Finite Group Databasebeta

← Group #13170792

Character table — Group #13170792

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order12223336666666663334666666666121244444436661212121212121212121212122222444121212121212121212121212121212122222666612121212121212121212121212121212444666612124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-111111111111111111111-111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1-1-1-111-11111-1-1-1-111-1-1111111-1-1-1-1-1-1111-111111111-1-1-1-1-11-111-1-1-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-11-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-11-1-111-1-111-111
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-11-11-1-1-1-11111-1-1111111-1-111-1-1-1-111-111111-1-1-1-11111-1-11-1-111-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-11-111-1-1-1-1111-11
χ71111111111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-11
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-11111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-11111-1-111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-111-1-1-1-1-1-1-1-1111
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1111-1111-1-111-1-1-111
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-11-1-11111-1-1-1-11111-1-1-11111111-1-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11-111-1-1-1-11111-1-111-1-1-11111-1-11-11
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111-1-1-111-1-11111-1-11-1111-1-11111-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-111-111-1-1-1-1-1-11111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-1-11111-1-1-1-1-1-11
χ17222222-122-122-1-1222-1-122-1-1-1-122-1-1-1-1222200-1-1-1-122-1-1-1-122-1-1-1-12222022-1-1-1-1-1-1-1-1222200000000-1-1-1-100220000-1-1-1-1-1-1-1-12000000-1-100000
χ18222222-122-122-1-1222-1-122-1-1-1-122-1-1-1-122-2-200-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-202-2-1-1-1-1111122-2-2000000001111002-20000-1-1-1-11111-20000001100000
χ19222222-122-122-1-1222-1-122-1-1-1-122-1-1-1-1-2-22200-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-20-221111-1-1-1-1-2-22200000000111100-2200001111-1-1-1-1-20000001100000
χ20222222-122-122-1-1222-1-122-1-1-1-122-1-1-1-1-2-2-2-200-1-1-1-122-1-1-1-122-1-1-1-122220-2-211111111-2-2-2-200000000-1-1-1-100-2-20000111111112000000-1-100000
χ21222222-122-122-1-1222-1-1-22-1-1-1-122-1-111222200-1-1-1-1-2-21111-2-2111122220-2-2-1-111-1-111222200000000-1-1-1-100-2-20000-1-111-1-111-20000001100000
χ22222222-122-122-1-1222-1-1-22-1-1-1-122-1-11122-2-200-1-1-1-1-2-21111-2-21111-2-2-2-20-22-1-11111-1-122-2-200000000111100-220000-1-11111-1-12000000-1-100000
χ23222222-122-122-1-1222-1-1-22-1-1-1-122-1-111-2-22200-1-1-1-1-2-21111-2-21111-2-2-2-202-211-1-1-1-111-2-222000000001111002-2000011-1-1-1-1112000000-1-100000
χ24222222-122-122-1-1222-1-1-22-1-1-1-122-1-111-2-2-2-200-1-1-1-1-2-21111-2-21111222202211-1-111-1-1-2-2-2-200000000-1-1-1-10022000011-1-111-1-1-20000001100000
χ2522222-122-122-1222-1-12-12-12-12-1-1-12-122002222-1-1-1-12-122-1-1-1-1-1-1-1-100002020000222200-1-122-1-1002200002-10-1-1-1-1-10000-1-1-1-100200-1-100000-10
χ2622222-122-122-1222-1-12-12-12-12-1-1-12-1220022-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10000-2020000222200-1-1-2-21100-2-20000-210-111110000-1-1-1-100-200110000010
χ2722222-122-122-1222-1-12-12-12-12-1-1-12-12200-2-222-1-1-1-12-122-1-1-1-1-1-1-1-1000020-20000-2-2-2-2001122-1-100-2-200002-101-1-1-1-10000111100-200110000010
χ2822222-122-122-1222-1-12-12-12-12-1-1-12-12200-2-2-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10000-20-20000-2-2-2-20011-2-21100220000-210111110000111100200-1-100000-10
χ2922222-122-122-1222-1-12-1-2-12-12-1-1-12-1-2-2002222-1-1-1-1-21-2-2111111110000-20-2000022-2-200-1-122-1-100220000-2101-1-1110000-1-11100-200-1-10000010
χ3022222-122-122-1222-1-12-1-2-12-12-1-1-12-1-2-20022-2-2-1-1-1-1-21-2-211111111000020-2000022-2-200-1-1-2-21100-2-200002-10111-1-10000-1-111002001100000-10
χ3122222-122-122-1222-1-12-1-2-12-12-1-1-12-1-2-200-2-222-1-1-1-1-21-2-2111111110000-2020000-2-222001122-1-100-2-20000-210-1-1-111000011-1-1002001100000-10
χ3222222-122-122-1222-1-12-1-2-12-12-1-1-12-1-2-200-2-2-2-2-1-1-1-1-21-2-21111111100002020000-2-2220011-2-211002200002-10-111-1-1000011-1-100-200-1-10000010
χ332222-122-122-1222-12-1-122-1-12-12-1-1-1222220022-1-1-1-1-12-1-122-1-1-1-1-1-1000022022220000-1-100-1-12222000000-12-10-1-1-1-1-1-1-1-10000020-1-1000000-100
χ342222-122-122-1222-12-1-122-1-12-12-1-1-12222200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-10000-22022220000-1-10011-2-2-2-20000001-2-101111-1-1-1-100000-2011000000100
χ352222-122-122-1222-12-1-122-1-12-12-1-1-1222-2-20022-1-1-1-1-12-1-122-1-1-1-1-1-100002-20-2-2-2-200001100-1-122-2-2000000-1210-1-1-1-1111100000-2011000000100
χ362222-122-122-1222-12-1-122-1-12-12-1-1-1222-2-200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-10000-2-20-2-2-2-20000110011-2-2220000001-210111111110000020-1-1000000-100
χ372222-122-122-1222-12-1-12-2-1-12-12-1-1-12-2-2220022-1-1-1-11-211-2-21111110000-2-2022-2-20000-1-100-1-122220000001-210-1-111-1-11100000-20-1-1000000100
χ382222-122-122-1222-12-1-12-2-1-12-12-1-1-12-2-22200-2-2-1-1-1-11-211-2-211111100002-2022-2-20000-1-10011-2-2-2-2000000-121011-1-1-1-111000002011000000-100
χ392222-122-122-1222-12-1-12-2-1-12-12-1-1-12-2-2-2-20022-1-1-1-11-211-2-21111110000-220-2-22200001100-1-122-2-20000001-2-10-1-11111-1-1000002011000000-100
χ402222-122-122-1222-12-1-12-2-1-12-12-1-1-12-2-2-2-200-2-2-1-1-1-11-211-2-21111110000220-2-2220000110011-2-222000000-12-1011-1-111-1-100000-20-1-1000000100
χ4122-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-20000000022-2-200000000000022-2-200000000000000000002-22-222-2-200000000000000000002-22-20000000
χ4222-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-20000000022-2-200000000000022-2-20000000000000000000-22-2222-2-20000000000000000000-22-220000000
χ4322-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-20000000022-2-2000000000000-2-22200000000000000000002-2-22-2-22200000000000000000002-2-220000000
χ4422-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-20000000022-2-2000000000000-2-2220000000000000000000-222-2-2-2220000000000000000000-222-20000000
χ452-22-2222-2-2-2222-2-2-22220-2-2-222-22-2-2002i−2i2i−2i002-2-220000000000002-22-20002i−2i002i−2i002i−2i2i−2i000000002-22-2000000002i−2i002i−2i0000000000000000
χ462-22-2222-2-2-2222-2-2-22220-2-2-222-22-2-2002i−2i−2i2i002-2-22000000000000-22-220002i−2i00−2i2i002i−2i−2i2i00000000-22-22000000002i−2i00−2i2i0000000000000000
χ472-22-2222-2-2-2222-2-2-22220-2-2-222-22-2-200−2i2i2i−2i002-2-22000000000000-22-22000−2i2i002i−2i00−2i2i2i−2i00000000-22-2200000000−2i2i002i−2i0000000000000000
χ482-22-2222-2-2-2222-2-2-22220-2-2-222-22-2-200−2i2i−2i2i002-2-220000000000002-22-2000−2i2i00−2i2i00−2i2i−2i2i000000002-22-200000000−2i2i00−2i2i0000000000000000
χ492-22-222-1-2-2122-11-2-22-1-10-211-1-1-2211−i3i32i−2i2i−2i00-111-100−i3i3−i3i300−i3−i3i3i32-22-2000−ii3−3−ii3−32i−2i2i−2i00000000-11-1100000000−ii3−3−ii3−30000000−i3i300000
χ502-22-222-1-2-2122-11-2-22-1-10-211-1-1-2211−i3i32i−2i−2i2i00-111-100−i3i3−i3i300−i3−i3i3i3-22-22000−ii3−3i−i−332i−2i−2i2i000000001-11-100000000−ii3−3i−i−330000000i3−i300000
χ512-22-222-1-2-2122-11-2-22-1-10-211-1-1-2211−i3i3−2i2i2i−2i00-111-100−i3i3−i3i300−i3−i3i3i3-22-22000i−i−33−ii3−3−2i2i2i−2i000000001-11-100000000i−i−33−ii3−30000000i3−i300000
χ522-22-222-1-2-2122-11-2-22-1-10-211-1-1-2211−i3i3−2i2i−2i2i00-111-100−i3i3−i3i300−i3−i3i3i32-22-2000i−i−33i−i−33−2i2i−2i2i00000000-11-1100000000i−i−33i−i−330000000−i3i300000
χ532-22-222-1-2-2122-11-2-22-1-10-211-1-1-2211i3−i32i−2i2i−2i00-111-100i3−i3i3−i300i3i3−i3−i32-22-2000−ii−33−ii−332i−2i2i−2i00000000-11-1100000000−ii−33−ii−330000000i3−i300000
χ542-22-222-1-2-2122-11-2-22-1-10-211-1-1-2211i3−i32i−2i−2i2i00-111-100i3−i3i3−i300i3i3−i3−i3-22-22000−ii−33i−i3−32i−2i−2i2i000000001-11-100000000−ii−33i−i3−30000000−i3i300000
χ552-22-222-1-2-2122-11-2-22-1-10-211-1-1-2211i3−i3−2i2i2i−2i00-111-100i3−i3i3−i300i3i3−i3−i3-22-22000i−i3−3−ii−33−2i2i2i−2i000000001-11-100000000i−i3−3−ii−330000000−i3i300000
χ562-22-222-1-2-2122-11-2-22-1-10-211-1-1-2211i3−i3−2i2i−2i2i00-111-100i3−i3i3−i300i3i3−i3−i32-22-2000i−i3−3i−i3−3−2i2i−2i2i00000000-11-1100000000i−i3−3i−i3−30000000i3−i300000
χ572-2-22222-2-2-2-2-2-22222220-2-2-2-2-22-2220000002-22-22-20000000000002-2-220000000000000002-22-200002-2-2200002-200000000000000000002-2000
χ582-2-22222-2-2-2-2-2-22222220-2-2-2-2-22-2220000002-22-22-2000000000000-222-20000000000000002-22-20000-222-200002-20000000000000000000-22000
χ592-2-22222-2-2-2-2-2-22222220-2-2-2-2-22-222000000-222-22-20000000000002-2-22000000000000000-22-2200002-2-220000-220000000000000000000-22000
χ602-2-22222-2-2-2-2-2-22222220-2-2-2-2-22-222000000-222-22-2000000000000-222-2000000000000000-22-220000-222-20000-2200000000000000000002-2000
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χ6344444-2-24-2-24-2-2-24-2-2-21-4-2-21-21-2-2-21220044001111-4222-1-122-1-1-1-1000000-40000-2-22200-2-200000000000000020000000011-1-100000000000000
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χ854-44-4-2442-4-4-244-42-4-2-24022-4-242-22-4004i−4i0000-222-200000000000000000004i−4i000000−2i2i0000000000000000000000−2i2i00000000000000000000
χ864-44-4-2442-4-4-244-42-4-2-24022-4-242-22-400−4i4i0000-222-20000000000000000000−4i4i0000002i−2i00000000000000000000002i−2i00000000000000000000
χ874-44-4-24-22-42-24-222-4-21-202-121-22-2-12−2i32i34i−4i00001-1-1100i3−i3−2i32i300i3i3−i3−i30000000−2i2i23−230000−2i2i0000000000000000000000i−i−33000000000000000000
χ884-44-4-24-22-42-24-222-4-21-202-121-22-2-12−2i32i3−4i4i00001-1-1100i3−i3−2i32i300i3i3−i3−i300000002i−2i−232300002i−2i0000000000000000000000−ii3−3000000000000000000
χ894-44-4-24-22-42-24-222-4-21-202-121-22-2-122i3−2i34i−4i00001-1-1100−i3i32i3−2i300−i3−i3i3i30000000−2i2i−23230000−2i2i0000000000000000000000i−i3−3000000000000000000
χ904-44-4-24-22-42-24-222-4-21-202-121-22-2-122i3−2i3−4i4i00001-1-1100−i3i32i3−2i300−i3−i3i3i300000002i−2i23−2300002i−2i0000000000000000000000−ii−33000000000000000000
χ914-4-4444-2-4-42-4-42-2444-2-20-422224-4-2-200000000-22-220000000000004-4-4400000000000000000000000-222-2000000000000000000000000000000
χ924-4-4444-2-4-42-4-42-2444-2-20-422224-4-2-200000000-22-22000000000000-444-4000000000000000000000002-2-22000000000000000000000000000000
χ934-4-444-24-42-4-42-444-2-24-202-42-42-224-20000004-4-22-2200000000000000000000000000000004-4-22000000000000-22000000000000000000000000
χ944-4-444-24-42-4-42-444-2-24-202-42-42-224-2000000-44-22-220000000000000000000000000000000-442-20000000000002-2000000000000000000000000
χ954-4-44-2442-4-42-4-44-24-2-24022-42-4-22-240000004-4-22-220000000000000000000000000000000-224-4000000000000-22000000000000000000000000
χ964-4-44-2442-4-42-4-44-24-2-24022-42-4-22-24000000-44-22-2200000000000000000000000000000002-2-440000000000002-2000000000000000000000000
χ974-4-44-2-2422-422-44-2-21-2-20-122221-1-2-20000004-41-11-10000003i−3i3i−3i3i−3i0000000000000000000-22-220000000000001-13i−3i0000000000000000000000
χ984-4-44-2-2422-422-44-2-21-2-20-122221-1-2-20000004-41-11-1000000−3i3i−3i3i−3i3i0000000000000000000-22-220000000000001-1−3i3i0000000000000000000000
χ994-4-44-2-2422-422-44-2-21-2-20-122221-1-2-2000000-441-11-10000003i−3i3i−3i3i−3i00000000000000000002-22-2000000000000-11−3i3i0000000000000000000000
χ1004-4-44-2-2422-422-44-2-21-2-20-122221-1-2-2000000-441-11-1000000−3i3i−3i3i−3i3i00000000000000000002-22-2000000000000-113i−3i0000000000000000000000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000
χ10388-8-88-4-48-4-4-8444-84-4-420-4-424-2444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-48-4-48-44-8444-8-42-40-42-4-2444-240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-48-4-4844-8-8442-4-402-4-444-2-2440000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-4-4-44444442220222-2-2-2-2-2-200000000-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-4-4-44444442220222-2-2-2-2-2-200000000-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4844-8-4-48-8442-4-40-244-4-4-2244000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4444-4-4-44442220-2-2-222-22-2-2−4i34i3000000-111-1002i3−2i32i3−2i300−i3−i3i3i30000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4444-4-4-44442220-2-2-222-22-2-24i3−4i3000000-111-100−2i32i3−2i32i300i3i3−i3−i30000000000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-4-844-844-48-4-4-42044-24-2-44-42000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-44-844-84-4-48-42-404-24-24-442-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444444-4-4-42220-2-2-2-2-22-22200000000-11-110000006i−6i−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444444-4-4-42220-2-2-2-2-22-22200000000-11-11000000−6i6i3i−3i3i−3i0000000000000000000000000000000000000000000000000000000000000

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