Finite Group Databasebeta

← Group #13168426

Character table — Group #13168426

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order122233366666666633346666666661212121212121212444412121212366612121212121212121222446612121212121212121212121212121212121212124466666661212121212244441212121212126121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-111-1-11111111111111111111111-1-1-1-1-1-1-111111-11-1-1-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-111-1-1-1-11-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-11111111111111111111111-1111111-1-1-1-1-1-11111111111-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111-1-11111111111111111111-1-11-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11-1-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-11111-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-111-1-11111-1-1-1-1111-1-111-1-1-111-1-1-1-111-11111-1-1-11-11-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-111-1-111-111-1-11-1-1-11-1-111-1-11-11-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-11111-1-1-1-11111-1-11-1-111-1-1-111-1-1-111-1111-1-111-1-11-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-111-1-111-111-1-111-11-1-1-1-1-11111-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-1-111-1-11-1-11111-11-1-1-1-1-11111-1-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1111-1-111-111-1111-1-111-1-111-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111-1-111-1-111-1-111-1-1-1-11111111-1-111-1-11-1-1111-1-1-11-1-111-1-11-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-111-1-1-1-1111111-111-1-1111-1-111-1-111-11111-1-1-11-1-11
χ17222222-1-1222-1-12222-1-12-1-1-12-122-1-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-12202-1-10000-1-1222200000000000022-1-1-1-1-1-1-1-1-1-120200-1-10000-10000
χ18222222-1-1222-1-12222-1-12-1-1-12-122-1-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-202110000-1-12222000000000000-2-211111-1-1-1-1-1-20-20011000010000
χ19222222-1-1222-1-12222-1-12-1-1-12-122-1-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1220-2-1-1000011-2-2-2-200000000000022-1-1-1-1-111111-20-20011000010000
χ20222222-1-1222-1-12222-1-12-1-1-12-122-1-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-211000011-2-2-2-2000000000000-2-2111111111120200-1-10000-10000
χ21222222-1-1222-1-12222-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-222000000-1-1-1-11111111112-20-2-1-10000-1-1-2-2220000000000002-21-1-1111-1-111-20200-1-1000010000
χ22222222-1-1222-1-12222-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-220-2110000-1-1-2-222000000000000-22-111-1-11-1-11120-200110000-10000
χ23222222-1-1222-1-12222-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-11111111112-202-1-100001122-2-20000000000002-21-1-111-111-1-120-200110000-10000
χ24222222-1-1222-1-12222-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-1111111111-22021100001122-2-2000000000000-22-111-1-1-111-1-1-20200-1-1000010000
χ2522222-1222-1-12222-1-12-122-1-1-1-1-1-12222-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-1222022-1-1-1-100000022-1-1-1-1-1-1-1-100-1-12-1-1-1-100000000220000000-1-100
χ2622222-1222-1-12222-1-12-122-1-1-1-1-1-12222-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-1-2-220-2-2-1-1-1-100000022-1-1-1-1-1-1-1-10011-2111100000000-2-200000001100
χ2722222-1222-1-12222-1-12-122-1-1-1-1-1-12222-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-122-20221111000000-2-21111111100-1-12-1-1-1-100000000-2-200000001100
χ2822222-1222-1-12222-1-12-122-1-1-1-1-1-12222-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-2-2-20-2-21111000000-2-2111111110011-2111100000000220000000-1-100
χ2922222-1222-1-12222-1-12-1-22-1-1-1-1-1-122-2-211111100222222-1-1-1-1-211-2-211112-2-2022-1-111000000-2-2-1-1-1-1111100-11-2-1-111000000002-20000000-1100
χ3022222-1222-1-12222-1-12-1-22-1-1-1-1-1-122-2-211111100222222-1-1-1-1-211-2-21111-22-20-2-2-1-111000000-2-2-1-1-1-11111001-1211-1-100000000-2200000001-100
χ3122222-1222-1-12222-1-12-1-22-1-1-1-1-1-122-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-211112-2202211-1-1000000221111-1-1-1-100-11-2-1-11100000000-2200000001-100
χ3222222-1222-1-12222-1-12-1-22-1-1-1-1-1-122-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-21111-2220-2-211-1-1000000221111-1-1-1-1001-1211-1-1000000002-20000000-1100
χ332222-1222-12222-1-12-1-122-122-12-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1002200222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12200000002-1-1-1-10200000-1-1-1-100000
χ342222-1222-12222-1-12-1-122-122-12-1-1-1-1-1-122-1-1-1-122-2-21111-1-1-1-1222-1-1-1-1-1-100-2200-2-2-2-222-1-1-1-11111111111-2-200000002-1-1-1-10-200000111100000
χ352222-1222-12222-1-12-1-122-122-12-1-1-1-1-1-122-1-1-1-1-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1002-2002222-2-21111-1-1-1-1-1-1-1-1-1-1-2-20000000-211110-200000111100000
χ362222-1222-12222-1-12-1-122-122-12-1-1-1-1-1-122-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-100-2-200-2-2-2-2-2-211111111111111220000000-211110200000-1-1-1-100000
χ372222-1222-12222-1-12-1-12-2-122-12-1-1-1-111-2-211112222-1-1-1-1-1-1-1-1-2-2-211111100-2-20022-2-22211-1-111-1-1-1-11111220000000-2-1-1110-200000-1-11100000
χ382222-1222-12222-1-12-1-12-2-122-12-1-1-1-111-2-2111122-2-21111-1-1-1-1-2-2-2111111002-200-2-2222211-1-1-1-11111-1-1-1-1-2-20000000-2-1-111020000011-1-100000
χ392222-1222-12222-1-12-1-12-2-122-12-1-1-1-111-2-21111-2-222-1-1-1-1-1-1-1-1-2-2-211111100-220022-2-2-2-2-1-11111-1-1-1-11111-2-20000000211-1-1020000011-1-100000
χ402222-1222-12222-1-12-1-12-2-122-12-1-1-1-111-2-21111-2-2-2-21111-1-1-1-1-2-2-2111111002200-2-222-2-2-1-111-1-11111-1-1-1-1220000000211-1-10-200000-1-11100000
χ4122-2-2222-2-22-2-22-22-22220-22-2-2-22-22-2000000002-22i−2i2i2i−2i−2i22-2-20000000000000002i−2i002-2002-2002i2i−2i−2i00002i−2i000000002-20000000002i−2i0000000
χ4222-2-2222-2-22-2-22-22-22220-22-2-2-22-22-2000000002-2−2i2i−2i−2i2i2i22-2-2000000000000000−2i2i002-2002-200−2i−2i2i2i0000−2i2i000000002-2000000000−2i2i0000000
χ4322-2-2222-2-22-2-22-22-22220-22-2-2-22-22-200000000-222i−2i2i2i−2i−2i22-2-20000000000000002i−2i00-2200-22002i2i−2i−2i0000−2i2i00000000-22000000000−2i2i0000000
χ4422-2-2222-2-22-2-22-22-22220-22-2-2-22-22-200000000-22−2i2i−2i−2i2i2i22-2-2000000000000000−2i2i00-2200-2200−2i−2i2i2i00002i−2i00000000-220000000002i−2i0000000
χ4522-2-2-122-212-2-221-1-2-1-12012-21-2-11-113−30033−3−32-22i−2i−i−iii-1-1110003−333−3−30000002i−2i002-23−3-11−i3i3−i−iii−i3−i3i3i32i−2i00000000-113−30000000−ii−i3i300000
χ4622-2-2-122-212-2-221-1-2-1-12012-21-2-11-113−30033−3−32-2−2i2iii−i−i-1-1110003−333−3−3000000−2i2i002-23−3-11i3−i3ii−i−ii3i3−i3−i3−2i2i00000000-113−30000000i−ii3−i300000
χ4722-2-2-122-212-2-221-1-2-1-12012-21-2-11-113−30033−3−3-222i−2i−i−iii-1-1110003−333−3−30000002i−2i00-22−331-1−i3i3−i−iii−i3−i3i3i3−2i2i000000001-1−330000000i−ii3−i300000
χ4822-2-2-122-212-2-221-1-2-1-12012-21-2-11-113−30033−3−3-22−2i2iii−i−i-1-1110003−333−3−3000000−2i2i00-22−331-1i3−i3ii−i−ii3i3−i3−i32i−2i000000001-1−330000000−ii−i3i300000
χ4922-2-2-122-212-2-221-1-2-1-12012-21-2-11-11−3300−3−3332-22i−2i−i−iii-1-111000−33−3−3330000002i−2i002-2−33-11i3−i3−i−iiii3i3−i3−i32i−2i00000000-11−330000000−iii3−i300000
χ5022-2-2-122-212-2-221-1-2-1-12012-21-2-11-11−3300−3−3332-2−2i2iii−i−i-1-111000−33−3−333000000−2i2i002-2−33-11−i3i3ii−i−i−i3−i3i3i3−2i2i00000000-11−330000000i−i−i3i300000
χ5122-2-2-122-212-2-221-1-2-1-12012-21-2-11-11−3300−3−333-222i−2i−i−iii-1-111000−33−3−3330000002i−2i00-223−31-1i3−i3−i−iiii3i3−i3−i3−2i2i000000001-13−30000000i−i−i3i300000
χ5222-2-2-122-212-2-221-1-2-1-12012-21-2-11-11−3300−3−333-22−2i2iii−i−i-1-111000−33−3−333000000−2i2i00-223−31-1−i3i3ii−i−i−i3−i3i3i32i−2i000000001-13−30000000−iii3−i300000
χ5344444-2-2-24-2-2-2-244-2-2-214-211-21-2-2-2-244-2-2-2-2-2-2000000001111-211-2-211114400-2-20000000000000000000000-2-2-21111000000000000000000000
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χ5544444-2-2-24-2-2-2-244-2-2-21-4-211-21-2-2-2-2-4-42222220000000011112-1-122-1-1-1-14-400-2-20000000000000000000000-22211-1-1000000000000000000000
χ5644444-2-2-24-2-2-2-244-2-2-21-4-211-21-2-2-2-2-4-42222220000000011112-1-122-1-1-1-1-44002200000000000000000000002-2-2-1-111000000000000000000000
χ574444-24-2-2-244-2-2-2-24-21-241-2-2-2-2-2-211-2-244-2-2-2-2440000001111-2-2-21111110004000000-2-2-2-2-2-20000000000000000000-211110000000000000000
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χ594444-24-2-2-244-2-2-2-24-21-2-41-2-2-2-2-2-21122-4-42222440000001111222-1-1-1-1-1-1000-4000000-2-222-2-20000000000000000000211-1-10000000000000000
χ604444-24-2-2-244-2-2-2-24-21-2-41-2-2-2-2-2-21122-4-42222-4-40000001111222-1-1-1-1-1-1000400000022-2-2220000000000000000000-2-1-1110000000000000000
χ614444-2-244-2-2-244-2-2-21-2-24-2-2-21-211-2-2-2-2-2-211110044-2-2-2-211114-2-2-2-21111004000-2-2-2-2000000-2-211111111000000000000000000000000000000
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χ7644-4-4-2-24-42-22-442-221-2-202-22-121-1-22−23230033−3−300−4i4i2i2i−2i−2i11-1-1000−232333−3−30000002i−2i00000000−2i32i3−i−iiii3i3−i3−i3000000000000000000000000000000
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χ814-44-44-24442-2-4-4-4-42-24-2042-2222-2-4-40000000000000000-22-2200000000000000000−2323000000000000−2323−2323000000000000000000000000000000
χ824-44-4-2444-2-44-4-422-4-2-240-2-442-42-222000000000000−2i32i3−2i32i3-22-22000000000000000000000000000−2i32i3−2i32i30000000000000000000000000000000000
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χ844-44-4-2-244-22-2-4-42221-2-20-22-2-12-112200003i−3i3i−3i0000−2i32i3−2i32i31-11-1000003i−3i3i−3i0000000023−2300000000i3−i3i3−i3−33−33000000000000000000000000000000
χ854-44-4-2-244-22-2-4-42221-2-20-22-2-12-112200003i−3i3i−3i00002i3−2i32i3−2i31-11-1000003i−3i3i−3i00000000−232300000000−i3i3−i3i33−33−3000000000000000000000000000000
χ864-44-4-2-244-22-2-4-42221-2-20-22-2-12-11220000−3i3i−3i3i0000−2i32i3−2i32i31-11-100000−3i3i−3i3i00000000−232300000000i3−i3i3−i33−33−3000000000000000000000000000000
χ874-44-4-2-244-22-2-4-42221-2-20-22-2-12-11220000−3i3i−3i3i00002i3−2i32i3−2i31-11-100000−3i3i−3i3i0000000023−2300000000−i3i3−i3i3−33−33000000000000000000000000000000
χ884-4-44444-4-4-4-44-44-444440-4-4-444-4-4-4400000000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-22-4-4-4-224-444-2-202224-2-4-42-20000000000000000-222-20000000000000−2i32i30000000000000000000000000−2i32i300000000000000000000000
χ904-4-4444-22-4-4-4-224-444-2-202224-2-4-42-20000000000000000-222-200000000000002i3−2i300000000000000000000000002i3−2i300000000000000000000000
χ914-4-444-24-4-4224-44-4-2-24-20-422-2-222-4400−2i32i3−2i32i32i3−2i300000000-222-20−2i32i300−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ924-4-444-24-4-4224-44-4-2-24-20-422-2-222-44002i3−2i32i3−2i3−2i32i300000000-222-202i3−2i3002i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ934-4-444-2-22-422-224-4-2-2-2102-1-1-21222-200−2i32i3−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i30000−2i32i30000000000000000000000000i3−i33-3000000000000000000000
χ944-4-444-2-22-422-224-4-2-2-2102-1-1-21222-200−2i32i3−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i300002i3−2i30000000000000000000000000−i3i3-33000000000000000000000
χ954-4-444-2-22-422-224-4-2-2-2102-1-1-21222-2002i3−2i32i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i30000−2i32i30000000000000000000000000i3−i3-33000000000000000000000
χ964-4-444-2-22-422-224-4-2-2-2102-1-1-21222-2002i3−2i32i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i300002i3−2i30000000000000000000000000−i3i33-3000000000000000000000
χ974-4-44-244-42-4-44-4-224-2-2402-4-4-24222-200000000000023−23−2323-222-200000000000000000000000000023−23−23230000000000000000000000000000000000
χ984-4-44-244-42-4-44-4-224-2-2402-4-4-24222-2000000000000−232323−23-222-2000000000000000000000000000−232323−230000000000000000000000000000000000
χ994-4-44-2-24-42224-4-22-21-2-202221-2-1-12-200−2i32i3i3−i3−i3i3000023−23−23231-1-110−2i32i300i3−i3−i3i3000000000000000000−333−3−3i3i3i−3i000000000000000000000000000000
χ1004-4-44-2-24-42224-4-22-21-2-202221-2-1-12-200−2i32i3i3−i3−i3i30000−232323−231-1-110−2i32i300i3−i3−i3i30000000000000000003−3−333i−3i−3i3i000000000000000000000000000000
χ1014-4-44-2-24-42224-4-22-21-2-202221-2-1-12-2002i3−2i3−i3i3i3−i3000023−23−23231-1-1102i3−2i300−i3i3i3−i3000000000000000000−333−33i−3i−3i3i000000000000000000000000000000
χ1024-4-44-2-24-42224-4-22-21-2-202221-2-1-12-2002i3−2i3−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
χ10588-8-88-4-44-8-444-4-884-4-42042-24-2-44-44000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-444-444-44-442220-22-2-2-22-22-243−4300−23−23232300000000-1-111000−232333−3−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-444-444-44-442220-22-2-2-22-22-2−4343002323−23−2300000000-1-11100023−23−3−33300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-484-444-8-84-4-420-4-224-24-44400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-4-4-4-884444-8-42-4024-4444-4-2-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-4-44-44444422202-22-2-2-22-2-200006i−6i6i−6i00000000-11-1100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4-4-44-44444422202-22-2-2-22-2-20000−6i6i−6i6i00000000-11-11000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-444-8-8-44-448-42-40-244-4-444-2200000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-44444-44-44-42220-2-2-222-2-2-2200−4i34i32i3−2i3−2i32i300000000-111-102i3−2i300−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-44444-44-44-42220-2-2-222-2-2-22004i3−4i3−2i32i32i3−2i300000000-111-10−2i32i300i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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