Finite Group Databasebeta

← Group #13150714

Character table — Group #13150714

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order122244443666121212122466121233666666121212121212121236666666666612121212121212121212121222444444444424444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ61111111111111111-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ91111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11-11-11-1111111-1-111-1-111-1-111-1-1-1-1-1-1
χ101111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-111-1-1111-1-1-1-111-1-11111-1-1-1-111-1-111
χ111111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11-11-1-111-1-111-1-111-1-11111-1-111-1-1
χ121111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-11-111-1-1-1-1-111-1-111-1-1-1-111-1-1111111
χ131111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-1111111-1-111-1-111-1-1-11-11-1111-1-111-1-1-1-111-1-11111-1-1-1-111
χ141111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-1111111-1-1-1-111-1-1111-1-111-11111-1-11111-1-1-1-111-1-111-1-1-1-1
χ151111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-111-111-11-1-1-1-1-1-1-11111-1-111-1-111-1-11111
χ161111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111-1-111-1-11111-1-11-11-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ1722222222222222222222222-122-1-12-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222000022000000-1-1000000000000-1-1-1-100-1-1
χ1822222222222222222222222-122-1-12-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000-2-20000001100000000000011110011
χ192222222222222222222222-12-1-122-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222200000000002200-1-10000000000-1-1-1-10000-1-100
χ202222222222222222222222-12-1-122-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000000000-2-200110000000000111100001100
χ212222222222222222-2-2-2-2-2-22-122-1-12-12222-1-1-1-1-1-2-211-1-11111-1-2-211-1-1-1-11111000022220000-2-200000011000000000000-1-1-1-10011
χ222222222222222222-2-2-2-2-2-22-122-1-12-12222-1-1-1-1-1-2-211-1-11111-1-2-211-1-1-1-111110000-2-2-2-2000022000000-1-1000000000000111100-1-1
χ232222222222222222-2-2-2-2-2-2-12-1-122-12-1-1-1-12222-111-2-2-1-11111-111-2-2-1-1-1-1111122220000000000-2-200-1-1000000000011110000-1-100
χ242222222222222222-2-2-2-2-2-2-12-1-122-12-1-1-1-12222-111-2-2-1-11111-111-2-2-1-1-1-11111-2-2-2-200000000002200110000000000-1-1-1-100001100
χ252222-2-2-2-22222-2-2-2-22-222-2-22-122-1-12-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-21111111111000022-2-200002-2000000-1-1000000000000-1-1110011
χ262222-2-2-2-22222-2-2-2-22-222-2-22-122-1-12-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-211111111110000-2-2220000-220000001100000000000011-1-100-1-1
χ272222-2-2-2-22222-2-2-2-22-222-2-2-12-1-122-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-21111111122-2-200000000002-200-1-10000000000-1-11100001100
χ282222-2-2-2-22222-2-2-2-22-222-2-2-12-1-122-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-211111111-2-2220000000000-220011000000000011-1-10000-1-100
χ292222-2-2-2-22222-2-2-2-2-22-2-2222-122-1-12-1-2-2-2-21111-1-2-211-1-11111-122-1-11111-1-1-1-1000022-2-20000-2200000011000000000000-1-11100-1-1
χ302222-2-2-2-22222-2-2-2-2-22-2-2222-122-1-12-1-2-2-2-21111-1-2-211-1-11111-122-1-11111-1-1-1-10000-2-22200002-2000000-1-100000000000011-1-10011
χ312222-2-2-2-22222-2-2-2-2-22-2-222-12-1-122-121111-2-2-2-2-111-2-2-1-11111-1-1-1221111-1-1-1-122-2-20000000000-2200-1-1000000000011-1-100001100
χ322222-2-2-2-22222-2-2-2-2-22-2-222-12-1-122-121111-2-2-2-2-111-2-2-1-11111-1-1-1221111-1-1-1-1-2-22200000000002-200110000000000-1-1110000-1-100
χ3322-2-222-2-222-2-222-2-200000022-2-2-2-22222-2-222-2-220000-2-200002000022-2-20000000000002i−2i2i−2i00000000002i−2i2i−2i0000000000000000
χ3422-2-222-2-222-2-222-2-200000022-2-2-2-22222-2-222-2-220000-2-200002000022-2-2000000000000−2i2i−2i2i0000000000−2i2i−2i2i0000000000000000
χ3522-2-2-2-22222-2-2-2-22200000022-2-2-2-222-2-222-2-22220000-2-2000020000-2-2220000000000002i−2i−2i2i00000000002i−2i−2i2i0000000000000000
χ3622-2-2-2-22222-2-2-2-22200000022-2-2-2-222-2-222-2-22220000-2-2000020000-2-222000000000000−2i2i2i−2i0000000000−2i2i2i−2i0000000000000000
χ372-22-22i−2i2i−2i2-22-22i−2i2i−2i000000222-22-2-2-22i−2i2i−2i2i−2i2i−2i200002-20000-200002i−2i2i−2i000000002-22i−2i000000000000000000000000002-22i−2i0000
χ382-22-22i−2i2i−2i2-22-22i−2i2i−2i000000222-22-2-2-22i−2i2i−2i2i−2i2i−2i200002-20000-200002i−2i2i−2i00000000-22−2i2i00000000000000000000000000-22−2i2i0000
χ392-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-12-2-11-212i−2i2i−2i−ii−ii-100−i3i3-11−i3−i3i3i31003−3−ii−ii33−3−300002-22i−2i000000000000−i3i3000000000000-11−ii003−3
χ402-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-12-2-11-212i−2i2i−2i−ii−ii-100−i3i3-11−i3−i3i3i31003−3−ii−ii33−3−30000-22−2i2i000000000000i3−i30000000000001-1i−i00−33
χ412-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-12-2-11-212i−2i2i−2i−ii−ii-100i3−i3-11i3i3−i3−i3100−33−ii−ii−3−33300002-22i−2i000000000000i3−i3000000000000-11−ii00−33
χ422-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-12-2-11-212i−2i2i−2i−ii−ii-100i3−i3-11i3i3−i3−i3100−33−ii−ii−3−3330000-22−2i2i000000000000−i3i30000000000001-1i−i003−3
χ432-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000222-22-2-2-2−2i2i−2i2i−2i2i−2i2i200002-20000-20000−2i2i−2i2i000000002-2−2i2i000000000000000000000000002-2−2i2i0000
χ442-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000222-22-2-2-2−2i2i−2i2i−2i2i−2i2i200002-20000-20000−2i2i−2i2i00000000-222i−2i00000000000000000000000000-222i−2i0000
χ452-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-12-2-11-21−2i2i−2i2ii−ii−i-100−i3i3-11−i3−i3i3i3100−33i−ii−i−3−33300002-2−2i2i000000000000−i3i3000000000000-11i−i00−33
χ462-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-12-2-11-21−2i2i−2i2ii−ii−i-100−i3i3-11−i3−i3i3i3100−33i−ii−i−3−3330000-222i−2i000000000000i3−i30000000000001-1−ii003−3
χ472-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-12-2-11-21−2i2i−2i2ii−ii−i-100i3−i3-11i3i3−i3−i31003−3i−ii−i33−3−300002-2−2i2i000000000000i3−i3000000000000-11i−i003−3
χ482-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-12-2-11-21−2i2i−2i2ii−ii−i-100i3−i3-11i3i3−i3−i31003−3i−ii−i33−3−30000-222i−2i000000000000−i3i30000000000001-1−ii00−33
χ492-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-22-22-2-22i−2i−2i2i2i−2i−2i2i20000-220000-200002i−2i−2i2i00002-22i−2i000000000000002-20000000000000000002i−2i00
χ502-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-22-22-2-22i−2i−2i2i2i−2i−2i2i20000-220000-200002i−2i−2i2i0000-22−2i2i00000000000000-22000000000000000000−2i2i00
χ512-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-1-221-2−iii−i2i−2i−2i2i-1−i3i3001-1−i3i3−i3i313−300−iii−i3−33−32-22i−2i00000000000000-110000000000−i3i33−30000−ii00
χ522-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-1-221-2−iii−i2i−2i−2i2i-1−i3i3001-1−i3i3−i3i313−300−iii−i3−33−3-22−2i2i000000000000001-10000000000i3−i3−330000i−i00
χ532-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-1-221-2−iii−i2i−2i−2i2i-1i3−i3001-1i3−i3i3−i31−3300−iii−i−33−332-22i−2i00000000000000-110000000000i3−i3−330000−ii00
χ542-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-1-221-2−iii−i2i−2i−2i2i-1i3−i3001-1i3−i3i3−i31−3300−iii−i−33−33-22−2i2i000000000000001-10000000000−i3i33−30000i−i00
χ552-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-22-22-2-2−2i2i2i−2i−2i2i2i−2i20000-220000-20000−2i2i2i−2i00002-2−2i2i000000000000002-2000000000000000000−2i2i00
χ562-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-22-22-2-2−2i2i2i−2i−2i2i2i−2i20000-220000-20000−2i2i2i−2i0000-222i−2i00000000000000-220000000000000000002i−2i00
χ572-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-1-221-2i−i−ii−2i2i2i−2i-1−i3i3001-1−i3i3−i3i31−3300i−i−ii−33−332-2−2i2i00000000000000-110000000000−i3i3−330000i−i00
χ582-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-1-221-2i−i−ii−2i2i2i−2i-1−i3i3001-1−i3i3−i3i31−3300i−i−ii−33−33-222i−2i000000000000001-10000000000i3−i33−30000−ii00
χ592-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-1-221-2i−i−ii−2i2i2i−2i-1i3−i3001-1i3−i3i3−i313−300i−i−ii3−33−32-2−2i2i00000000000000-110000000000i3−i33−30000i−i00
χ602-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-1-221-2i−i−ii−2i2i2i−2i-1i3−i3001-1i3−i3i3−i313−300i−i−ii3−33−3-222i−2i000000000000001-10000000000−i3i3−330000−ii00
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122221111-1-1-1-1000000000000000000000000000000000000000000
χ634444-4-4-4-44444-4-4-4-44-444-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ644444-4-4-4-44444-4-4-4-4-44-4-444-2-2-2-2-2-2-2-2222222221222211-1-1-1-11-2-2-2-2-1-1-1-11111000000000000000000000000000000000000000000
χ6544-4-444-4-444-4-444-4-40000004-2-4-4224-244-4-4-2-222-20000220000-20000-2-2220000000000000000000000000000000000000000000000
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χ7044-4-4-4-44444-4-4-4-444000000-2422-4-4-2422-2-2-4-444-20000220000-2000022-2-20000000000000000000000000000000000000000000000
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χ7244-4-4-4-44444-4-4-4-444000000-2-22222-2-222-2-222-2-210000-1-1-333-310000-1-1113-3-33000000000000000000000000000000000000000000
χ734-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-24-224-42-4−2i2i−2i2i4i−4i4i−4i-20000-22000020000−2i2i−2i2i0000000000000000000000000000000000000000000000
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χ754-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-2-2-22-2222−2i2i−2i2i−2i2i−2i2i1002i3−2i31-1−i3−i3i3i3-100−2323i−ii−i33−3−3000000000000000000000000000000000000000000
χ764-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-24-224-42-42i−2i2i−2i−4i4i−4i4i-20000-220000200002i−2i2i−2i0000000000000000000000000000000000000000000000
χ774-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-2-2-22-22222i−2i2i−2i2i−2i2i−2i100−2i32i31-1i3i3−i3−i3-100−2323−ii−ii33−3−3000000000000000000000000000000000000000000
χ784-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-2-2-22-22222i−2i2i−2i2i−2i2i−2i1002i3−2i31-1−i3−i3i3i3-10023−23−ii−ii−3−333000000000000000000000000000000000000000000
χ794-4-444i−4i−4i4i4-4-444i−4i−4i4i0000004-2-442-2-424i−4i−4i4i−2i2i2i−2i-200002-2000020000−2i2i2i−2i0000000000000000000000000000000000000000000000
χ804-4-444i−4i−4i4i4-4-444i−4i−4i4i000000-2-22-22-222−2i2i2i−2i−2i2i2i−2i1−2i32i300-11i3−i3i3−i3-123−2300i−i−ii−33−33000000000000000000000000000000000000000000
χ814-4-444i−4i−4i4i4-4-444i−4i−4i4i000000-2-22-22-222−2i2i2i−2i−2i2i2i−2i12i3−2i300-11−i3i3−i3i3-1−232300i−i−ii3−33−3000000000000000000000000000000000000000000
χ824-4-44−4i4i4i−4i4-4-44−4i4i4i−4i0000004-2-442-2-42−4i4i4i−4i2i−2i−2i2i-200002-20000200002i−2i−2i2i0000000000000000000000000000000000000000000000
χ834-4-44−4i4i4i−4i4-4-44−4i4i4i−4i000000-2-22-22-2222i−2i−2i2i2i−2i−2i2i1−2i32i300-11i3−i3i3−i3-1−232300−iii−i3−33−3000000000000000000000000000000000000000000
χ844-4-44−4i4i4i−4i4-4-44−4i4i4i−4i000000-2-22-22-2222i−2i−2i2i2i−2i−2i2i12i3−2i300-11−i3i3−i3i3-123−2300−iii−i−33−33000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000000022220000220000-1-1-1-1-1-1-1-1000000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000000000000000-2-2-2-20000-2-2000011111111000000000000
χ8766666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000000022220000-2-20000-1-1-1-11111000000000000
χ8866666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000000000-2-2-2-200002200001111-1-1-1-1000000000000
χ896666-6-6-6-6-3-3-3-333336-6-3-33300000000000000000000000000000000000000000000000022-2-200002-20000-1-111-1-111000000000000
χ906666-6-6-6-6-3-3-3-333336-6-3-333000000000000000000000000000000000000000000000000-2-2220000-22000011-1-111-1-1000000000000
χ916666-6-6-6-6-3-3-3-33333-6633-3-300000000000000000000000000000000000000000000000022-2-20000-220000-1-11111-1-1000000000000
χ926666-6-6-6-6-3-3-3-33333-6633-3-3000000000000000000000000000000000000000000000000-2-22200002-2000011-1-1-1-111000000000000
χ9366-6-666-6-6-3-333-3-33300−3i33i3−3i33i30000000000000000000000000000000000000000000000002i−2i2i−2i0000000000−ii−ii3−33−3000000000000
χ9466-6-666-6-6-3-333-3-33300−3i33i3−3i33i3000000000000000000000000000000000000000000000000−2i2i−2i2i0000000000i−ii−i−33−33000000000000
χ9566-6-666-6-6-3-333-3-333003i3−3i33i3−3i30000000000000000000000000000000000000000000000002i−2i2i−2i0000000000−ii−ii−33−33000000000000
χ9666-6-666-6-6-3-333-3-333003i3−3i33i3−3i3000000000000000000000000000000000000000000000000−2i2i−2i2i0000000000i−ii−i3−33−3000000000000
χ9766-6-6-6-666-3-33333-3-300−3i33i33i3−3i30000000000000000000000000000000000000000000000002i−2i−2i2i0000000000−iii−i3−3−33000000000000
χ9866-6-6-6-666-3-33333-3-300−3i33i33i3−3i3000000000000000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii−333−3000000000000
χ9966-6-6-6-666-3-33333-3-3003i3−3i3−3i33i30000000000000000000000000000000000000000000000002i−2i−2i2i0000000000−iii−i−333−3000000000000
χ10066-6-6-6-666-3-33333-3-3003i3−3i3−3i33i3000000000000000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii3−3−33000000000000
χ10112-1212-1212i−12i12i−12i-66-66−6i6i−6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-12−12i12i−12i12i-66-666i−6i6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-121212i−12i−12i12i-666-6−6i6i6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-1212−12i12i12i−12i-666-66i−6i−6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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