Finite Group Databasebeta

← Group #13168627

Character table — Group #13168627

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order122233366666666633346666666661212444436661212121212121212121212122444661212121212121212121212121212224444441212121266612121212121212121212121212446612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-11-1-11111111111-1-11111-1-111-1-11111-1-1-111-1-1-111111111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111-111111111-1-1-1-1-11-1-1-1-1111-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-11-1-1-111-1-1-1111
χ51111111111111111111111111111111-1-11111111111111111111-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1111-1-1-1-111111-1-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-11-1-1-1-1111-111
χ71111111111111111111111111111111-1-1-1-111111111111111111-11-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-111-1-11-111-1-111-11-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-111-1-1-111111-1-11-11-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-111-1-111-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-11-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-11-111111-1-1-1-11111-1-1-1-1-1-111-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111111-11-1-1-1-1-11111-1-111-1-1-1-1-1-1111-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-1-111-1-111-111111-1-11-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-111-1-111-111-1
χ17222222-122-1-122-122-1-122-1-12-1-122-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1020200-1-1-1-122-1-1-1-1002222002200-1-1-1-100022000-1-1-1-1-1-1-1-100-1-100000000
χ18222222-122-1-122-122-1-122-1-12-1-122-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-1020-200-1-1-1-1-2-211110022-2-200-2-2001111000-22000-1-1-1-11111001100000000
χ19222222-122-1-122-122-1-122-1-12-1-122-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-10-20200111122-1-1-1-100-2-2-2-200-2-20011110002-20001111-1-1-1-1001100000000
χ20222222-122-1-122-122-1-122-1-12-1-122-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-20-2001111-2-2111100-2-222002200-1-1-1-1000-2-20001111111100-1-100000000
χ21222222-122-1-122-122-1-12-2-1-12-1-122-1-1112222-1-1-1-1-2-2-2-2111111110-20-200-1-11122-1-11100222200-2-2001111000-2-2000-1-111-1-11100-1-100000000
χ22222222-122-1-122-122-1-12-2-1-12-1-122-1-11122-2-2-1-1-1-1-2-2-2-2111111110-20200-1-111-2-211-1-10022-2-2002200-1-1-1-10002-2000-1-11111-1-1001100000000
χ23222222-122-1-122-122-1-12-2-1-12-1-122-1-111-2-222-1-1-1-1-2-2-2-211111111020-20011-1-122-1-11100-2-2-2-2002200-1-1-1-1000-2200011-1-1-1-111001100000000
χ24222222-122-1-122-122-1-12-2-1-12-1-122-1-111-2-2-2-2-1-1-1-1-2-2-2-21111111102020011-1-1-2-211-1-100-2-22200-2-20011110002200011-1-111-1-100-1-100000000
χ2522222-122-1222-12-122-1-122-1-12-1-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-12022220000-1-12222-1-100000000220000-1-1-1-102-1-10000-1-1-1-12000-1-1000-100
χ2622222-122-1222-12-122-1-122-1-12-1-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-1-20-22-2-20000-1-122221100000000-2-20000111-10-2110000-1-1-1-1-200011000100
χ2722222-122-1222-12-122-1-122-1-12-1-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1202-222000011-2-2-2-2-1-100000000-2-20000-1-1-1102-1-100001111-200011000100
χ2822222-122-1222-12-122-1-122-1-12-1-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20-2-2-2-2000011-2-2-2-2110000000022000011110-211000011112000-1-1000-100
χ2922222-122-1222-12-122-1-1-22-1-12-1-1-12-1-2-20022-1-1-1-1-2111-2-211111120-2-2220000-1-122-2-21100000000-2-20000-1-1-110-2110000-1-111200011000-100
χ3022222-122-1222-12-122-1-1-22-1-12-1-1-12-1-2-20022-1-1-1-1-2111-2-2111111-202-2-2-20000-1-122-2-2-1-100000000220000111102-1-10000-1-111-2000-1-1000100
χ3122222-122-1222-12-122-1-1-22-1-12-1-1-12-1-2-200-2-2-1-1-1-1-2111-2-211111120-2222000011-2-2221100000000220000-1-1-1-10-211000011-1-1-2000-1-1000100
χ3222222-122-1222-12-122-1-1-22-1-12-1-1-12-1-2-200-2-2-1-1-1-1-2111-2-2111111-2022-2-2000011-2-222-1-100000000-2-20000111-102-1-1000011-1-1200011000-100
χ332222-122-1222-1222-1-12-12-12-1-12-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-12220-1-1222200000022-1-10022000000002-1-10-1-1-1-1-1-1-1-10000020000-1-1-1000
χ342222-122-1222-1222-1-12-12-12-1-12-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1-22-20112222000000-2-2-1-100-2-200000000-2110-1111-1-1-1-100000-20000111000
χ352222-122-1222-1222-1-12-12-12-1-12-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-12-220-1-1-2-2-2-2000000221100-2-2000000002-1-101-1-1-1111100000-20000111000
χ362222-122-1222-1222-1-12-12-12-1-12-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-2011-2-2-2-2000000-2-211002200000000-2110111111110000020000-1-1-1000
χ372222-122-1222-1222-1-12-1-2-12-1-12-1-1-12-2-22200-1-1-1-11-21111-2-211112-2-20-1-122-2-2000000-2-2-1-10022000000002-1-101111-1-11100000-20000-1-11000
χ382222-122-1222-1222-1-12-1-2-12-1-12-1-1-12-2-22200-1-1-1-11-21111-2-21111-2-2201122-2-200000022-1-100-2-200000000-21101-1-1-1-1-111000002000011-1000
χ392222-122-1222-1222-1-12-1-2-12-1-12-1-1-12-2-2-2-200-1-1-1-11-21111-2-2111122-20-1-1-2-222000000-2-21100-2-2000000002-1-10-111111-1-1000002000011-1000
χ402222-122-1222-1222-1-12-1-2-12-1-12-1-1-12-2-2-2-200-1-1-1-11-21111-2-21111-222011-2-2220000002211002200000000-2110-1-1-1-111-1-100000-20000-1-11000
χ4122-2-2222-2-22-2-2-2-2222220-22-2-2-2-222-200000022-2-200000000000000000000000000000000002-22i−2i2i−2i2i2i−2i−2i000000000000000000002i−2i2-20000
χ4222-2-2222-2-22-2-2-2-2222220-22-2-2-2-222-200000022-2-200000000000000000000000000000000002-2−2i2i−2i2i−2i−2i2i2i00000000000000000000−2i2i2-20000
χ4322-2-2222-2-22-2-2-2-2222220-22-2-2-2-222-200000022-2-20000000000000000000000000000000000-222i−2i−2i2i2i2i−2i−2i00000000000000000000−2i2i-220000
χ4422-2-2222-2-22-2-2-2-2222220-22-2-2-2-222-200000022-2-20000000000000000000000000000000000-22−2i2i2i−2i−2i−2i2i2i000000000000000000002i−2i-220000
χ452-2-22222-2-2-2-2222-2-22220-2-2-2222-2-2-2002i−2i2i−2i2-2-220000000000000000002i−2i002i−2i2i−2i00002i−2i2-20000000000000000002i−2i002i−2i00002-200000000
χ462-2-22222-2-2-2-2222-2-22220-2-2-2222-2-2-2002i−2i−2i2i2-2-220000000000000000002i−2i00−2i2i−2i2i00002i−2i-220000000000000000002i−2i00−2i2i0000-2200000000
χ472-2-22222-2-2-2-2222-2-22220-2-2-2222-2-2-200−2i2i2i−2i2-2-22000000000000000000−2i2i002i−2i2i−2i0000−2i2i-22000000000000000000−2i2i002i−2i0000-2200000000
χ482-2-22222-2-2-2-2222-2-22220-2-2-2222-2-2-200−2i2i−2i2i2-2-22000000000000000000−2i2i00−2i2i−2i2i0000−2i2i2-2000000000000000000−2i2i00−2i2i00002-200000000
χ492-2-2222-1-2-21122-1-2-2-1-12011-2-1-12-211−i3i32i−2i2i−2i-111-10000−i3i3−i3i3−i3−i3i3i3000000−ii3−32i−2i−ii3−3002i−2i2-2000000−i3i3−i3i300000000−ii3−3−ii3−300-1100000000
χ502-2-2222-1-2-21122-1-2-2-1-12011-2-1-12-211−i3i32i−2i−2i2i-111-10000−i3i3−i3i3−i3−i3i3i3000000−ii3−3−2i2ii−i−33002i−2i-22000000i3−i3i3−i300000000−ii3−3i−i−33001-100000000
χ512-2-2222-1-2-21122-1-2-2-1-12011-2-1-12-211−i3i3−2i2i2i−2i-111-10000−i3i3−i3i3−i3−i3i3i3000000i−i−332i−2i−ii3−300−2i2i-22000000i3−i3i3−i300000000i−i−33−ii3−3001-100000000
χ522-2-2222-1-2-21122-1-2-2-1-12011-2-1-12-211−i3i3−2i2i−2i2i-111-10000−i3i3−i3i3−i3−i3i3i3000000i−i−33−2i2ii−i−3300−2i2i2-2000000−i3i3−i3i300000000i−i−33i−i−3300-1100000000
χ532-2-2222-1-2-21122-1-2-2-1-12011-2-1-12-211i3−i32i−2i2i−2i-111-10000i3−i3i3−i3i3i3−i3−i3000000−ii−332i−2i−ii−33002i−2i2-2000000i3−i3i3−i300000000−ii−33−ii−3300-1100000000
χ542-2-2222-1-2-21122-1-2-2-1-12011-2-1-12-211i3−i32i−2i−2i2i-111-10000i3−i3i3−i3i3i3−i3−i3000000−ii−33−2i2ii−i3−3002i−2i-22000000−i3i3−i3i300000000−ii−33i−i3−3001-100000000
χ552-2-2222-1-2-21122-1-2-2-1-12011-2-1-12-211i3−i3−2i2i2i−2i-111-10000i3−i3i3−i3i3i3−i3−i3000000i−i3−32i−2i−ii−3300−2i2i-22000000−i3i3−i3i300000000i−i3−3−ii−33001-100000000
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χ5744444-2-24-2-2-24-2-2-24-21-24-21-2-21-2-2-21-2-2004411114-2-2-2-2-21111110004000000-2-2-2-2-2-20000000000000000000-2000000001111000000000000
χ5844444-2-24-2-2-24-2-2-24-21-24-21-2-21-2-2-21-2-200-4-411114-2-2-2-2-2111111000-40000002222220000000000000000000200000000-1-1-1-1000000000000
χ5944444-2-24-2-2-24-2-2-24-21-2-4-21-2-21-2-2-212200441111-422222-1-1-1-1-1-1000-4000000-2-2-2-222000000000000000000020000000011-1-1000000000000
χ6044444-2-24-2-2-24-2-2-24-21-2-4-21-2-21-2-2-212200-4-41111-422222-1-1-1-1-1-100040000002222-2-20000000000000000000-200000000-1-111000000000000
χ614444-24-2-24-2-2-24-24-21-2-241-2-21-2-2-21-2-2-244001111-24-2-211-2-21111040000-2-2-2-200000000-2-20000000000000000-200011110000000000000000
χ624444-24-2-24-2-2-24-24-21-2-241-2-21-2-2-21-2-2-2-4-4001111-24-2-211-2-211110-400002222000000002200000000000000002000-1-1-1-10000000000000000
χ634444-24-2-24-2-2-24-24-21-2-2-41-2-21-2-2-21-222440011112-422-1-122-1-1-1-10-40000-2-22200000000-2-20000000000000000200011-1-10000000000000000
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χ884-4-444-2-2-42224-2-22-4-21-202-12-21-222-1−2i32i3004i−4i1-1-110000−2i32i3i3−i3i3i3−i3−i30000000000−2i2i−2i2i23−230000000000000000000000000000i−i−33000000000000
χ894-4-444-2-2-42224-2-22-4-21-202-12-21-222-1−2i32i300−4i4i1-1-110000−2i32i3i3−i3i3i3−i3−i300000000002i−2i2i−2i−23230000000000000000000000000000−ii3−3000000000000
χ904-4-444-2-2-42224-2-22-4-21-202-12-21-222-12i3−2i3004i−4i1-1-1100002i3−2i3−i3i3−i3−i3i3i30000000000−2i2i−2i2i−23230000000000000000000000000000i−i3−3000000000000
χ914-4-444-2-2-42224-2-22-4-21-202-12-21-222-12i3−2i300−4i4i1-1-1100002i3−2i3−i3i3−i3−i3i3i300000000002i−2i2i−2i23−230000000000000000000000000000−ii−33000000000000
χ924-4-44-2442-4-4-4-244-42-24-202-42-24-222-4004i−4i00-222-20000000000000000004i−4i0000000000−2i2i00000000000000000000−2i2i000000000000000000
χ934-4-44-2442-4-4-4-244-42-24-202-42-24-222-400−4i4i00-222-2000000000000000000−4i4i00000000002i−2i000000000000000000002i−2i000000000000000000
χ944-4-44-24-22-422-24-2-421-2-20-1221-2-22-12−2i32i34i−4i001-1-110000i3−i3−2i32i3i3i3−i3−i3000000−2i2i23−2300000000−2i2i00000000000000000000i−i−330000000000000000
χ954-4-44-24-22-422-24-2-421-2-20-1221-2-22-12−2i32i3−4i4i001-1-110000i3−i3−2i32i3i3i3−i3−i30000002i−2i−2323000000002i−2i00000000000000000000−ii3−30000000000000000
χ964-4-44-24-22-422-24-2-421-2-20-1221-2-22-122i3−2i34i−4i001-1-110000−i3i32i3−2i3−i3−i3i3i3000000−2i2i−232300000000−2i2i00000000000000000000i−i3−30000000000000000
χ974-4-44-24-22-422-24-2-421-2-20-1221-2-22-122i3−2i3−4i4i001-1-110000−i3i32i3−2i3−i3−i3i3i30000002i−2i23−23000000002i−2i00000000000000000000−ii−330000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-4-84-44-844-48-42-404244-24-4-4-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-44-8-444-848-42-4-40-2-44-244-42400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-48448-844-8-4-4-4-4204-4-244-22-4400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-444-44444-4-42220-22-2-2-2-222-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-444-44444-4-42220-22-2-2-2-222-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-48-44-4-8444-8-42-40-4-2-44-244420000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-48-4-484-44-84-842-4-4024-4-2444-2-40000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4-4-44-44444422202-22-2-2-2-2-22000000-11-11006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4-4-44-44444422202-22-2-2-2-2-22000000-11-1100−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-4844-8-8-4-4844-4-42044-2-4-42-2440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-44444-4-4-4442220-2-2-2222-2-2-2−4i34i30000-111-100002i3−2i32i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-44444-4-4-4442220-2-2-2222-2-2-24i3−4i30000-111-10000−2i32i3−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000

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