Finite Group Databasebeta

← Group #13168029

Character table — Group #13168029

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order122233366666666633346666666661212121212121212224412121212366612121212121212121222446666661212121212121212121212121212121244666666666121212224446666121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1111111-1-1111111111111111111-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1-111-1-11-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-111-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-111111111-1-111111111-1-1111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111-1-11111111111111111111-1-11-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-11-1-1-1-111-1-111-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111-1-11111-1-1-1-1-1-11-11-1-1-11111-11-1-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111-11111-1-111-1-1-1-1-11-11-1-1-1-1111-111-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1111111-1-11111-1-1-1-1-1-11111-1-11-1-11111-1-1-1-1-111-1-111111-1-1-1-111-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-111-1-1-11-111-111-1-1-1-111-1-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-111-1-11111-111-111-1-1-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-11111111-1-111111-1-1-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1111111-1-1-1-11111111-1-1-1-111-1-1111-1-11-11-1-1-1-1111-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-111111-11-11-1-1-11111-11-11-1
χ17222222-12-1222-1-1222-1-12-1-1-12-1-122-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-1220222-1-1-1-100000022000000000022-1-1-1-1-1-1-1-1-1-10220000-1-100-10000
χ18222222-12-1222-1-1222-1-12-1-1-12-1-122-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20222-1-111000000220000000000-2-21-1-11111-1-1-10-2-20000110010000
χ19222222-12-1222-1-1222-1-12-1-1-12-1-122-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1220-2-2-211-1-1000000-2-2000000000022-111-1-1-1-11110-2-20000110010000
χ20222222-12-1222-1-1222-1-12-1-1-12-1-122-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-21111000000-2-20000000000-2-211111111110220000-1-100-10000
χ21222222-12-1222-1-1222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-222000000-1-1-1-11111111112-20-222-1-1-1-1000000-2-200000000002-21-1-1-1-11111102-20000-1-10010000
χ22222222-12-1222-1-1222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-220-222-1-111000000-2-20000000000-22-1-1-111-1-11110-2200001100-10000
χ23222222-12-1222-1-1222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-11111111112-202-2-211-1-10000002200000000002-2111-1-111-1-1-10-2200001100-10000
χ24222222-12-1222-1-1222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-1111111111-2202-2-21111000000220000000000-22-11111-1-1-1-1-102-20000-1-10010000
χ2522222-12-1222-122-12-1-122-122-1-12-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-10022-1-122002222-1-1-1-1-1-1-1-1-1-1-1-122000-1-100002-1-120000-1-100-1-100000
χ2622222-12-1222-122-12-1-122-122-1-12-1-1-1-1-122-1-1-1-122-2-21111-1-1-1-1222-1-1-1-1-1-100-22-1-12200-2-2-2-211-1-111111111-2-2000-1-100002-1-1-2000011001100000
χ2722222-12-1222-122-12-1-122-122-1-12-1-1-1-1-122-1-1-1-1-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1002-211-2-2002222-1-111-1-1-1-1-1-1-1-1-2-2000110000-211-2000011001100000
χ2822222-12-1222-122-12-1-122-122-1-12-1-1-1-1-122-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-100-2-211-2-200-2-2-2-211111111111122000110000-21120000-1-100-1-100000
χ2922222-12-1222-122-12-1-12-2-122-1-12-1-1-111-2-211112222-1-1-1-1-1-1-1-1-2-2-211111100-2-2-1-1220022-2-21111-1-1-1-1111122000-1-10000-211-200001100-1-100000
χ3022222-12-1222-122-12-1-12-2-122-1-12-1-1-111-2-2111122-2-21111-1-1-1-1-2-2-2111111002-2-1-12200-2-222-1-1111111-1-1-1-1-2-2000-1-10000-21120000-1-1001100000
χ3122222-12-1222-122-12-1-12-2-122-1-12-1-1-111-2-21111-2-222-1-1-1-1-1-1-1-1-2-2-211111100-2211-2-20022-2-211-1-1-1-1-1-11111-2-20001100002-1-120000-1-1001100000
χ3222222-12-1222-122-12-1-12-2-122-1-12-1-1-111-2-21111-2-2-2-21111-1-1-1-1-2-2-2111111002211-2-200-2-222-1-1-1-11111-1-1-1-1220001100002-1-1-200001100-1-100000
χ332222-12222-1-12222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-12220000022-1-1-1-12200-1-1-1-1-1-1-1-100-1-1200-1-1-1-1000000220000000-1-100
χ342222-12222-1-12222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-1-2-2200000-2-2-1-1-1-12200-1-1-1-1-1-1-1-10011-2001111000000-2-200000001100
χ352222-12222-1-12222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-122-200000221111-2-2001111111100-1-1200-1-1-1-1000000-2-200000001100
χ362222-12222-1-12222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-2-2-200000-2-21111-2-200111111110011-2001111000000220000000-1-100
χ372222-12222-1-12222-1-12-1-22-1-1-12-1-1-12-2-211111100222222-1-1-1-1-211-2-211112-2-20000022-1-111-2-200-1-1-1-1111100-11-200-1-1110000002-20000000-1100
χ382222-12222-1-12222-1-12-1-22-1-1-12-1-1-12-2-211111100222222-1-1-1-1-211-2-21111-22-200000-2-2-1-111-2-200-1-1-1-11111001-120011-1-1000000-2200000001-100
χ392222-12222-1-12222-1-12-1-22-1-1-12-1-1-12-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-211112-22000002211-1-122001111-1-1-1-100-11-200-1-111000000-2200000001-100
χ402222-12222-1-12222-1-12-1-22-1-1-12-1-1-12-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-21111-22200000-2-211-1-122001111-1-1-1-1001-120011-1-10000002-20000000-1100
χ4122-2-2222-2-22-22-22-2-2222022-2-2-2-22-2-2000000002-22i−2i2i2i−2i−2i22-2-200000000000002-22-2002i−2i0000002i2i−2i−2i00002i−2i0002-200000000000000002i−2i00000
χ4222-2-2222-2-22-22-22-2-2222022-2-2-2-22-2-2000000002-2−2i2i−2i−2i2i2i22-2-200000000000002-22-200−2i2i000000−2i−2i2i2i0000−2i2i0002-20000000000000000−2i2i00000
χ4322-2-2222-2-22-22-22-2-2222022-2-2-2-22-2-200000000-222i−2i2i2i−2i−2i22-2-20000000000000-22-22002i−2i0000002i2i−2i−2i0000−2i2i000-220000000000000000−2i2i00000
χ4422-2-2222-2-22-22-22-2-2222022-2-2-2-22-2-200000000-22−2i2i−2i−2i2i2i22-2-20000000000000-22-2200−2i2i000000−2i−2i2i2i00002i−2i000-2200000000000000002i−2i00000
χ4522-2-22-121-22-2-1-221-2-1-120-12-211-2-1113−30033−3−32-22i−2i−i−iii-1-1110003−333−3−30000-112-2002i−2i00−i3i33−3−i−iii−i3−i3i3i32i−2i000-11000003−300000−i3i300−ii00000
χ4622-2-22-121-22-2-1-221-2-1-120-12-211-2-1113−30033−3−32-2−2i2iii−i−i-1-1110003−333−3−30000-112-200−2i2i00i3−i33−3ii−i−ii3i3−i3−i3−2i2i000-11000003−300000i3−i300i−i00000
χ4722-2-22-121-22-2-1-221-2-1-120-12-211-2-1113−30033−3−3-222i−2i−i−iii-1-1110003−333−3−300001-1-22002i−2i00−i3i3−33−i−iii−i3−i3i3i3−2i2i0001-100000−3300000i3−i300i−i00000
χ4822-2-22-121-22-2-1-221-2-1-120-12-211-2-1113−30033−3−3-22−2i2iii−i−i-1-1110003−333−3−300001-1-2200−2i2i00i3−i3−33ii−i−ii3i3−i3−i32i−2i0001-100000−3300000−i3i300−ii00000
χ4922-2-22-121-22-2-1-221-2-1-120-12-211-2-111−3300−3−3332-22i−2i−i−iii-1-111000−33−3−3330000-112-2002i−2i00i3−i3−33−i−iiii3i3−i3−i32i−2i000-1100000−3300000i3−i300−ii00000
χ5022-2-22-121-22-2-1-221-2-1-120-12-211-2-111−3300−3−3332-2−2i2iii−i−i-1-111000−33−3−3330000-112-200−2i2i00−i3i3−33ii−i−i−i3−i3i3i3−2i2i000-1100000−3300000−i3i300i−i00000
χ5122-2-22-121-22-2-1-221-2-1-120-12-211-2-111−3300−3−333-222i−2i−i−iii-1-111000−33−3−33300001-1-22002i−2i00i3−i33−3−i−iiii3i3−i3−i3−2i2i0001-1000003−300000−i3i300i−i00000
χ5222-2-22-121-22-2-1-221-2-1-120-12-211-2-111−3300−3−333-22−2i2iii−i−i-1-111000−33−3−33300001-1-2200−2i2i00−i3i33−3ii−i−i−i3−i3i3i32i−2i0001-1000003−300000i3−i300−ii00000
χ5344444-2-2-2-244-2-2-2-24-21-241-2-2-21-2-2-21-2-244-2-2-2-2440000001111-2-2-21111110004-2-2-2-200000000-2-20000000000000110000-2110000000000000000
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χ5544444-2-2-2-244-2-2-2-24-21-2-41-2-2-21-2-2-2122-4-42222440000001111222-1-1-1-1-1-1000-4-2-2-2-2000000002200000000000001100002-1-10000000000000000
χ5644444-2-2-2-244-2-2-2-24-21-2-41-2-2-21-2-2-2122-4-42222-4-40000001111222-1-1-1-1-1-10004222200000000-2-20000000000000-1-10000-2110000000000000000
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χ594444-24-24-2-2-24-2-24-2-2-21-4-211-2-21-2-2-2-4-42222220000000011112-1-122-1-1-1-14-4000000-2-2000000000000000000-2220011-1-10000000000000000000
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χ614444-2-24-24-2-2-244-2-21-2-24-2-2-21-2-211-2-2-2-2-211110044-2-2-2-211114-2-2-2-211110040000000-2-2-2-2-2-20011111111000000000000000000000000000000
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χ7644-4-4-2-242-4-22-2-44221-2-20-2-22-1221-12−23230033−3−300−4i4i2i2i−2i−2i11-1-1000−232333−3−300000000002i−2i00−2i32i300−i−iiii3i3−i3−i3000000000000000000000000000000
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χ814-44-44-242-4-4424-4-2-4-2-2402-4422-42-2-20000000000002i3−2i32i3−2i3-22-220000000000000000000000000002i3−2i32i3−2i30000000000000000000000000000000000
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χ854-44-4-2-242-42-224-4-221-2-2022-2-122-11-200003i−3i3i−3i00002i3−2i32i3−2i31-11-1000003i−3i3i−3i000000000000−23230000−i3i3−i3i33−33−3000000000000000000000000000000
χ864-44-4-2-242-42-224-4-221-2-2022-2-122-11-20000−3i3i−3i3i0000−2i32i3−2i32i31-11-100000−3i3i−3i3i000000000000−23230000i3−i3i3−i33−33−3000000000000000000000000000000
χ874-44-4-2-242-42-224-4-221-2-2022-2-122-11-20000−3i3i−3i3i00002i3−2i32i3−2i31-11-100000−3i3i−3i3i00000000000023−230000−i3i3−i3i3−33−33000000000000000000000000000000
χ884-4-4444444-4-4-4-4-4-444440-4-4-4444-4-4-400000000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-24-2-4-4-422-444-2-202224-2-2-4-420000000000000000-222-200000000000000000−2i32i300000000000000000000000−2i32i3000000000000000000000
χ904-4-4444-24-2-4-4-422-444-2-202224-2-2-4-420000000000000000-222-2000000000000000002i3−2i3000000000000000000000002i3−2i3000000000000000000000
χ914-4-444-24-24-4-42-4-424-2-2402-4-4-2-2422200000000000023−23−2323-222-200000000000000000000000000023−23−23230000000000000000000000000000000000
χ924-4-444-24-24-4-42-4-424-2-2402-4-4-2-24222000000000000−232323−23-222-2000000000000000000000000000−232323−230000000000000000000000000000000000
χ934-4-44-2444422-4-4-4-4-2-24-20-422-24-222-400−2i32i3−2i32i32i3−2i300000000-222-20−2i32i300−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ944-4-44-2444422-4-4-4-4-2-24-20-422-24-222-4002i3−2i32i3−2i3−2i32i300000000-222-202i3−2i3002i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ954-4-44-24-24-222-422-4-2-2-2102-1-1-2-2122200−2i32i3−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i300000000−2i32i300000000000000000000000i3−i33-30000000000000000000
χ964-4-44-24-24-222-422-4-2-2-2102-1-1-2-2122200−2i32i3−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i3000000002i3−2i300000000000000000000000−i3i3-330000000000000000000
χ974-4-44-24-24-222-422-4-2-2-2102-1-1-2-21222002i3−2i32i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i300000000−2i32i300000000000000000000000i3−i3-330000000000000000000
χ984-4-44-24-24-222-422-4-2-2-2102-1-1-2-21222002i3−2i32i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i3000000002i3−2i300000000000000000000000−i3i33-30000000000000000000
χ994-4-44-2-24-24222-4-42-21-2-202221-2-2-1-1200−2i32i3i3−i3−i3i3000023−23−23231-1-110−2i32i300i3−i3−i3i3000000000000000000−333−3−3i3i3i−3i000000000000000000000000000000
χ1004-4-44-2-24-24222-4-42-21-2-202221-2-2-1-1200−2i32i3i3−i3−i3i30000−232323−231-1-110−2i32i300i3−i3−i3i30000000000000000003−3−333i−3i−3i3i000000000000000000000000000000
χ1014-4-44-2-24-24222-4-42-21-2-202221-2-2-1-12002i3−2i3−i3i3i3−i3000023−23−23231-1-1102i3−2i300−i3i3i3−i3000000000000000000−333−33i−3i−3i3i000000000000000000000000000000
χ1024-4-44-2-24-24222-4-42-21-2-202221-2-2-1-12002i3−2i3−i3i3i3−i30000−232323−231-1-1102i3−2i300−i3i3i3−i30000000000000000003−3−33−3i3i3i−3i000000000000000000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200000000-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200000000-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ10588-8-8-48-4-84-4484-4-84-4-420-42-244-2-444000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-444-44-44-444222022-2-2-2-22-2-243−4300−23−23232300000000-1-111000−232333−3−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-444-44-44-444222022-2-2-2-22-2-2−4343002323−23−2300000000-1-11100023−23−3−33300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-444-884-44-4-8-42-40-24-44-244-4200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-4-844-4-8-4484-4-4204-2244-24-4-400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4444-44-44-442220-2-22-2-2-2-22200006i−6i6i−6i00000000-11-1100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4444-44-44-442220-2-22-2-2-2-2220000−6i6i−6i6i00000000-11-11000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1128-8-888-4-4-4-4-8-844448-42-40-244-42-444-200000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4-4-4444444-42220-2-2-2222-2-2-200−4i34i32i3−2i3−2i32i300000000-111-102i3−2i300−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-4-4444444-42220-2-2-2222-2-2-2004i3−4i3−2i32i32i3−2i300000000-111-10−2i32i300i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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