Finite Group Databasebeta

← Group #13168182

Character table — Group #13168182

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212444412121212121212121212121212121212224444441212121212121212121212121212121212121212446612121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-11-1-1111111-1-1111111-1-1-1-1111111111-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-11111-1-1-1-111111-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-1-1111
χ51111111111111111111111111111111-1-1111111111111111111-111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-11-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111111111-1-111-1-1-1-111-1-1-1-1-1-11-1-1-11111-1-111-1-1-1111-1-111-11-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-11-1-111-1-111-1-111-1-11-1-1-111111-11-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1-1-111111111-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-111-1-11111-11-1111-1-1-1-11111-1-111-1-1-1-1-1-111-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-111111-11-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-11111-1-1111111-1-1111111-1-111-1-111-1-1-1-111-1-11111-1-1-1-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-1-1-11-111-1-111-1-111-1-1111-1-1-111111-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1111-1-1-1-111-1-111-1111-1-111-111-1
χ17222222-1-1222-1-12222-1-122-1-1-12-1-12-1222200-1-1-1-1-1222-1-1-1-1-1-1-1-12220222222-1-1-1-1000000220000000000-1-120-1-1-1-10000-1-1-1-120-1-10000-1000
χ18222222-1-1222-1-12222-1-122-1-1-12-1-12-1222200-1-1-1-1-1222-1-1-1-1-1-1-1-12-2-20-2-22222-1-111000000-2-20000000000-11-2011110000-1-1-1-1-201100001000
χ19222222-1-1222-1-12222-1-122-1-1-12-1-12-122-2-200-1-1-1-1-1222-1-1-1-1-1-1-1-1-222022-2-2-2-211-1-1000000-2-200000000001-120-1-1-1-100001111-201100001000
χ20222222-1-1222-1-12222-1-122-1-1-12-1-12-122-2-200-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-20-2-2-2-2-2-2111100000022000000000011-2011110000111120-1-10000-1000
χ21222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-11-2-2-211111111-22-20-2-222-2-2-1-1-1-1000000220000000000112011-1-10000-1-111-20-1-100001000
χ22222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-11-2-2-211111111-2-2202222-2-2-1-111000000-2-200000000001-1-20-1-1110000-1-11120110000-1000
χ23222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-11-2-2-21111111122-20-2-2-2-22211-1-1000000-2-20000000000-112011-1-1000011-1-120110000-1000
χ24222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-11-2-2-2111111112-22022-2-2221111000000220000000000-1-1-20-1-111000011-1-1-20-1-100001000
χ2522222-1222-1-12222-1-12-12-12-1-1-122-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1200200-1-1-1-1220022-1-1-1-100002222-1-1-1-120020000-1-1-1-1-1-1-1-1000000-1-10000
χ2622222-1222-1-12222-1-12-12-12-1-1-122-1-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-1200-200-1-1-1-12200-2-211110000-2-2-2-21111200-200001111-1-1-1-1000000110000
χ2722222-1222-1-12222-1-12-12-12-1-1-122-1-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-2002001111-2-20022-1-1-1-10000-2-2-2-21111-20020000-1-1-1-11111000000110000
χ2822222-1222-1-12222-1-12-12-12-1-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-200-2001111-2-200-2-2111100002222-1-1-1-1-200-2000011111111000000-1-10000
χ2922222-1222-1-12222-1-12-1-2-12-1-1-122-1-1112222-1-1-1-1-2-211-2-2111111-200-200-1-111220022-1-1110000-2-2221111-200-20000-1-111-1-111000000-1-10000
χ3022222-1222-1-12222-1-12-1-2-12-1-1-122-1-11122-2-2-1-1-1-1-2-211-2-2111111-200200-1-1112200-2-211-1-1000022-2-2-1-1-1-1-2002000011-1-1-1-111000000110000
χ3122222-1222-1-12222-1-12-1-2-12-1-1-122-1-111-2-222-1-1-1-1-2-211-2-2111111200-20011-1-1-2-20022-1-111000022-2-2-1-1-1-1200-20000-1-11111-1-1000000110000
χ3222222-1222-1-12222-1-12-1-2-12-1-1-122-1-111-2-2-2-2-1-1-1-1-2-211-2-211111120020011-1-1-2-200-2-211-1-10000-2-22211112002000011-1-111-1-1000000-1-10000
χ332222-1222-12222-1-12-1-122-1-122-1-1-1-12220022-1-1-1-12-1-1-1-1-122-1-1-1-10222-1-100000022-1-1222200220000000002-1-1-1-1-1-1-1-1-1-100000200-1-1000-100
χ342222-1222-12222-1-12-1-122-1-122-1-1-1-12220022-1-1-1-12-1-1-1-1-122-1-1-1-10-2-2211000000-2-2-1-1222200-2-2000000000-21-11111-1-1-1-100000-20011000100
χ352222-1222-12222-1-12-1-122-1-122-1-1-1-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1022-2-1-10000002211-2-2-2-200-2-20000000002-11-1-1-1-1111100000-20011000100
χ362222-1222-12222-1-12-1-122-1-122-1-1-1-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-10-2-2-211000000-2-211-2-2-2-20022000000000-2111111111100000200-1-1000-100
χ372222-1222-12222-1-12-1-12-2-1-122-1-1-1-12-2-20022-1-1-1-1-211111-2-2111102-2-21100000022-1-122-2-200-2-2000000000-2-1111-1-1-1-1110000020011000-100
χ382222-1222-12222-1-12-1-12-2-1-122-1-1-1-12-2-20022-1-1-1-1-211111-2-211110-22-2-1-1000000-2-2-1-122-2-20022000000000211-1-111-1-11100000-200-1-1000100
χ392222-1222-12222-1-12-1-12-2-1-122-1-1-1-12-2-200-2-2-1-1-1-1-211111-2-2111102-22110000002211-2-2220022000000000-2-1-111-1-111-1-100000-200-1-1000100
χ402222-1222-12222-1-12-1-12-2-1-122-1-1-1-12-2-200-2-2-1-1-1-1-211111-2-211110-222-1-1000000-2-211-2-22200-2-200000000021-1-1-11111-1-10000020011000-100
χ4122-2-2222-2-22-22-22-2-22220-2-2-2-22-22-22002-22i−2i2-2-220000000000000000002-2002-2002i−2i2i−2i000000002i−2i0000000000002i−2i002-2000000002i−2i0000
χ4222-2-2222-2-22-22-22-2-22220-2-2-2-22-22-22002-2−2i2i2-2-220000000000000000002-2002-200−2i2i−2i2i00000000−2i2i000000000000−2i2i002-200000000−2i2i0000
χ4322-2-2222-2-22-22-22-2-22220-2-2-2-22-22-2200-222i−2i2-2-22000000000000000000-2200-22002i−2i2i−2i00000000−2i2i0000000000002i−2i00-2200000000−2i2i0000
χ4422-2-2222-2-22-22-22-2-22220-2-2-2-22-22-2200-22−2i2i2-2-22000000000000000000-2200-2200−2i2i−2i2i000000002i−2i000000000000−2i2i00-22000000002i−2i0000
χ4522-2-22-12-2-2-112-22-21-12-101-211-1-221-1−i3i32-22i−2i-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i32-2002i−2i−ii3−30000002i−2i33−3−300000000−ii3−3-11−i3i3000000−ii0000
χ4622-2-22-12-2-2-112-22-21-12-101-211-1-221-1−i3i32-2−2i2i-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i32-200−2i2ii−i−33000000−2i2i−3−33300000000i−i−33-11−i3i3000000i−i0000
χ4722-2-22-12-2-2-112-22-21-12-101-211-1-221-1−i3i3-222i−2i-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i3-22002i−2i−ii3−3000000−2i2i−3−33300000000−ii3−31-1i3−i3000000i−i0000
χ4822-2-22-12-2-2-112-22-21-12-101-211-1-221-1−i3i3-22−2i2i-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i3-2200−2i2ii−i−330000002i−2i33−3−300000000i−i−331-1i3−i3000000−ii0000
χ4922-2-22-12-2-2-112-22-21-12-101-211-1-221-1i3−i32-22i−2i-111-100i3−i300i3−i3i3i3−i3−i3000000-11i3−i32-2002i−2i−ii−330000002i−2i−3−33300000000−ii−33-11i3−i3000000−ii0000
χ5022-2-22-12-2-2-112-22-21-12-101-211-1-221-1i3−i32-2−2i2i-111-100i3−i300i3−i3i3i3−i3−i3000000-11i3−i32-200−2i2ii−i3−3000000−2i2i33−3−300000000i−i3−3-11i3−i3000000i−i0000
χ5122-2-22-12-2-2-112-22-21-12-101-211-1-221-1i3−i3-222i−2i-111-100i3−i300i3−i3i3i3−i3−i30000001-1−i3i3-22002i−2i−ii−33000000−2i2i33−3−300000000−ii−331-1−i3i3000000i−i0000
χ5222-2-22-12-2-2-112-22-21-12-101-211-1-221-1i3−i3-22−2i2i-111-100i3−i300i3−i3i3i3−i3−i30000001-1−i3i3-2200−2i2ii−i3−30000002i−2i−3−33300000000i−i3−31-1−i3i3000000−ii0000
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χ5744444-2-2-24-2-2-2-244-2-2-214-2-211-2-2-2-21-2-244001111-24-2-2-2-2111111400000-2-2-2-2-2-200000000000000000000-2000000000001111000000000000
χ5844444-2-2-24-2-2-2-244-2-2-214-2-211-2-2-2-21-2-2-4-4001111-24-2-2-2-2111111-40000022222200000000000000000000200000000000-1-1-1-1000000000000
χ5944444-2-2-24-2-2-2-244-2-2-21-4-2-211-2-2-2-2122440011112-42222-1-1-1-1-1-1-400000-2-222-2-20000000000000000000020000000000011-1-1000000000000
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χ614444-24-2-2-244-2-2-2-24-21-24-21-2-2-211-2-24400001111-2-2-2-211-2-211110440-2-2000000-2-20000000000000000000-2-20111100000000000000000000
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χ864-44-4-244-4-2-44-4422-4-2-240-22-442-222-4000000-22-220000000000000000−2i32i3000000000000000000000000000000−2i32i30000000000000000000000
χ874-44-4-244-4-2-44-4422-4-2-240-22-442-222-4000000-22-2200000000000000002i3−2i30000000000000000000000000000002i3−2i30000000000000000000000
χ884-44-4-24-22-2-442-222-4-21-20-2-12-221-1220000001-11-100003i−3i003i−3i3i−3i0000−2i32i300000023−230000000000000000000000i3−i3−3300000000000000000000
χ894-44-4-24-22-2-442-222-4-21-20-2-12-221-1220000001-11-100003i−3i003i−3i3i−3i00002i3−2i3000000−23230000000000000000000000−i3i33−300000000000000000000
χ904-44-4-24-22-2-442-222-4-21-20-2-12-221-1220000001-11-10000−3i3i00−3i3i−3i3i0000−2i32i3000000−23230000000000000000000000i3−i33−300000000000000000000
χ914-44-4-24-22-2-442-222-4-21-20-2-12-221-1220000001-11-10000−3i3i00−3i3i−3i3i00002i3−2i300000023−230000000000000000000000−i3i3−3300000000000000000000
χ924-4-4444-2-2-4-4-422-4444-2-20-4-2-22-42242000000-2-222000000000000000000000000000000004-40000000000000000000000000000-2200000000
χ934-4-4444-2-2-4-4-422-4444-2-20-4-2-22-42242000000-2-22200000000000000000000000000000000-4400000000000000000000000000002-200000000
χ944-4-444-244-422-4-4-44-2-24-2024-222-4-4-22000000-2-2220000000000000000000000000000000000004i−4i00−2i2i−2i2i0000000000000000000000000000
χ954-4-444-244-422-4-4-44-2-24-2024-222-4-4-22000000-2-222000000000000000000000000000000000000−4i4i002i−2i2i−2i0000000000000000000000000000
χ964-4-44-24442-4-4-4-42-24-2-2402-24-4222-2-4000000-2-22200000000000000000000000000000000004i−4i0000000000000000000000000000−2i2i000000
χ974-4-44-24442-4-4-4-42-24-2-2402-24-4222-2-4000000-2-2220000000000000000000000000000000000−4i4i00000000000000000000000000002i−2i000000
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
χ10088-8-8-48-4448-8-44-44-8-42-404-244-4-224-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-444-44-44-4442220-2-2-2-22-22-22−4i34i30000-111-1002i3−2i3002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-444-44-44-4442220-2-2-2-22-22-224i3−4i30000-111-100−2i32i300−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-4484-44-4-8-84-4-420-44-224-444-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-48-8-44-4-884442-4-40244-4-2-44-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-44-44-44-444422202-2-22-22-2-2-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-44-44-44-444422202-2-22-22-2-2-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-4-4-84444-88-4-4-4204-42-2444-4-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-4-44-8-8444-48-42-4042-444-2-2-4400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-488444-8-84-4-42-4-40-2-4-44-2442400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-4444444-4-42220-222-2-2-2-22-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-4444444-4-42220-222-2-2-2-22-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000

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