Finite Group Databasebeta

← Group #13147856

Character table — Group #13147856

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order12224444366612121212441212121233666666121212121212121236661212121212121212121212121212121212121212224444444444224444666666121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-11-11-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111111-1-11111-1-1-1-1-1-111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-1-1-1111111-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1
χ91111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-11-1111111-1-1-1-111-1-1-1-111-1-111-1-1
χ101111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111-1-11-111111-1-1-1-1-1-1-1-11111-1-111-1-111
χ111111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-111-1-11-1-1-1-111111111-1-1-1-1-1-111-1-111
χ121111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1-11111-1-1111111-1-111-1-1
χ131111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1111-1-1-1-1-1-11111-1-11111-1-1-1-111
χ141111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-111-11-111-1-111-1-111-1-111-1-1-1-11111-1-1
χ151111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-111-1-1-111-1-111-1-111-1-111-1-11111-1-1
χ161111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1-11-1-1111111-1-1-1-111-1-111-1-1-1-111
χ1722222222222222222222222-12-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000202000000-1-10000-1-1-1-1-1-100000000
χ1822222222222222222222222-12-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000-20-200000011000011111100000000
χ192222222222222222222222-12-1222-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1222-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ212222222222222222-2-2-2-2-2-22-12-1-1-1222222-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-1111111110000222200000-20-2000000110000-1-1-1-11100000000
χ222222222222222222-2-2-2-2-2-22-12-1-1-1222222-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-1111111110000-2-2-2-200000202000000-1-100001111-1-100000000
χ232222222222222222-2-2-2-2-2-2-12-1222-1-1-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-1111111110000000022220000-2-20000000000000000-1-1-1-11111
χ242222222222222222-2-2-2-2-2-2-12-1222-1-1-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-11111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
χ252222-2-2-2-22222-2-2-2-22-222-2-22-12-1-1-122-2-2-2-21111-1-1-1-1-1-11122-2-21111-1-1-1-11111000022-2-20000020-2000000-1-10000-1-1111100000000
χ262222-2-2-2-22222-2-2-2-22-222-2-22-12-1-1-122-2-2-2-21111-1-1-1-1-1-11122-2-21111-1-1-1-111110000-2-22200000-20200000011000011-1-1-1-100000000
χ272222-2-2-2-22222-2-2-2-22-222-2-2-12-1222-1-11111-2-2-2-2-1-1-1-122-2-2-1-1111111-1-1-1-111110000000022-2-200002-20000000000000000-1-111-1-111
χ282222-2-2-2-22222-2-2-2-22-222-2-2-12-1222-1-11111-2-2-2-2-1-1-1-122-2-2-1-1111111-1-1-1-1111100000000-2-2220000-22000000000000000011-1-111-1-1
χ292222-2-2-2-22222-2-2-2-2-22-2-2222-12-1-1-122-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-1000022-2-200000-202000000110000-1-111-1-100000000
χ302222-2-2-2-22222-2-2-2-2-22-2-2222-12-1-1-122-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-10000-2-2220000020-2000000-1-1000011-1-11100000000
χ312222-2-2-2-22222-2-2-2-2-22-2-222-12-1222-1-11111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-10000000022-2-20000-220000000000000000-1-11111-1-1
χ322222-2-2-2-22222-2-2-2-2-22-2-222-12-1222-1-11111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-100000000-2-22200002-2000000000000000011-1-1-1-111
χ3322-2-222-2-22-2-2222-2-20000002222-2-2-2-222-2-222-2-222-2-20000000022-2-20000000000002i−2i2i−2i000000000000000000002i−2i2i−2i0000000000
χ3422-2-222-2-22-2-2222-2-20000002222-2-2-2-222-2-222-2-222-2-20000000022-2-2000000000000−2i2i−2i2i00000000000000000000−2i2i−2i2i0000000000
χ3522-2-222-2-22-2-2222-2-20000002-12-111-2-222-2-2-1-111-1-1113−33−30000-1-11133−3−333−3−300002i−2i2i−2i00000000000000−i3i30000−ii−ii−i3i300000000
χ3622-2-222-2-22-2-2222-2-20000002-12-111-2-222-2-2-1-111-1-1113−33−30000-1-11133−3−333−3−30000−2i2i−2i2i00000000000000i3−i30000i−ii−ii3−i300000000
χ3722-2-222-2-22-2-2222-2-20000002-12-111-2-222-2-2-1-111-1-111−33−330000-1-111−3−333−3−33300002i−2i2i−2i00000000000000i3−i30000−ii−iii3−i300000000
χ3822-2-222-2-22-2-2222-2-20000002-12-111-2-222-2-2-1-111-1-111−33−330000-1-111−3−333−3−3330000−2i2i−2i2i00000000000000−i3i30000i−ii−i−i3i300000000
χ3922-2-2-2-2222-2-22-2-2220000002222-2-2-2-2-2-222-2-22222-2-200000000-2-2220000000000002i−2i−2i2i000000000000000000002i−2i−2i2i0000000000
χ4022-2-2-2-2222-2-22-2-2220000002222-2-2-2-2-2-222-2-22222-2-200000000-2-222000000000000−2i2i2i−2i00000000000000000000−2i2i2i−2i0000000000
χ4122-2-2-2-2222-2-22-2-2220000002-12-111-2-2-2-22211-1-1-1-1113−3−33000011-1-133−3−3−3−33300002i−2i−2i2i00000000000000−i3i30000−iii−ii3−i300000000
χ4222-2-2-2-2222-2-22-2-2220000002-12-111-2-2-2-22211-1-1-1-1113−3−33000011-1-133−3−3−3−3330000−2i2i2i−2i00000000000000i3−i30000i−i−ii−i3i300000000
χ4322-2-2-2-2222-2-22-2-2220000002-12-111-2-2-2-22211-1-1-1-111−333−3000011-1-1−3−33333−3−300002i−2i−2i2i00000000000000i3−i30000−iii−i−i3i300000000
χ4422-2-2-2-2222-2-22-2-2220000002-12-111-2-2-2-22211-1-1-1-111−333−3000011-1-1−3−33333−3−30000−2i2i2i−2i00000000000000−i3i30000i−i−iii3−i300000000
χ452-22-22i−2i2i−2i22-2-22i−2i2i−2i00000022-2-22-22-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i000000002-22i−2i000000000000002-200002i−2i0000000000000000
χ462-22-22i−2i2i−2i22-2-22i−2i2i−2i00000022-2-22-22-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i00000000-22−2i2i00000000000000-220000−2i2i0000000000000000
χ472-22-2−2i2i−2i2i22-2-2−2i2i−2i2i00000022-2-22-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i000000002-2−2i2i000000000000002-20000−2i2i0000000000000000
χ482-22-2−2i2i−2i2i22-2-2−2i2i−2i2i00000022-2-22-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i00000000-222i−2i00000000000000-2200002i−2i0000000000000000
χ492-2-222i−2i−2i2i2-22-22i−2i−2i2i00000022-2-2-22-222i−2i−2i2i2i−2i−2i2i2-2-22000000002i−2i−2i2i00000000000000002-22i−2i00000000000000000000002-22i−2i0000
χ502-2-222i−2i−2i2i2-22-22i−2i−2i2i00000022-2-2-22-222i−2i−2i2i2i−2i−2i2i2-2-22000000002i−2i−2i2i0000000000000000-22−2i2i0000000000000000000000-22−2i2i0000
χ512-2-222i−2i−2i2i2-22-22i−2i−2i2i000000-121-2-221-1−iii−i2i−2i−2i2i-111-100003−3−i3i3−iii−i3−33−3−i3i3−i3i3000000002-22i−2i0000000000000000000000-11−ii3−3−i3i3
χ522-2-222i−2i−2i2i2-22-22i−2i−2i2i000000-121-2-221-1−iii−i2i−2i−2i2i-111-100003−3−i3i3−iii−i3−33−3−i3i3−i3i300000000-22−2i2i00000000000000000000001-1i−i−33i3−i3
χ532-2-222i−2i−2i2i2-22-22i−2i−2i2i000000-121-2-221-1−iii−i2i−2i−2i2i-111-10000−33i3−i3−iii−i−33−33i3−i3i3−i3000000002-22i−2i0000000000000000000000-11−ii−33i3−i3
χ542-2-222i−2i−2i2i2-22-22i−2i−2i2i000000-121-2-221-1−iii−i2i−2i−2i2i-111-10000−33i3−i3−iii−i−33−33i3−i3i3−i300000000-22−2i2i00000000000000000000001-1i−i3−3−i3i3
χ552-2-22−2i2i2i−2i2-22-2−2i2i2i−2i00000022-2-2-22-22−2i2i2i−2i−2i2i2i−2i2-2-2200000000−2i2i2i−2i00000000000000002-2−2i2i00000000000000000000002-2−2i2i0000
χ562-2-22−2i2i2i−2i2-22-2−2i2i2i−2i00000022-2-2-22-22−2i2i2i−2i−2i2i2i−2i2-2-2200000000−2i2i2i−2i0000000000000000-222i−2i0000000000000000000000-222i−2i0000
χ572-2-22−2i2i2i−2i2-22-2−2i2i2i−2i000000-121-2-221-1i−i−ii−2i2i2i−2i-111-100003−3i3−i3i−i−ii3−33−3i3−i3i3−i3000000002-2−2i2i0000000000000000000000-11i−i3−3i3−i3
χ582-2-22−2i2i2i−2i2-22-2−2i2i2i−2i000000-121-2-221-1i−i−ii−2i2i2i−2i-111-100003−3i3−i3i−i−ii3−33−3i3−i3i3−i300000000-222i−2i00000000000000000000001-1−ii−33−i3i3
χ592-2-22−2i2i2i−2i2-22-2−2i2i2i−2i000000-121-2-221-1i−i−ii−2i2i2i−2i-111-10000−33−i3i3i−i−ii−33−33−i3i3−i3i3000000002-2−2i2i0000000000000000000000-11i−i−33−i3i3
χ602-2-22−2i2i2i−2i2-22-2−2i2i2i−2i000000-121-2-221-1i−i−ii−2i2i2i−2i-111-10000−33−i3i3i−i−ii−33−33−i3i3−i3i300000000-222i−2i00000000000000000000001-1−ii3−3i3−i3
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111222222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ634444-4-4-4-44444-4-4-4-44-444-4-4-2-2-2-2-2-2-2-2222222221111-2-222-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000000000
χ644444-4-4-4-44444-4-4-4-4-44-4-444-2-2-2-2-2-2-2-222222222111122-2-222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000000000
χ6544-4-444-4-44-4-4444-4-4000000-24-24-4-422-2-22244-4-4-2-22200000000-2-22200000000000000000000000000000000000000000000000000
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χ6744-4-444-4-44-4-4444-4-4000000-2-2-2-22222-2-222-2-22211-1-1−2323−2323000011-1-133−3−333−3−3000000000000000000000000000000000000000000
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χ7044-4-4-4-4444-4-44-4-444000000-2-2-2-2222222-2-222-2-211-1-1−232323−230000-1-11133−3−3−3−333000000000000000000000000000000000000000000
χ714-44-44i−4i4i−4i44-4-44i−4i4i−4i0000004-2-42-224-44i−4i4i−4i−2i2i−2i2i-22-2200000000−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ724-44-44i−4i4i−4i44-4-44i−4i4i−4i000000-242-44-4-22−2i2i−2i2i4i−4i4i−4i-22-2200000000−2i2i−2i2i00000000000000000000000000000000000000000000000000
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χ744-44-44i−4i4i−4i44-4-44i−4i4i−4i000000-2-222-22-22−2i2i−2i2i−2i2i−2i2i1-11-100000000i−ii−i-333-33i−3i−3i3i000000000000000000000000000000000000000000
χ754-44-4−4i4i−4i4i44-4-4−4i4i−4i4i0000004-2-42-224-4−4i4i−4i4i2i−2i2i−2i-22-22000000002i−2i2i−2i00000000000000000000000000000000000000000000000000
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χ774-44-4−4i4i−4i4i44-4-4−4i4i−4i4i000000-2-222-22-222i−2i2i−2i2i−2i2i−2i1-11-100000000−ii−ii3-3-333i−3i−3i3i000000000000000000000000000000000000000000
χ784-44-4−4i4i−4i4i44-4-4−4i4i−4i4i000000-2-222-22-222i−2i2i−2i2i−2i2i−2i1-11-100000000−ii−ii-333-3−3i3i3i−3i000000000000000000000000000000000000000000
χ794-4-444i−4i−4i4i4-44-44i−4i−4i4i0000004-2-422-2-444i−4i−4i4i−2i2i2i−2i-222-200000000−2i2i2i−2i00000000000000000000000000000000000000000000000000
χ804-4-444i−4i−4i4i4-44-44i−4i−4i4i000000-2-2222-22-2−2i2i2i−2i−2i2i2i−2i1-1-11000023−23−2i32i3i−i−ii−33−33i3−i3i3−i3000000000000000000000000000000000000000000
χ814-4-444i−4i−4i4i4-44-44i−4i−4i4i000000-2-2222-22-2−2i2i2i−2i−2i2i2i−2i1-1-110000−23232i3−2i3i−i−ii3−33−3−i3i3−i3i3000000000000000000000000000000000000000000
χ824-4-44−4i4i4i−4i4-44-4−4i4i4i−4i0000004-2-422-2-44−4i4i4i−4i2i−2i−2i2i-222-2000000002i−2i−2i2i00000000000000000000000000000000000000000000000000
χ834-4-44−4i4i4i−4i4-44-4−4i4i4i−4i000000-2-2222-22-22i−2i−2i2i2i−2i−2i2i1-1-11000023−232i3−2i3−iii−i−33−33−i3i3−i3i3000000000000000000000000000000000000000000
χ844-4-44−4i4i4i−4i4-44-4−4i4i4i−4i000000-2-2222-22-22i−2i−2i2i2i−2i−2i2i1-1-110000−2323−2i32i3−iii−i3−33−3i3−i3i3−i3000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000222200000000202000-1-1-1-100-1-1-1-100000000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000-2-2-2-200000000-20-2000111100111100000000000000
χ8766666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000222200000000-20-2000-1-11100-1-11100000000000000
χ8866666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000-2-2-2-20000000020200011-1-10011-1-100000000000000
χ896666-6-6-6-6-3-3-3-333336-6-3-333000000000000000000000000000000000000000022-2-20000000020-2000-1-1-1-100111100000000000000
χ906666-6-6-6-6-3-3-3-333336-6-3-3330000000000000000000000000000000000000000-2-22200000000-202000111100-1-1-1-100000000000000
χ916666-6-6-6-6-3-3-3-33333-6633-3-3000000000000000000000000000000000000000022-2-200000000-202000-1-1110011-1-100000000000000
χ926666-6-6-6-6-3-3-3-33333-6633-3-30000000000000000000000000000000000000000-2-2220000000020-200011-1-100-1-11100000000000000
χ936-66-66i−6i6i−6i-3-333−3i3i−3i3i00−3i33i333−3300000000000000000000000000000000000000002-22i−2i00000000000000-11−i3i300−ii3−300000000000000
χ946-66-66i−6i6i−6i-3-333−3i3i−3i3i00−3i33i333−330000000000000000000000000000000000000000-22−2i2i000000000000001-1i3−i300i−i−3300000000000000
χ956-66-66i−6i6i−6i-3-333−3i3i−3i3i003i3−3i3−333300000000000000000000000000000000000000002-22i−2i00000000000000-11i3−i300−ii−3300000000000000
χ966-66-66i−6i6i−6i-3-333−3i3i−3i3i003i3−3i3−33330000000000000000000000000000000000000000-22−2i2i000000000000001-1−i3i300i−i3−300000000000000
χ976-66-6−6i6i−6i6i-3-3333i−3i3i−3i00−3i33i3−333300000000000000000000000000000000000000002-2−2i2i00000000000000-11−i3i300i−i−3300000000000000
χ986-66-6−6i6i−6i6i-3-3333i−3i3i−3i00−3i33i3−33330000000000000000000000000000000000000000-222i−2i000000000000001-1i3−i300−ii3−300000000000000
χ996-66-6−6i6i−6i6i-3-3333i−3i3i−3i003i3−3i333−3300000000000000000000000000000000000000002-2−2i2i00000000000000-11i3−i300i−i3−300000000000000
χ1006-66-6−6i6i−6i6i-3-3333i−3i3i−3i003i3−3i333−330000000000000000000000000000000000000000-222i−2i000000000000001-1−i3i300−ii−3300000000000000
χ1011212-12-121212-12-12-666-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-12-12-12-121212-666-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-121212i−12i−12i12i-66-66−6i6i6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-1212−12i12i12i−12i-66-666i−6i−6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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