Finite Group Databasebeta

← Group #13168709

Character table — Group #13168709

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order1222333666666666333466666666612122222366612121212121212121212121244446666666612121212121212124444444412121212666612121212121212121212121244121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-111-1111111111111-1-1-1-111-1-111-1-111111111-11-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111-1-111-1-111-1-11111-1-111-1-1-1-1-1-1-1-111-1-1111-111-1-111111-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-1-111-1-1-1-1-1-1-11-1-1-1-111-1111
χ51111111111111111111111111111111-1-11111111111111111111-111-1-111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111-111-1-1111111-11-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-11-1-111-1-1-1-11-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11-11-1-1-1-1-11111-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-111-111111-1-1-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11-1-1-1-1-111-1-11-111-1-1111-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-11111-1-1-1-1111111111111-1-11-1-11-1-111-1-111-1-1-1-11111-1-1-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-111-1-1111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1111-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1-1-111-1-11111111111-1-111-111-111-1-111-1-1-1-1-1-11111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-111111-1-1111-111-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111111-1-1-11-11
χ17222222-122-122-1-1222-1-122-1-1-1-12-1-12-1-12222-1-1-1-122-1-1-1-122-1-1-1-102202222-1-1-1-1-1-1-1-1000022002200-1-1-1-1-1-1-1-10202-1-1-1-1000000-1-100000000
χ18222222-122-122-1-1222-1-122-1-1-1-12-1-12-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-102-2022-2-2-1-111-1-1110000-2-200-2-2001111-1-111020-2-1-1110000001100000000
χ19222222-122-122-1-1222-1-122-1-1-1-12-1-12-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-10-220-2-22211-1-111-1-10000-2-200-2-200111111-1-10-20211-1-10000001100000000
χ20222222-122-122-1-1222-1-122-1-1-1-12-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-10-2-20-2-2-2-211111111000022002200-1-1-1-111110-20-21111000000-1-100000000
χ21222222-122-122-1-1222-1-1-22-1-1-1-12-1-12112222-1-1-1-1-2-21111-2-211110-2-202222-1-1-1-1111100002200-2-2001111-1-1-1-10-20-21111000000-1-100000000
χ22222222-122-122-1-1222-1-1-22-1-1-1-12-1-121122-2-2-1-1-1-1-2-21111-2-211110-22022-2-2-1-11111-1-10000-2-2002200-1-1-1-1-1-1110-20211-1-10000001100000000
χ23222222-122-122-1-1222-1-1-22-1-1-1-12-1-1211-2-222-1-1-1-1-2-21111-2-2111102-20-2-22211-1-1-1-1110000-2-2002200-1-1-1-111-1-1020-2-1-1110000001100000000
χ24222222-122-122-1-1222-1-1-22-1-1-1-12-1-1211-2-2-2-2-1-1-1-1-2-21111-2-211110220-2-2-2-21111-1-1-1-100002200-2-200111111110202-1-1-1-1000000-1-100000000
χ2522222-122-122-122-12-12-12-12-12-1-12-1-1222200-1-1-1-12-122-1-1-1-1-1-1-1-12202-1-10022002200-1-122002200000000-1-1002-1-10-1-100-1-1-1-12000-1-100-1000
χ2622222-122-122-122-12-12-12-12-12-1-12-1-1222200-1-1-1-12-122-1-1-1-1-1-1-1-1-220-2-1-1002200220011-2-200-2-200000000-1-100-2-110-1-1001111-200011001000
χ2722222-122-122-122-12-12-12-12-12-1-12-1-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-12-2021100-2-200-2-200-1-12200-2-200000000110021-101100-1-1-1-1-200011001000
χ2822222-122-122-122-12-12-12-12-12-1-12-1-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20-21100-2-200-2-20011-2-20022000000001100-2110110011112000-1-100-1000
χ2922222-122-122-122-12-12-1-2-12-12-1-12-1-1-2-22200-1-1-1-1-21-2-2111111112-20-2-1-1002200-2-200-1-1-2-2002200000000-1-1002110110011-1-1-2000-1-1001000
χ3022222-122-122-122-12-12-1-2-12-12-1-12-1-1-2-22200-1-1-1-1-21-2-211111111-2-202-1-1002200-2-200112200-2-200000000-1-100-21-101100-1-11120001100-1000
χ3122222-122-122-122-12-12-1-2-12-12-1-12-1-1-2-2-2-200-1-1-1-1-21-2-211111111220-21100-2-2002200-1-1-2-200-2-20000000011002-110-1-10011-1-120001100-1000
χ3222222-122-122-122-12-12-1-2-12-12-1-12-1-1-2-2-2-200-1-1-1-1-21-2-211111111-22021100-2-200220011220022000000001100-2-1-10-1-100-1-111-2000-1-1001000
χ332222-122-122-12222-1-1-122-1-12-12-1-12-1220022-1-1-1-1-12-1-122-1-1-1-1-1-1202200-1-10022002222-1-100000022000000-1-1-102-100-1-1-1-1-1-1020000-1-10-100
χ342222-122-122-12222-1-1-122-1-12-12-1-12-1220022-1-1-1-1-12-1-122-1-1-1-1-1-1-202-200-1-100220022-2-211000000-2-2000000-1-110-2-100-1-111110-20000110100
χ352222-122-122-12222-1-1-122-1-12-12-1-12-12200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-120-22001100-2-200-2-222-1-1000000-2-200000011-10210011-1-1-1-10-20000110100
χ362222-122-122-12222-1-1-122-1-12-12-1-12-12200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-20-2-2001100-2-200-2-2-2-211000000220000001110-2100111111020000-1-10-100
χ372222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-20022-1-1-1-11-211-2-211111120-2-200-1-1002200-2-22211000000-2-2000000-1-1-10-21001111-1-1020000110-100
χ382222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-20022-1-1-1-11-211-2-2111111-20-2200-1-1002200-2-2-2-2-1-100000022000000-1-110210011-1-1110-20000-1-10100
χ392222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-200-2-2-1-1-1-11-211-2-2111111202-2001100-2-2002222110000002200000011-10-2-100-1-111-1-10-20000-1-10100
χ402222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-200-2-2-1-1-1-11-211-2-2111111-2022001100-2-20022-2-2-1-1000000-2-200000011102-100-1-1-1-111020000110-100
χ4122-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-2002-22-222-2-200000000000000002-22-22-22-2000000002-200000000002-22-2000000000000002-200000000
χ4222-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-2002-2-2222-2-200000000000000002-2-222-2-2200000000-2200000000002-2-2200000000000000-2200000000
χ4322-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-200-222-222-2-20000000000000000-222-2-222-200000000-220000000000-222-200000000000000-2200000000
χ4422-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-200-22-2222-2-20000000000000000-22-22-22-22000000002-20000000000-22-22000000000000002-200000000
χ4522-2-222-1221-2-2-11-2-22-1-102-1-111-211-23−32-22-2-1-111003−33−30033−3−300002-22-2-11-113−33−300002-200000033−3−3-11-1100003−33−3000000-1100000000
χ4622-2-222-1221-2-2-11-2-22-1-102-1-111-211-23−32-2-22-1-111003−33−30033−3−300002-2-22-111-13−3−330000-22000000−3−333-111-100003−3−330000001-100000000
χ4722-2-222-1221-2-2-11-2-22-1-102-1-111-211-23−3-222-2-1-111003−33−30033−3−30000-222-21-1-11−333−30000-22000000−3−3331-1-110000−333−30000001-100000000
χ4822-2-222-1221-2-2-11-2-22-1-102-1-111-211-23−3-22-22-1-111003−33−30033−3−30000-22-221-11-1−33−3300002-200000033−3−31-11-10000−33−33000000-1100000000
χ4922-2-222-1221-2-2-11-2-22-1-102-1-111-211-2−332-22-2-1-11100−33−3300−3−33300002-22-2-11-11−33−3300002-2000000−3−333-11-110000−33−33000000-1100000000
χ5022-2-222-1221-2-2-11-2-22-1-102-1-111-211-2−332-2-22-1-11100−33−3300−3−33300002-2-22-111-1−333−30000-2200000033−3−3-111-10000−333−30000001-100000000
χ5122-2-222-1221-2-2-11-2-22-1-102-1-111-211-2−33-222-2-1-11100−33−3300−3−3330000-222-21-1-113−3−330000-2200000033−3−31-1-1100003−3−330000001-100000000
χ5222-2-222-1221-2-2-11-2-22-1-102-1-111-211-2−33-22-22-1-11100−33−3300−3−3330000-22-221-11-13−33−300002-2000000−3−3331-11-100003−33−3000000-1100000000
χ532-22-2222-2-222-2-2-22-22220-2-2-222-2-2-220000002-2-2200000000000000000000000000000000002-22i−2i2i−2i2i−2i2i−2i000000000000000000002-22i−2i0000
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χ944-4-44-2-2422-42-2-442-21-2-20-122221-2-2-10000001-11-10000003i−3i3i−3i3i−3i000000000000000023−23−2i32i3000000000000000000000000i3−i3−33000000000000
χ954-4-44-2-2422-42-2-442-21-2-20-122221-2-2-10000001-11-10000003i−3i3i−3i3i−3i0000000000000000−23232i3−2i3000000000000000000000000−i3i33−3000000000000
χ964-4-44-2-2422-42-2-442-21-2-20-122221-2-2-10000001-11-1000000−3i3i−3i3i−3i3i000000000000000023−232i3−2i3000000000000000000000000−i3i3−33000000000000
χ974-4-44-2-2422-42-2-442-21-2-20-122221-2-2-10000001-11-1000000−3i3i−3i3i−3i3i0000000000000000−2323−2i32i3000000000000000000000000i3−i33−3000000000000
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
χ10088-8-8-4-48-4-4-8448-8442-4-402-4-444-244-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4-4444-44442220222-2-2-2-2-2-243−430000-1-11100−2323−23230033−3−3000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-4444-44442220222-2-2-2-2-2-2−43430000-1-1110023−2323−2300−3−333000000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-4-84-48444-4-8-4-42044-2-4244-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-44-8-4-4-84484-42-404-242-44-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-48448-44-8-8-442-4-40-244-4-4-24420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-444-4-4444-442220-2-2-222-2-2-22000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-444-4-4444-442220-2-2-222-2-2-22000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-4-844-8-44-448-4-42044-24-2-4-4240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-44-84484-4-8-4-42-404-24-24-42-440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-44444-44-44-42220-2-2-2-2-2222-2000000-11-110000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-44444-44-44-42220-2-2-2-2-2222-2000000-11-11000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000000000

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