Finite Group Databasebeta

← Group #13147858

Character table — Group #13147858

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order122244443666121212124412121212336666661212121212121212366612121212121212121212121212121212121212122244444444444444446612121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ51111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-11-11-11-111-1-111-1-111-1-111-1-111-1-111-1-1
χ101111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111-1-11-1111-1-111-1-1-1-111-1-111-1-111-1-111
χ111111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-111-1-11-1-111-1-11111-1-111-1-1-1-111-1-111
χ121111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-11-111-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ131111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-11-11-1111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-111-11-111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-111-1-1-11111-1-111-1-1-1-111-1-11111-1-1
χ161111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-11-11-1-11-1-11111-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222222-12-122-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222-12-122-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ192222222222222222222222-12-12-1-122-1-1-1-12222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-100002222000000220000000000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222-12-12-1-122-1-1-1-12222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000-2-200000000001111111100000000
χ212222222222222222-2-2-2-2-2-22-12-122-1-12222-1-1-1-1-1-1-1-1-2-211-2-211-1-1-1-1111111110000000022220000-2-20000000000000000-1-1-1-11111
χ222222222222222222-2-2-2-2-2-22-12-122-1-12222-1-1-1-1-1-1-1-1-2-211-2-211-1-1-1-11111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
χ232222222222222222-2-2-2-2-2-2-12-12-1-122-1-1-1-12222-1-1-1-111-2-211-2-2-1-1-1-11111111100002222000000-2-20000000000-1-1-1-1111100000000
χ242222222222222222-2-2-2-2-2-2-12-12-1-122-1-1-1-12222-1-1-1-111-2-211-2-2-1-1-1-1111111110000-2-2-2-20000002200000000001111-1-1-1-100000000
χ252222-2-2-2-22222-2-2-2-22-222-2-22-12-122-1-1-2-2-2-21111-1-1-1-122-1-1-2-2111111-1-1-1-111110000000022-2-200002-20000000000000000-1-111-1-111
χ262222-2-2-2-22222-2-2-2-22-222-2-22-12-122-1-1-2-2-2-21111-1-1-1-122-1-1-2-2111111-1-1-1-1111100000000-2-2220000-22000000000000000011-1-111-1-1
χ272222-2-2-2-22222-2-2-2-22-222-2-2-12-12-1-1221111-2-2-2-2-1-1-1-1-1-12211-2-21111-1-1-1-11111000022-2-20000002-20000000000-1-111-1-11100000000
χ282222-2-2-2-22222-2-2-2-22-222-2-2-12-12-1-1221111-2-2-2-2-1-1-1-1-1-12211-2-21111-1-1-1-111110000-2-222000000-22000000000011-1-111-1-100000000
χ292222-2-2-2-22222-2-2-2-2-22-2-2222-12-122-1-1-2-2-2-21111-1-1-1-1-2-21122-1-111111111-1-1-1-10000000022-2-20000-220000000000000000-1-11111-1-1
χ302222-2-2-2-22222-2-2-2-2-22-2-2222-12-122-1-1-2-2-2-21111-1-1-1-1-2-21122-1-111111111-1-1-1-100000000-2-22200002-2000000000000000011-1-1-1-111
χ312222-2-2-2-22222-2-2-2-2-22-2-222-12-12-1-1221111-2-2-2-2-1-1-1-111-2-2-1-12211111111-1-1-1-1000022-2-2000000-220000000000-1-11111-1-100000000
χ322222-2-2-2-22222-2-2-2-2-22-2-222-12-12-1-1221111-2-2-2-2-1-1-1-111-2-2-1-12211111111-1-1-1-10000-2-2220000002-2000000000011-1-1-1-11100000000
χ3322-2-222-2-222-2-222-2-20000002222-2-2-2-222-2-222-2-222-2-20000000022-2-2000000002-22-2000000000000002-22-200000000000000000000
χ3422-2-222-2-222-2-222-2-20000002222-2-2-2-222-2-222-2-222-2-20000000022-2-200000000-22-2200000000000000-22-2200000000000000000000
χ3522-2-2-2-22222-2-2-2-2220000002222-2-2-2-2-2-222-2-22222-2-200000000-2-222000000002-2-22000000000000002-2-2200000000000000000000
χ3622-2-2-2-22222-2-2-2-2220000002222-2-2-2-2-2-222-2-22222-2-200000000-2-22200000000-222-200000000000000-222-200000000000000000000
χ372-22-22i−2i2i−2i2-22-22i−2i2i−2i00000022-2-22-22-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i00000000000000002-22i−2i00000000000000000000002-22i−2i0000
χ382-22-22i−2i2i−2i2-22-22i−2i2i−2i00000022-2-22-22-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i0000000000000000-22−2i2i0000000000000000000000-22−2i2i0000
χ392-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-212-2-112i−2i2i−2i−ii−ii-11-1100−i3i3003−3−ii−ii−i3−i3i3i333−3−3000000002-22i−2i0000000000000000000000-11−ii−i3i33−3
χ402-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-212-2-112i−2i2i−2i−ii−ii-11-1100−i3i3003−3−ii−ii−i3−i3i3i333−3−300000000-22−2i2i00000000000000000000001-1i−ii3−i3−33
χ412-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-212-2-112i−2i2i−2i−ii−ii-11-1100i3−i300−33−ii−iii3i3−i3−i3−3−333000000002-22i−2i0000000000000000000000-11−iii3−i3−33
χ422-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-212-2-112i−2i2i−2i−ii−ii-11-1100i3−i300−33−ii−iii3i3−i3−i3−3−33300000000-22−2i2i00000000000000000000001-1i−i−i3i33−3
χ432-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-2-22-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i00000000000000002-2−2i2i00000000000000000000002-2−2i2i0000
χ442-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-2-22-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i0000000000000000-222i−2i0000000000000000000000-222i−2i0000
χ452-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-212-2-11−2i2i−2i2ii−ii−i-11-1100−i3i300−33i−ii−i−i3−i3i3i3−3−333000000002-2−2i2i0000000000000000000000-11i−i−i3i3−33
χ462-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-212-2-11−2i2i−2i2ii−ii−i-11-1100−i3i300−33i−ii−i−i3−i3i3i3−3−33300000000-222i−2i00000000000000000000001-1−iii3−i33−3
χ472-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-212-2-11−2i2i−2i2ii−ii−i-11-1100i3−i3003−3i−ii−ii3i3−i3−i333−3−3000000002-2−2i2i0000000000000000000000-11i−ii3−i33−3
χ482-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-212-2-11−2i2i−2i2ii−ii−i-11-1100i3−i3003−3i−ii−ii3i3−i3−i333−3−300000000-222i−2i00000000000000000000001-1−ii−i3i3−33
χ492-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-2-2-22-222i−2i−2i2i2i−2i−2i2i2-2-22000000002i−2i−2i2i0000000000002i−2i2-20000000000000000002i−2i2-2000000000000
χ502-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-2-2-22-222i−2i−2i2i2i−2i−2i2i2-2-22000000002i−2i−2i2i000000000000−2i2i-22000000000000000000−2i2i-22000000000000
χ512-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-21-1-22−iii−i2i−2i−2i2i-111-13−300−i3i300−iii−i3−33−3−i3i3−i3i300002i−2i2-2000000000000000000−ii-11−i3i33−300000000
χ522-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-21-1-22−iii−i2i−2i−2i2i-111-13−300−i3i300−iii−i3−33−3−i3i3−i3i30000−2i2i-22000000000000000000i−i1-1i3−i3−3300000000
χ532-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-21-1-22−iii−i2i−2i−2i2i-111-1−3300i3−i300−iii−i−33−33i3−i3i3−i300002i−2i2-2000000000000000000−ii-11i3−i3−3300000000
χ542-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-21-1-22−iii−i2i−2i−2i2i-111-1−3300i3−i300−iii−i−33−33i3−i3i3−i30000−2i2i-22000000000000000000i−i1-1−i3i33−300000000
χ552-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-2-2-22-22−2i2i2i−2i−2i2i2i−2i2-2-2200000000−2i2i2i−2i0000000000002i−2i-220000000000000000002i−2i-22000000000000
χ562-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-2-2-22-22−2i2i2i−2i−2i2i2i−2i2-2-2200000000−2i2i2i−2i000000000000−2i2i2-2000000000000000000−2i2i2-2000000000000
χ572-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-21-1-22i−i−ii−2i2i2i−2i-111-13−300i3−i300i−i−ii3−33−3i3−i3i3−i300002i−2i-22000000000000000000−ii1-1−i3i3−3300000000
χ582-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-21-1-22i−i−ii−2i2i2i−2i-111-13−300i3−i300i−i−ii3−33−3i3−i3i3−i30000−2i2i2-2000000000000000000i−i-11i3−i33−300000000
χ592-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-21-1-22i−i−ii−2i2i2i−2i-111-1−3300−i3i300i−i−ii−33−33−i3i3−i3i300002i−2i-22000000000000000000−ii1-1i3−i33−300000000
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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
χ634444-4-4-4-44444-4-4-4-44-444-4-4-2-2-2-2-2-2-2-2222222221111-2-2-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000000000
χ644444-4-4-4-44444-4-4-4-4-44-4-444-2-2-2-2-2-2-2-22222222211112222-2-2-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000000000
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χ7244-4-4-4-44444-4-4-4-444000000-2-2-2-2222222-2-222-2-211-1-100000000-1-111−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000000000000000
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χ754-44-44i−4i4i−4i4-44-44i−4i4i−4i000000-2-222-22-22−2i2i−2i2i−2i2i−2i2i1-11-1002i3−2i300−2323i−ii−i−i3−i3i3i333−3−3000000000000000000000000000000000000000000
χ764-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-242-4-224-42i−2i2i−2i−4i4i−4i4i-22-22000000002i−2i2i−2i00000000000000000000000000000000000000000000000000
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χ784-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000-2-222-22-222i−2i2i−2i2i−2i2i−2i1-11-1002i3−2i30023−23−ii−ii−i3−i3i3i3−3−333000000000000000000000000000000000000000000
χ794-4-444i−4i−4i4i4-4-444i−4i−4i4i0000004-2-42-442-24i−4i−4i4i−2i2i2i−2i-222-200000000−2i2i2i−2i00000000000000000000000000000000000000000000000000
χ804-4-444i−4i−4i4i4-4-444i−4i−4i4i000000-2-2222-22-2−2i2i2i−2i−2i2i2i−2i1-1-1123−2300−2i32i300i−i−ii−33−33i3−i3i3−i3000000000000000000000000000000000000000000
χ814-4-444i−4i−4i4i4-4-444i−4i−4i4i000000-2-2222-22-2−2i2i2i−2i−2i2i2i−2i1-1-11−2323002i3−2i300i−i−ii3−33−3−i3i3−i3i3000000000000000000000000000000000000000000
χ824-4-44−4i4i4i−4i4-4-44−4i4i4i−4i0000004-2-42-442-2−4i4i4i−4i2i−2i−2i2i-222-2000000002i−2i−2i2i00000000000000000000000000000000000000000000000000
χ834-4-44−4i4i4i−4i4-4-44−4i4i4i−4i000000-2-2222-22-22i−2i−2i2i2i−2i−2i2i1-1-1123−23002i3−2i300−iii−i−33−33−i3i3−i3i3000000000000000000000000000000000000000000
χ844-4-44−4i4i4i−4i4-4-44−4i4i4i−4i000000-2-2222-22-22i−2i−2i2i2i−2i−2i2i1-1-11−232300−2i32i300−iii−i3−33−3i3−i3i3−i3000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000222200000000220000-1-1-1-1-1-1-1-10000000000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000-2-2-2-200000000-2-20000111111110000000000000000
χ8766666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000222200000000-2-20000-1-1-1-111110000000000000000
χ8866666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000-2-2-2-2000000002200001111-1-1-1-10000000000000000
χ896666-6-6-6-6-3-3-3-333336-6-3-333000000000000000000000000000000000000000022-2-2000000002-20000-1-111-1-1110000000000000000
χ906666-6-6-6-6-3-3-3-333336-6-3-3330000000000000000000000000000000000000000-2-22200000000-22000011-1-111-1-10000000000000000
χ916666-6-6-6-6-3-3-3-33333-6633-3-3000000000000000000000000000000000000000022-2-200000000-220000-1-11111-1-10000000000000000
χ926666-6-6-6-6-3-3-3-33333-6633-3-30000000000000000000000000000000000000000-2-222000000002-2000011-1-1-1-1110000000000000000
χ9366-6-666-6-6-3-333-3-3330033−3333−3300000000000000000000000000000000000000002-22-200000000000000-11-113−33−30000000000000000
χ9466-6-666-6-6-3-333-3-3330033−3333−330000000000000000000000000000000000000000-22-22000000000000001-11-1−33−330000000000000000
χ9566-6-666-6-6-3-333-3-33300−3333−333300000000000000000000000000000000000000002-22-200000000000000-11-11−33−330000000000000000
χ9666-6-666-6-6-3-333-3-33300−3333−33330000000000000000000000000000000000000000-22-22000000000000001-11-13−33−30000000000000000
χ9766-6-6-6-666-3-33333-3-30033−33−333300000000000000000000000000000000000000002-2-2200000000000000-111-13−3−330000000000000000
χ9866-6-6-6-666-3-33333-3-30033−33−33330000000000000000000000000000000000000000-222-2000000000000001-1-11−333−30000000000000000
χ9966-6-6-6-666-3-33333-3-300−333333−3300000000000000000000000000000000000000002-2-2200000000000000-111-1−333−30000000000000000
χ10066-6-6-6-666-3-33333-3-300−333333−330000000000000000000000000000000000000000-222-2000000000000001-1-113−3−330000000000000000
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).