Finite Group Databasebeta

← Group #13156307

Character table — Group #13156307

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818242424242424242424242424363636727272727272108108
order122233344666666666333666666666121212121212121212123666121212121212121222446666881212121224242424242424242424242424242424441212121266666612121212121241212441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11111
χ51111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-111-1-111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000222222000000000000-2-2-200000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000-2-2-2-2-2-200000000000022200000000
χ11222222-122222-12-1-1222-1-122-1-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100-1-1-1-1000000000000000022-1-1-1-122-1-1-1-122-1-1-1-12-1-100000000
χ12222222-122222-12-1-1222-1-122-1-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-1-1-1-10011110000000000000000-2-2111122-1-1-1-1-2-21111-21100000000
χ13222222-122222-12-1-1222-1-122-1-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222111100-1-1-1-10000000000000000-2-21111-2-2111122-1-1-1-1-21100000000
χ14222222-122222-12-1-1222-1-122-1-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111001111000000000000000022-1-1-1-1-2-21111-2-211112-1-100000000
χ15222222-1-2-2222-12-1-1222-1-122-1-1-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-1111111110000−i3−i3i3i300−i3−i3i3i3000000000000000022-1-1-1-100−i3−i3i3i300−i3−i3i3i3-21100000000
χ16222222-1-2-2222-12-1-1222-1-122-1-1-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-1111111110000−i3−i3i3i300i3i3−i3−i30000000000000000-2-2111100−i3−i3i3i300i3i3−i3−i32-1-100000000
χ17222222-1-2-2222-12-1-1222-1-122-1-1-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-1111111110000i3i3−i3−i300−i3−i3i3i30000000000000000-2-2111100i3i3−i3−i300−i3−i3i3i32-1-100000000
χ18222222-1-2-2222-12-1-1222-1-122-1-1-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-1111111110000i3i3−i3−i300i3i3−i3−i3000000000000000022-1-1-1-100i3i3−i3−i300i3i3−i3−i3-21100000000
χ1922222-1222-12-122222-1-12-1-1-12-1-1-12-122-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1220022222200002222-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-100000000020-1-10000
χ2022222-1222-12-122222-1-12-1-1-12-1-1-12-122-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-122002222-2-20000-2-2-2-2111111111111000000-1-1-1-1-1-1000000000-20110000
χ2122222-1222-12-122222-1-12-1-1-12-1-1-12-122-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-2-2-22200002222-1-1-1-1-1-1-1-1-1-1-1-1000000111111000000000-20110000
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χ232222-122222-122-122-12-1-12-1-1-122-1-12-1-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100220000222222-1-1-1-12222-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-10000200-1-100
χ242222-122222-122-122-12-1-12-1-1-122-1-12-1-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100220000-2-222221111-2-2-2-211111111000000000000-1-1-1-1-1-10000-2001100
χ252222-122222-122-122-12-1-12-1-1-122-1-12-1-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-2000022-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10000000000001111110000-2001100
χ262222-122222-122-122-12-1-12-1-1-122-1-12-1-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-20000-2-2-2-2-2-21111-2-2-2-2111111110000000000001111110000200-1-100
χ2722-2-22222-2-2222-2-2-2-2-2222-2-2-2-2-2222-2222-222-2-2-2-22-2-222-22-222-2-22-2002-22-200000000000000000000000000002-22-22-200000000000000000
χ2822-2-22222-2-2222-2-2-2-2-2222-2-2-2-2-2222-2222-222-2-2-2-22-2-222-22-222-2-2-2200-22-220000000000000000000000000000-22-22-2200000000000000000
χ2922-2-2222-22-2222-2-2-2-2-2222-2-2-2-2-2222-2-2-2-22-2-222222-2-22-22-22-2-222002i−2i0000002i−2i2i−2i00000000000000000000000000002i−2i2i−2i2i−2i00000000000
χ3022-2-2222-22-2222-2-2-2-2-2222-2-2-2-2-2222-2-2-2-22-2-222222-2-22-22-22-2-22200−2i2i000000−2i2i−2i2i0000000000000000000000000000−2i2i−2i2i−2i2i00000000000
χ3122-2-222-12-2-222-1-211-2-22-1-1-2-21112-1-1122-1122-2-2-2-2-111-1-11-11-1-1112-200-11-11003−3−3300000000000000000033−3−32-2-11-11003−3−3303−300000000
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χ3322-2-222-12-2-222-1-211-2-22-1-1-2-21112-1-1122-1122-2-2-2-2-111-1-11-11-1-111-22001-11-1003−3−33000000000000000000−3−333-221-11-1003−3−330−3300000000
χ3422-2-222-12-2-222-1-211-2-22-1-1-2-21112-1-1122-1122-2-2-2-2-111-1-11-11-1-111-22001-11-100−333−300000000000000000033−3−3-221-11-100−333−303−300000000
χ3522-2-222-1-22-222-1-211-2-22-1-1-2-21112-1-11-2-21-1-2-22222-111-11-11-111-1-1002i−2i−i3i3i3−i300−ii−ii00000000000000000033−3−300−i3i3i3−i32i−2i−ii−ii0−3300000000
χ3622-2-222-1-22-222-1-211-2-22-1-1-2-21112-1-11-2-21-1-2-22222-111-11-11-111-1-1002i−2ii3−i3−i3i300−ii−ii000000000000000000−3−33300i3−i3−i3i32i−2i−ii−ii03−300000000
χ3722-2-222-1-22-222-1-211-2-22-1-1-2-21112-1-11-2-21-1-2-22222-111-11-11-111-1-100−2i2i−i3i3i3−i300i−ii−i000000000000000000−3−33300−i3i3i3−i3−2i2ii−ii−i03−300000000
χ3822-2-222-1-22-222-1-211-2-22-1-1-2-21112-1-11-2-21-1-2-22222-111-11-11-111-1-100−2i2ii3−i3−i3i300i−ii−i00000000000000000033−3−300i3−i3−i3i3−2i2ii−ii−i0−3300000000
χ3922-2-22-122-212-12-2-2-2-21-12-111-211-12-1-22-12-2-1-1-2111-111-12-2-11-1-1112-2002-22-2000000000033−3−33333−3−3−3−3000000-11-11-11000000000003−30000
χ4022-2-22-122-212-12-2-2-2-21-12-111-211-12-1-22-12-2-1-1-2111-111-12-2-11-1-1112-2002-22-20000000000−3−333−3−3−3−33333000000-11-11-1100000000000−330000
χ4122-2-22-122-212-12-2-2-2-21-12-111-211-12-1-22-12-2-1-1-2111-111-12-2-11-1-111-2200-22-22000000000033−3−33333−3−3−3−30000001-11-11-100000000000−330000
χ4222-2-22-122-212-12-2-2-2-21-12-111-211-12-1-22-12-2-1-1-2111-111-12-2-11-1-111-2200-22-220000000000−3−333−3−3−3−333330000001-11-11-1000000000003−30000
χ4322-2-2-122-22-2-1221-2-21-2-1-12111-2-2-1-1211-2-2211-12-1-1-111-11-1-2211-1-1002i−2i0000002i−2i2i−2i−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3000000000000−ii−ii−ii00000003−300
χ4422-2-2-122-22-2-1221-2-21-2-1-12111-2-2-1-1211-2-2211-12-1-1-111-11-1-2211-1-1002i−2i0000002i−2i2i−2ii3i3−i3−i30000i3i3−i3−i3i3i3−i3−i3000000000000−ii−ii−ii0000000−3300
χ4522-2-2-122-22-2-1221-2-21-2-1-12111-2-2-1-1211-2-2211-12-1-1-111-11-1-2211-1-100−2i2i000000−2i2i−2i2i−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3000000000000i−ii−ii−i0000000−3300
χ4622-2-2-122-22-2-1221-2-21-2-1-12111-2-2-1-1211-2-2211-12-1-1-111-11-1-2211-1-100−2i2i000000−2i2i−2i2ii3i3−i3−i30000i3i3−i3−i3i3i3−i3−i3000000000000i−ii−ii−i00000003−300
χ472-22-2222002-2-2-22-22-2-22222-2-22-2-2-2-22000000000022-2-20000000000000000−i2i20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-22-22-2000000000000000000000−i2i2
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χ874-44-4-2-2400-222-4-2-44221-2-21-12-22-122-20000−3i3i00−3i3i11-1-10000−3i3i−3i3i00000000−2i22i20000i2−i2i2−i2i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ2300000000000000000000000000000
χ884-44-4-2-2400-222-4-2-44221-2-21-12-22-122-20000−3i3i00−3i3i11-1-10000−3i3i−3i3i000000002i2−2i20000−i2i2−i2i2−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ2300000000000000000000000000000
χ894-4-4444400-4-4-4-4-44-444444-444-44-4-4-4-400000000004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ904-4-4444-200-4-4-42-4-22444-2-2-44-22-2-42220000000000-22-22000000000000000000000000000000000000000023−23−232300000000000000000000000
χ914-4-4444-200-4-4-42-4-22444-2-2-44-22-2-42220000000000-22-220000000000000000000000000000000000000000−232323−2300000000000000000000000
χ924-4-444-24002-42-4-44-44-2-24-22-242-22-42-40000000000-22-2200000000000000000000000000i6−i6−i6i6i6−i6i6−i6−i6i6−i6i600000000000000000000000000000
χ934-4-444-24002-42-4-44-44-2-24-22-242-22-42-40000000000-22-2200000000000000000000000000−i6i6i6−i6−i6i6−i6i6i6−i6i6−i600000000000000000000000000000
χ944-4-44-24400-42-4-424-4-24-2-242-2-2-4422-420000000000-22-2200000000000000000000006−6−6600006−6−666−6−6600000000000000000000000000000
χ954-4-44-24400-42-4-424-4-24-2-242-2-2-4422-420000000000-22-220000000000000000000000−666−60000−666−6−666−600000000000000000000000000000
χ964-4-44-2-2400222-424-4-2-21-2-2-11-22-2-122200003i−3i00−3i3i1-11-100003i−3i−3i3i000000000000006−6−66i6−i6−i6i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300000000000000000000000000000
χ974-4-44-2-2400222-424-4-2-21-2-2-11-22-2-122200003i−3i00−3i3i1-11-100003i−3i−3i3i00000000000000−666−6−i6i6i6−i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300000000000000000000000000000
χ984-4-44-2-2400222-424-4-2-21-2-2-11-22-2-12220000−3i3i003i−3i1-11-10000−3i3i3i−3i000000000000006−6−66−i6i6i6−i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300000000000000000000000000000
χ994-4-44-2-2400222-424-4-2-21-2-2-11-22-2-12220000−3i3i003i−3i1-11-10000−3i3i3i−3i00000000000000−666−6i6−i6−i6i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300000000000000000000000000000
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χ1018888-4-4-4-8-8-4-4-4-4-4-4-4-4-42222222222224444-2-244-2-2-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-48-84-4-4-444444222-2-2-2-2-2222-2-4-4-442244-2-2-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-884-4-4-444444222-2-2-2-2-2222-2444-4-2-2-4-422-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-400-4-84484-4-84-4-42-4442-244-2-4000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-40084-84-44-44-8-42-4-44-2-444-242000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-400-4444-44-4442222-2-22-2-2-2-2200006i−6i006i−6i-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-400-4444-44-4442222-2-22-2-2-2-220000−6i6i00−6i6i-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-4004-844-8-448-4-4-424-4-4-2244-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-400-84-844-44-48-42-44-424-44-24-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-40044444-44-4-4222-222-22-2-2-2-200006i−6i00−6i6i-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-40044444-44-4-4222-222-22-2-2-2-20000−6i6i006i−6i-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.