Finite Group Databasebeta

← Group #13168721

Character table — Group #13168721

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order12223336666666663334666666666121222444436661212121212121212121212124446666121212121212121212121212224412121212661212121212121212121212121212444466121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-111111111111111111-111111111111-1-111-1-111111111111-11-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111111-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1111-1-111-1-111-1-111-1-1-1-111-1-1-11-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111-11
χ51111111111111111111111111111111-1-111111111111111111111-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1111-1-11111111111-1-1-1-111-1-1-1-11-1-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-111-1-1-1-11111-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-11-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-11-11-1-1-1-111-1-111-1-1-1-111-1-1-1-111-1-11
χ81111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111-11-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-11-11-1-11111-1-1-1-1-11-1111-1-1-1-11111-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111-1-111111111-1-11-1-1-1-1-1-1-11111-111-1-1-1-1-111111-1-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1111-1-1-1-11111-1-11-1-11-1-111-1-1-1-1-111
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-111-1-1111111-1-11-1-1-11111-1-1-1-1111-1-11-1-111-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-11111111-1-1-1-1-111-1-1-1-1-111-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-11111-11-1111-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-11-11-111111111-1-1-1
χ17222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-1222200-1-1-1-122-1-122-1-1-1-1-1-120222-1-1-1-122-1-100-1-1002222-1-1-1-1-1-12020-1-1-1-100-1-1000000-1-1000000000
χ18222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-122-2-200-1-1-1-122-1-122-1-1-1-1-1-120-222-1-1-1-1-2-211001100-2-2-2-21111-1-120-20-1-111001100000011000000000
χ19222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-1-2-22200-1-1-1-122-1-122-1-1-1-1-1-1-202-2-2111122-1-100-1-100-2-2-2-2111111-202011-1-100-1-100000011000000000
χ20222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-1-2-2-2-200-1-1-1-122-1-122-1-1-1-1-1-1-20-2-2-21111-2-2110011002222-1-1-1-111-20-2011110011000000-1-1000000000
χ21222222-122-1-122-1222-1-1-22-1-1-12-1-12-111222200-1-1-1-1-2-211-2-2111111-20-222-1-11122-1-100110022-2-21111-1-1-20-2011-1-10011000000-1-1000000000
χ22222222-122-1-122-1222-1-1-22-1-1-12-1-12-11122-2-200-1-1-1-1-2-211-2-2111111-20222-1-111-2-21100-1-100-2-222-1-1-1-1-1-1-2020111100-1-100000011000000000
χ23222222-122-1-122-1222-1-1-22-1-1-12-1-12-111-2-22200-1-1-1-1-2-211-2-211111120-2-2-211-1-122-1-1001100-2-222-1-1-1-11120-20-1-1-1-1001100000011000000000
χ24222222-122-1-122-1222-1-1-22-1-1-12-1-12-111-2-2-2-200-1-1-1-1-2-211-2-2111111202-2-211-1-1-2-21100-1-10022-2-21111112020-1-11100-1-1000000-1-1000000000
χ2522222-12-1222-1222-1-12-12-12-1-1-12-1-1222220022-1-1-1-12-1-1-1-1-122-1-1-1-1220-1-1222200002200-1-100000000-1-1-1-102-1-100-1-100-1-100220000-1-1000-10
χ2622222-12-1222-1222-1-12-12-12-1-1-12-1-12222200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-12-20-1-122220000-2-2001100000000-1-1-110-2-1-10011001100-2-200001100010
χ2722222-12-1222-1222-1-12-12-12-1-1-12-1-1222-2-20022-1-1-1-12-1-1-1-1-122-1-1-1-1-22011-2-2-2-200002200-1-100000000111-1021100-1-100-1-100-2-200001100010
χ2822222-12-1222-1222-1-12-12-12-1-1-12-1-1222-2-200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2011-2-2-2-20000-2-200110000000011110-2110011001100220000-1-1000-10
χ2922222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-2220022-1-1-1-1-211111-2-21111-2-20-1-122-2-200002200-1-100000000-1-1110-211001100-1-1002-20000-1-100010
χ3022222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-22200-2-2-1-1-1-1-211111-2-21111-220-1-122-2-20000-2-2001100000000-1-11-1021100-1-1001100-22000011000-10
χ3122222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-2-2-20022-1-1-1-1-211111-2-211112-2011-2-22200002200-1-10000000011-110-2-1-1001100-1-100-22000011000-10
χ3222222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-2-2-200-2-2-1-1-1-1-211111-2-2111122011-2-2220000-2-200110000000011-1-102-1-100-1-10011002-20000-1-100010
χ332222-1222-1222-12-12-1-122-1-122-1-12-1-122002222-1-1-1-1-1222-1-1-1-1-1-1-1-1022000000-1-122-1-12222000000000002-1-100-1-1-1-1-1-1-1-1220000-1-10000-100
χ342222-1222-1222-12-12-1-122-1-122-1-12-1-1220022-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10-22000000-1-1221122-2-200000000000-2-1100-1-111-1-111-2-20000110000100
χ352222-1222-1222-12-12-1-122-1-122-1-12-1-12200-2-222-1-1-1-1-1222-1-1-1-1-1-1-1-102-200000011-2-2-1-1-2-2220000000000021-10011-1-111-1-1-2-20000110000100
χ362222-1222-1222-12-12-1-122-1-122-1-12-1-12200-2-2-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-200000011-2-211-2-2-2-200000000000-2110011111111220000-1-10000-100
χ372222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-2002222-1-1-1-11-2-2-2111111110-2-2000000-1-122-1-1-2-22200000000000-21100-1-11111-1-12-20000-1-10000100
χ382222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-20022-2-2-1-1-1-11-2-2-21111111102-2000000-1-12211-2-2-2-20000000000021-100-1-1-1-11111-220000110000-100
χ392222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-200-2-222-1-1-1-11-2-2-2111111110-2200000011-2-2-1-1222200000000000-2-11001111-1-1-1-1-220000110000-100
χ402222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-200-2-2-2-2-1-1-1-11-2-2-21111111102200000011-2-21122-2-2000000000002-1-10011-1-1-1-1112-20000-1-10000100
χ4122-2-2222222-2-2-2-2-2-222202-22-2-22-2-2-2002-22-20022-2-20000000000000002-22-2002-22-20000002-20000002-20000002-200000000002-2000000000
χ4222-2-2222222-2-2-2-2-2-222202-22-2-22-2-2-2002-2-220022-2-20000000000000002-22-200-22-22000000-220000002-2000000-220000000000-22000000000
χ4322-2-2222222-2-2-2-2-2-222202-22-2-22-2-2-200-222-20022-2-2000000000000000-22-22002-22-2000000-22000000-220000002-20000000000-22000000000
χ4422-2-2222222-2-2-2-2-2-222202-22-2-22-2-2-200-22-220022-2-2000000000000000-22-2200-22-220000002-2000000-22000000-2200000000002-2000000000
χ4522-2-222-122-11-2-21-2-22-1-1021-11-2-11-213−32-22-200-1-111003−3003−333−3−30002-2-113−32-2-11003−3002-20033−3−3-1100003−3-11003−3000000-11000000000
χ4622-2-222-122-11-2-21-2-22-1-1021-11-2-11-213−32-2-2200-1-111003−3003−333−3−30002-2-113−3-221-100−3300-2200−3−333-1100003−31-100−330000001-1000000000
χ4722-2-222-122-11-2-21-2-22-1-1021-11-2-11-213−3-222-200-1-111003−3003−333−3−3000-221-1−332-2-11003−300-2200−3−3331-10000−33-11003−30000001-1000000000
χ4822-2-222-122-11-2-21-2-22-1-1021-11-2-11-213−3-22-2200-1-111003−3003−333−3−3000-221-1−33-221-100−33002-20033−3−31-10000−331-100−33000000-11000000000
χ4922-2-222-122-11-2-21-2-22-1-1021-11-2-11-21−332-22-200-1-11100−3300−33−3−3330002-2-11−332-2-1100−33002-200−3−333-110000−33-1100−33000000-11000000000
χ5022-2-222-122-11-2-21-2-22-1-1021-11-2-11-21−332-2-2200-1-11100−3300−33−3−3330002-2-11−33-221-1003−300-220033−3−3-110000−331-1003−30000001-1000000000
χ5122-2-222-122-11-2-21-2-22-1-1021-11-2-11-21−33-222-200-1-11100−3300−33−3−333000-221-13−32-2-1100−3300-220033−3−31-100003−3-1100−330000001-1000000000
χ5222-2-222-122-11-2-21-2-22-1-1021-11-2-11-21−33-22-2200-1-11100−3300−33−3−333000-221-13−3-221-1003−3002-200−3−3331-100003−31-1003−3000000-11000000000
χ532-22-2222-2-2-222-2-22-22220-22-2-22-22-2-20000002i−2i2-22-200000000000000000000000002i−2i002i−2i002i−2i2i−2i2i−2i000000000000002i−2i00000000002-2000
χ542-22-2222-2-2-222-2-22-22220-22-2-22-22-2-20000002i−2i2-22-200000000000000000000000002i−2i002i−2i00−2i2i−2i2i−2i2i000000000000002i−2i0000000000-22000
χ552-22-2222-2-2-222-2-22-22220-22-2-22-22-2-2000000−2i2i2-22-20000000000000000000000000−2i2i00−2i2i002i−2i2i−2i2i−2i00000000000000−2i2i0000000000-22000
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χ5744444-2-2-24-2-2-24-24-2-2-214-2-211-2-21-2-2-2-244000011114-211-2-2-2-21111400-2-2-2-2-2-200000000000000000011-20001100000000000000000000000
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χ6044444-2-2-24-2-2-24-24-2-2-21-4-2-211-2-21-2-222-4-400001111-42-1-12222-1-1-1-14002222-2-2000000000000000000-1-1-20001100000000000000000000000
χ614444-24-24-2-2-24-2-2-24-21-24-21-2-2-21-2-21-2-20044001111-24-2-2-2-2111111004000000-2-2-2-200-2-200000000000000-200011001100000000000000000
χ624444-24-24-2-2-24-2-2-24-21-24-21-2-2-21-2-21-2-200-4-4001111-24-2-2-2-211111100-400000022220022000000000000002000-1-100-1-100000000000000000
χ634444-24-24-2-2-24-2-2-24-21-2-4-21-2-2-21-2-212200440011112-42222-1-1-1-1-1-100-4000000-2-2-2-200220000000000000020001100-1-100000000000000000
χ644444-24-24-2-2-24-2-2-24-21-2-4-21-2-2-21-2-212200-4-40011112-42222-1-1-1-1-1-1004000000222200-2-200000000000000-2000-1-1001100000000000000000
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χ664444-2-24-2-244-2-24-2-21-2-241-2-2-21-2-21-2440000-4-41111-2-2-2-211-2-211110-400000000000220022000000000002020000-1-100-1-1000000000000000
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χ904-44-4-2-2422-44-22-4-221-2-20-1-22212-2-12000000−4i4i1-11-10000−3i3i00−3i3i−3i3i00000000000002i−2i002i−2i0000000000000000003-300−ii000000000000000
χ914-4-44444-4-4-4-4-444-444440-4-4-44-4-4-444000000004-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4444-2-4-422-44-2-444-2-20-422-2-4224-200000000-222-200000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ934-4-4444-2-4-422-44-2-444-2-20-422-2-4224-200000000-222-2000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ944-4-444-242-4-4-4244-4-2-24-202-42-22-42-2400000000-222-2000000000000000000000000000000000000000000000000000000000000000−2i32i300000
χ954-4-444-242-4-4-4244-4-2-24-202-42-22-42-2400000000-222-20000000000000000000000000000000000000000000000000000000000000002i3−2i300000
χ964-4-44-244-42-4-4-4-2424-2-24022-4422-4-2-200000000-222-2000000000000000000000000000000000000000000000000000000000000023−230000000
χ974-4-44-244-42-4-4-4-2424-2-24022-4422-4-2-200000000-222-20000000000000000000000000000000000000000000000000000000000000−23230000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-48-4-48-844-8442-4-4024-44-2-44-240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4-4-444444422202-22-2-22-2-2-243−43000000-1-11100−232300−232333−3−30000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-4-444444422202-22-2-22-2-2-2−4343000000-1-1110023−230023−23−3−3330000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-44-84-4-4-8484-4-4204-4-2-2-44244000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-4-844-4844-4-8-42-404244-4-2-44-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4444-4-444-442220-22-2-22-22-2-200000000-11-1100006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4444-4-444-442220-22-2-22-22-2-200000000-11-110000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-44-84448-4-8-4-4-42044-2244-2-4-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-4-8444-8-4-448-42-404-24-44-24-42000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-4844-8-84-484-42-4-40-244-4-2442-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-444444-4-44-42220-2-2-22-2-2-22200000000-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-444444-4-44-42220-2-2-22-2-2-22200000000-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000

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