20-201100000100
χ2822222-122-1-122222-12-12-122-12-1-1-122-1-100-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1-2-20-2000000-2-2-2-2-2-2111100000011-2000001111111102020-1-100000-100
χ2922222-122-1-122222-1-2-12-1-2-2-12-1-1-122-1-10022-1-2111-2-211-1-1-111112-20-200000022-2-222-1-1110000001-1-200000-1-111-1-1110-20201100000-100
χ3022222-122-1-122222-1-2-12-1-2-2-12-1-1-122-1-10022-1-2111-2-211-1-1-11111-220-200000022-2-2-2-2-1-1-1-100000011200000-1-11111-1-1020-20-1-100000100
χ3122222-122-1-122222-1-2-12-1-2-2-12-1-1-122-1-100-2-2-1-2111-2-211-1-1-111112-202000000-2-222221111000000-1-1-20000011-1-1-1-111020-20-1-100000100
χ3222222-122-1-122222-1-2-12-1-2-2-12-1-1-122-1-100-2-2-1-2111-2-211-1-1-11111-2202000000-2-222-2-211-1-1000000-1120000011-1-111-1-10-20201100000-100
χ332222-122222-122-1-122-1-1222-1-12-1-1-1-1222200-1-12-1-1-1-122-1-1-1-1-1-1-12220-1-122220000-1-1002200000002-1-1-1-1-1-10000-1-1-1-1002020000-1-1-1000
χ342222-122222-122-1-122-1-1222-1-12-1-1-1-1222200-1-12-1-1-1-122-1-1-1-1-1-1-1-2-220-1-1222200001100-2-20000000-21-1-1-1-1-10000111100-20-20000111000
χ352222-122222-122-1-122-1-1222-1-12-1-1-1-122-2-200-1-12-1-1-1-122-1-1-1-1-1-1-122-2011-2-2-2-20000-1-1002200000002-1111110000-1-1-1-100-20-20000111000
χ362222-122222-122-1-122-1-1222-1-12-1-1-1-122-2-200-1-12-1-1-1-122-1-1-1-1-1-1-1-2-2-2011-2-2-2-200001100-2-20000000-211111100001111002020000-1-1-1000
χ372222-122222-122-1-12-2-1-12-2-2-1-12-1-1-1-1222200-11-21111-2-2-1-1-111112-2-20-1-122-2-20000-1-100-2-20000000211-1-1110000-1-11100-2020000-1-11000
χ382222-122222-122-1-12-2-1-12-2-2-1-12-1-1-1-1222200-11-21111-2-2-1-1-11111-22-20-1-122-2-200001100220000000-2-11-1-111000011-1-10020-2000011-1000
χ392222-122222-122-1-12-2-1-12-2-2-1-12-1-1-1-122-2-200-11-21111-2-2-1-1-111112-22011-2-2220000-1-100-2-2000000021-111-1-10000-1-1110020-2000011-1000
χ402222-122222-122-1-12-2-1-12-2-2-1-12-1-1-1-122-2-200-11-21111-2-2-1-1-11111-222011-2-22200001100220000000-2-1-111-1-1000011-1-100-2020000-1-11000
χ4122-2-222222-2-2-2-22-2-2022200-2222-2-2-2-2-22i−2i2i−2i2000000002-2-2000000002i−2i2i−2i002i−2i00002i−2i002-222-2-200002i−2i002i−2i000000000000000000000
χ4222-2-222222-2-2-2-22-2-2022200-2222-2-2-2-2-22i−2i−2i2i2000000002-2-2000000002i−2i2i−2i00−2i2i0000−2i2i00-22-2-22200002i−2i00−2i2i000000000000000000000
χ4322-2-222222-2-2-2-22-2-2022200-2222-2-2-2-2-2−2i2i2i−2i2000000002-2-200000000−2i2i−2i2i002i−2i00002i−2i00-22-2-2220000−2i2i002i−2i000000000000000000000
χ4422-2-222222-2-2-2-22-2-2022200-2222-2-2-2-2-2−2i2i−2i2i2000000002-2-200000000−2i2i−2i2i00−2i2i0000−2i2i002-222-2-20000−2i2i00−2i2i000000000000000000000
χ4522-2-222-1-12-2-2112-2-202-1-1−i3i3-2-1-12-211112i−2i2i−2i-10000−i3i3−i3i3-111−i3−i3i3i300002i−2i−ii3−3−ii3−3002i−2i002-2-1-1110000−ii3−3−ii3−300000000000−i3i3000000
χ4622-2-222-1-12-2-2112-2-202-1-1−i3i3-2-1-12-211112i−2i−2i2i-10000−i3i3−i3i3-111−i3−i3i3i300002i−2i−ii3−3i−i−3300−2i2i00-2211-1-10000−ii3−3i−i−3300000000000i3−i3000000
χ4722-2-222-1-12-2-2112-2-202-1-1−i3i3-2-1-12-21111−2i2i2i−2i-10000−i3i3−i3i3-111−i3−i3i3i30000−2i2ii−i−33−ii3−3002i−2i00-2211-1-10000i−i−33−ii3−300000000000i3−i3000000
χ4822-2-222-1-12-2-2112-2-202-1-1−i3i3-2-1-12-21111−2i2i−2i2i-10000−i3i3−i3i3-111−i3−i3i3i30000−2i2ii−i−33i−i−3300−2i2i002-2-1-1110000i−i−33i−i−3300000000000−i3i3000000
χ4922-2-222-1-12-2-2112-2-202-1-1i3−i3-2-1-12-211112i−2i2i−2i-10000i3−i3i3−i3-111i3i3−i3−i300002i−2i−ii−33−ii−33002i−2i002-2-1-1110000−ii−33−ii−3300000000000i3−i3000000
χ5022-2-222-1-12-2-2112-2-202-1-1i3−i3-2-1-12-211112i−2i−2i2i-10000i3−i3i3−i3-111i3i3−i3−i300002i−2i−ii−33i−i3−300−2i2i00-2211-1-10000−ii−33i−i3−300000000000−i3i3000000
χ5122-2-222-1-12-2-2112-2-202-1-1i3−i3-2-1-12-21111−2i2i2i−2i-10000i3−i3i3−i3-111i3i3−i3−i30000−2i2ii−i3−3−ii−33002i−2i00-2211-1-10000i−i3−3−ii−3300000000000−i3i3000000
χ5222-2-222-1-12-2-2112-2-202-1-1i3−i3-2-1-12-21111−2i2i−2i2i-10000i3−i3i3−i3-111i3i3−i3−i30000−2i2ii−i3−3i−i3−300−2i2i002-2-1-1110000i−i3−3i−i3−300000000000i3−i3000000
χ5344444-2-2-2-2-24-2-244-24-2-21-2-2-2-21-2-2-2-211004414-2-2-2-2-21111111110004000000-2-2-2-200-2-200000000-2000000011110000000000000000000
χ5444444-2-2-2-2-24-2-244-24-2-21-2-2-2-21-2-2-2-21100-4-414-2-2-2-2-2111111111000-4000000222200220000000020000000-1-1-1-10000000000000000000
χ5544444-2-2-2-2-24-2-244-2-4-2-2122-2-21-2-2-2-21100441-422222-1-1111-1-1-1-1000-4000000-2-22200-2-2000000002000000011-1-10000000000000000000
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χ594444-24-2-244-2-2-2-2-24-4-21-222-21-2-2-211-2-2440012-422-1-122111-1-1-1-100-40-2-2-2-2220000000000000000000211-1-100000000000000000000000
χ604444-24-2-244-2-2-2-2-24-4-21-222-21-2-2-211-2-2-4-40012-422-1-122111-1-1-1-100402222-2-20000000000000000000-2-1-11100000000000000000000000
χ614444-2-244-2-2-244-2-2-241-2-2441-2-211-2-2-2-200001-2-211-2-2-2-2111111144000000000000-2-200-2-20000000-2-20000000001111000000000000000
χ624444-2-244-2-2-244-2-2-241-2-2441-2-211-2-2-2-200001-2-211-2-2-2-21111111-4-4000000000000220022000000022000000000-1-1-1-1000000000000000
χ634444-2-244-2-2-244-2-2-2-41-2-2-4-41-2-211-2-2-2-20000122-1-12222111-1-1-1-14-4000000000000-2-200220000000-2200000000011-1-1000000000000000
χ644444-2-244-2-2-244-2-2-2-41-2-2-4-41-2-211-2-2-2-20000122-1-12222111-1-1-1-1-440000000000002200-2-200000002-2000000000-1-111000000000000000
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χ774-44-4444-4-4-444-4-4-44044400-4-4-4-444-44-40000400000000-44-40000000000000000000000000000000000000000000000000000000000000
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χ804-44-44-24-42244-4-4-4-20-24-2002-422-24-4-220000-2000000002-22000000000000000000000000000000000000000000000000000−2i32i300000000
χ814-44-44-24-42244-4-4-4-20-24-2002-422-24-4-220000-2000000002-220000000000000000000000000000000000000000000000000002i3−2i300000000
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χ894-4-44-244-4-442-442-2-40-2-2400-22-4222-2-440000-20000000022-200000000000000000023−23000000000000000000000023−2300000000000000000
χ904-4-44-244-4-442-442-2-40-2-2400-22-4222-2-440000-20000000022-2000000000000000000−23230000000000000000000000−232300000000000000000
χ914-4-44-2-24-42-22-442-2201-2-200122-1-12-22-200001003-30000-1-113-33-30000000000000023−230023−23000000000000000000−33−33000000000000000
χ924-4-44-2-24-42-22-442-2201-2-200122-1-12-22-200001003-30000-1-113-33-300000000000000−232300−23230000000000000000003−33−3000000000000000
χ934-4-44-2-24-42-22-442-2201-2-200122-1-12-22-20000100-330000-1-11-33-330000000000000023−2300−2323000000000000000000−333−3000000000000000
χ944-4-44-2-24-42-22-442-2201-2-200122-1-12-22-20000100-330000-1-11-33-3300000000000000−23230023−230000000000000000003−3−33000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-48222-4-42222222220000-1-4-4222222-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4-8222442222222220000-144-2-2-2-2-2-2-1-1-11111000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-488-444-8-8-44402-4-400-2-4-42-2444400002000000002-2-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-4-4-44444-4440222−4i34i3-2222-2-2-2-2-20000-100002i3−2i32i3−2i3-111−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4-4-44444-44402224i3−4i3-2222-2-2-2-2-20000-10000−2i32i3−2i32i3-111i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1008-88-88-4-44448-44-8-8-40-4-420044-24-4-442-20000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-44-8-8-4-444480-42-4004-244-42-2-440000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-48-844-48-844-402-4-400-244-22-44-440000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4444-4-4444-4022200-2-2-2-222-22-20000-1000000001-11−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4444-4-4444-4022200-2-2-2-222-22-20000-1000000001-113i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000
χ1058-8-888-4-444-4-84-4-8840-4-4200-44-2444-4-220000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-44-8844-44-4-80-42-400-4-2444-224-40000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444-444-44-440222002-2-2-2-2-22-220000-1006-6000011-1-33-33000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444-444-44-440222002-2-2-2-2-22-220000-100-66000011-13-33-3000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).