Finite Group Databasebeta

← Group #13168392

Character table — Group #13168392

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212444412121212121212121212121212121212441212121212121212121212121212121212121212244446612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-11111111111111-1-11-1-1-1-111111111-11-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-111-1-1-111-1-1-11-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11-1-1-1111-1-1-1-11-111
χ51111111111111111111111111111111-1-1111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-11111-1-1-1-111111-1-1-1111-1-1-1-11-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-1-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-111-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111111111-1-1111111-1-11-1-1-11111-1-111-1-11-11-1-111-1-1-1-1-11-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-11111-1-1111111-11-1-111-1-111-1-111-1-1-1-1-111-1-111-1-11-11-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-111-111-11-1-1-1-111111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-11-1111111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-11-1111111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1111-1-1-1-11111-1-1-111-11-1-1-1-11111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-111-1-1-1-1111111111-111-1-111-1-111-1-111-1-1-111-1-111-1-11-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-1-1-1-1-1-1-11111111111-1111-1-1-1-111-1-1111-11-1-111-1-1-1-1-111-1
χ17222222-1-1222-1-12222-1-122-1-1-12-1-12-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-10222222222-1-1-1-1000000000000-1-120-1-1-1-10000-1-1-1-120002-1-10000-1000
χ18222222-1-1222-1-12222-1-122-1-1-12-1-12-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-102-2-2-2-22222-1-111000000000000-11-2011110000-1-1-1-1-2000-21100001000
χ19222222-1-1222-1-12222-1-122-1-1-12-1-12-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10-22222-2-2-2-211-1-10000000000001-120-1-1-1-100001111-2000-21100001000
χ20222222-1-1222-1-12222-1-122-1-1-12-1-12-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-2-2-2-2-2-2-2-2111100000000000011-2011110000111120002-1-10000-1000
χ21222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-20022-1-1-1-11-2-2-2111111110-22-2-2-222-2-2-1-1-1-1000000000000112011-1-10000-1-1112000-2-1-100001000
χ22222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-20022-1-1-1-11-2-2-2111111110-2-222222-2-2-1-1110000000000001-1-20-1-1110000-1-111-20002110000-1000
χ23222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-200-2-2-1-1-1-11-2-2-211111111022-2-2-2-2-22211-1-1000000000000-112011-1-1000011-1-1-20002110000-1000
χ24222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-200-2-2-1-1-1-11-2-2-21111111102-2222-2-2221111000000000000-1-1-20-1-111000011-1-12000-2-1-100001000
χ2522222-1222-1-12222-1-12-12-12-1-1-122-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1220000-1-1-1-1220022-1-1-1-122-1-1-1-120020000-1-1-1-1-1-1-1-1020000000-1-10000
χ2622222-1222-1-12222-1-12-12-12-1-1-122-1-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-12-200001111-2-20022-1-1-1-1-2-21111-20020000-1-1-1-111110-20000000110000
χ2722222-1222-1-12222-1-12-12-12-1-1-122-1-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-220000-1-1-1-12200-2-21111-2-21111200-200001111-1-1-1-10-20000000110000
χ2822222-1222-1-12222-1-12-12-12-1-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-2-200001111-2-200-2-2111122-1-1-1-1-200-2000011111111020000000-1-10000
χ2922222-1222-1-12222-1-12-1-2-12-1-1-122-1-1112222-1-1-1-1-2-211-2-2111111-2-20000-1-111220022-1-11122-1-1-1-1-200-20000-1-111-1-1110-20000000110000
χ3022222-1222-1-12222-1-12-1-2-12-1-1-122-1-11122-2-2-1-1-1-1-2-211-2-2111111-22000011-1-1-2-20022-1-111-2-21111200-20000-1-11111-1-1020000000-1-10000
χ3122222-1222-1-12222-1-12-1-2-12-1-1-122-1-111-2-222-1-1-1-1-2-211-2-21111112-20000-1-1112200-2-211-1-1-2-21111-2002000011-1-1-1-111020000000-1-10000
χ3222222-1222-1-12222-1-12-1-2-12-1-1-122-1-111-2-2-2-2-1-1-1-1-2-211-2-211111122000011-1-1-2-200-2-211-1-122-1-1-1-12002000011-1-111-1-10-20000000110000
χ332222-1222-12222-1-12-1-122-1-122-1-1-1-12222200-1-1-1-12-1-1-1-1-122-1-1-1-12022-1-100000022-1-1222200000002-1-1-1-1-1-1-1-1-1-100000022000-1-1000-100
χ342222-1222-12222-1-12-1-122-1-122-1-1-1-12222200-1-1-1-12-1-1-1-1-122-1-1-1-120-2-211000000-2-2-1-122220000000-21-11111-1-1-1-1000000-2-200011000100
χ352222-1222-12222-1-12-1-122-1-122-1-1-1-1222-2-200-1-1-1-12-1-1-1-1-122-1-1-1-1-2022-1-10000002211-2-2-2-200000002-11-1-1-1-11111000000-2-200011000100
χ362222-1222-12222-1-12-1-122-1-122-1-1-1-1222-2-200-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2-211000000-2-211-2-2-2-20000000-2111111111100000022000-1-1000-100
χ372222-1222-12222-1-12-1-12-2-1-122-1-1-1-12-2-22200-1-1-1-1-211111-2-21111-202-21100000022-1-122-2-20000000-2-1111-1-1-1-1110000002-200011000-100
χ382222-1222-12222-1-12-1-12-2-1-122-1-1-1-12-2-22200-1-1-1-1-211111-2-21111-20-22-1-1000000-2-2-1-122-2-20000000211-1-111-1-111000000-22000-1-1000100
χ392222-1222-12222-1-12-1-12-2-1-122-1-1-1-12-2-2-2-200-1-1-1-1-211111-2-21111202-2110000002211-2-2220000000-2-1-111-1-111-1-1000000-22000-1-1000100
χ402222-1222-12222-1-12-1-12-2-1-122-1-1-1-12-2-2-2-200-1-1-1-1-211111-2-2111120-22-1-1000000-2-211-2-222000000021-1-1-11111-1-10000002-200011000-100
χ412-22-2222-2-22-22-22-2-22220-2-2-2-22-22-22002i−2i2-22-2-220000000000000000002-2002-2002i−2i2i−2i002i−2i2i2i−2i−2i000000002i−2i002-200000000000000000
χ422-22-2222-2-22-22-22-2-22220-2-2-2-22-22-22002i−2i-222-2-22000000000000000000-2200-22002i−2i2i−2i00−2i2i−2i−2i2i2i000000002i−2i00-2200000000000000000
χ432-22-2222-2-22-22-22-2-22220-2-2-2-22-22-2200−2i2i2-22-2-220000000000000000002-2002-200−2i2i−2i2i00−2i2i−2i−2i2i2i00000000−2i2i002-200000000000000000
χ442-22-2222-2-22-22-22-2-22220-2-2-2-22-22-2200−2i2i-222-2-22000000000000000000-2200-2200−2i2i−2i2i002i−2i2i2i−2i−2i00000000−2i2i00-2200000000000000000
χ452-22-22-12-2-2-112-22-21-12-101-211-1-221-1−i3i32i−2i2-2-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i32-2002i−2i−ii3−32i−2i−i−iii00000000−ii3−3-11−i3i30000000003−30000
χ462-22-22-12-2-2-112-22-21-12-101-211-1-221-1−i3i32i−2i-22-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i3-22002i−2i−ii3−3−2i2iii−i−i00000000−ii3−31-1i3−i3000000000−330000
χ472-22-22-12-2-2-112-22-21-12-101-211-1-221-1−i3i3−2i2i2-2-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i32-200−2i2ii−i−33−2i2iii−i−i00000000i−i−33-11−i3i3000000000−330000
χ482-22-22-12-2-2-112-22-21-12-101-211-1-221-1−i3i3−2i2i-22-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i3-2200−2i2ii−i−332i−2i−i−iii00000000i−i−331-1i3−i30000000003−30000
χ492-22-22-12-2-2-112-22-21-12-101-211-1-221-1i3−i32i−2i2-2-111-100i3−i300i3−i3i3i3−i3−i3000000-11i3−i32-2002i−2i−ii−332i−2i−i−iii00000000−ii−33-11i3−i3000000000−330000
χ502-22-22-12-2-2-112-22-21-12-101-211-1-221-1i3−i32i−2i-22-111-100i3−i300i3−i3i3i3−i3−i30000001-1−i3i3-22002i−2i−ii−33−2i2iii−i−i00000000−ii−331-1−i3i30000000003−30000
χ512-22-22-12-2-2-112-22-21-12-101-211-1-221-1i3−i3−2i2i2-2-111-100i3−i300i3−i3i3i3−i3−i3000000-11i3−i32-200−2i2ii−i3−3−2i2iii−i−i00000000i−i3−3-11i3−i30000000003−30000
χ522-22-22-12-2-2-112-22-21-12-101-211-1-221-1i3−i3−2i2i-22-111-100i3−i300i3−i3i3i3−i3−i30000001-1−i3i3-2200−2i2ii−i3−32i−2i−i−iii00000000i−i3−31-1−i3i3000000000−330000
χ5344444-2-2-24-2-2-2-244-2-2-214-2-211-2-2-2-21-2-200441111-24-2-2-2-2111111040000-2-2-2-2-2-200000000000000-2000000000001111000000000000000
χ5444444-2-2-24-2-2-2-244-2-2-214-2-211-2-2-2-21-2-200-4-41111-24-2-2-2-21111110-4000022222200000000000000200000000000-1-1-1-1000000000000000
χ5544444-2-2-24-2-2-2-244-2-2-21-4-2-211-2-2-2-2122004411112-42222-1-1-1-1-1-10-40000-2-222-2-20000000000000020000000000011-1-1000000000000000
χ5644444-2-2-24-2-2-2-244-2-2-21-4-2-211-2-2-2-212200-4-411112-42222-1-1-1-1-1-104000022-2-22200000000000000-200000000000-1-111000000000000000
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χ604444-24-2-2-244-2-2-2-24-21-2-4-21-2-2-211-2-2-4-4000011112222-1-122-1-1-1-100-44-2-2000000220000000000000-22011-1-100000000000000000000000
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χ824-44-4-2-24-42-224-4-2221-2-20-122212-2-1-22i3−2i34i−4i001-1-1100−i3i3002i3−2i3−i3−i3i3i300000000000000−2i2i−2i2i−232300000000000000i−i3−30000000000000000000
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χ844-4-44444-44-44-44-4-4-444404-4-44-44-4-4-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
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χ904-4-44-244-4-2-44-4422-4-2-240-22-442-222-4000000-22-2200000000000000002i3−2i30000000000000000000000002i3−2i30000000000000000000000000
χ914-4-44-24-22-2-442-222-4-21-20-2-12-221-1220000001-11-100003i−3i003i−3i3i−3i0000−2i32i300000023−230000000000000000i3−i3−3300000000000000000000000
χ924-4-44-24-22-2-442-222-4-21-20-2-12-221-1220000001-11-100003i−3i003i−3i3i−3i00002i3−2i3000000−23230000000000000000−i3i33−300000000000000000000000
χ934-4-44-24-22-2-442-222-4-21-20-2-12-221-1220000001-11-10000−3i3i00−3i3i−3i3i0000−2i32i3000000−23230000000000000000i3−i33−300000000000000000000000
χ944-4-44-24-22-2-442-222-4-21-20-2-12-221-1220000001-11-10000−3i3i00−3i3i−3i3i00002i3−2i300000023−230000000000000000−i3i3−3300000000000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-4-4-84444-88-4-4-4204-42-2444-4-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-4-44-8-8444-48-42-4042-444-2-2-4400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-488444-8-84-4-42-4-40-2-4-44-2442400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-4444444-4-42220-222-2-2-2-22-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4444444-4-42220-222-2-2-2-22-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000
χ1028-88-8-48-4448-8-44-44-8-42-404-244-4-224-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-444-44-44-4442220-2-2-2-22-22-22−4i34i30000-111-1002i3−2i3002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-444-44-44-4442220-2-2-2-22-22-224i3−4i30000-111-100−2i32i300−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1058-8-888-4-4484-44-4-8-84-4-420-44-224-444-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48-8-44-4-884442-4-40244-4-2-44-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-44-44-44-444422202-2-22-22-2-2-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-44-44-44-444422202-2-22-22-2-2-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000

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