Finite Group Databasebeta

← Group #13147789

Character table — Group #13147789

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order12224444366612121212441212121233666666121212121212121236661212121212121212121212121212121212121212224444444444224444666666121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111-1-1111111-1-1-1-1
χ91111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-11-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ101111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111-1-11-11-1-11111-1-11111-1-1-1-1-1-111-1-111
χ111111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-111-1-1111-1-1-1-111-1-1-1-11111-1-111-1-111
χ121111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ131111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-11-1-111-1-111-1-111-1-11111-1-1-1-111
χ141111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-111-11-11111-1-1-1-111-1-1-1-111-1-11111-1-1
χ151111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-111-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ161111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1-1111-1-111-1-111-1-111-1-111-1-1-1-111
χ1722222222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122220000000020200000-1-1-1-1000000-1-1-1-100000000
χ1822222222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-20-2000001111000000111100000000
χ192222222222222222222222-12-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ212222222222222222-2-2-2-2-2-22-12-1-122-12222-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-111111111222200000000-20-200000-1-111000000-1-11100000000
χ222222222222222222-2-2-2-2-2-22-12-1-122-12222-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-111111111-2-2-2-2000000002020000011-1-100000011-1-100000000
χ232222222222222222-2-2-2-2-2-2-12-122-1-12-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-1111111110000000022220000-2-20000000000000000-1-1-1-11111
χ242222222222222222-2-2-2-2-2-2-12-122-1-12-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-11111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
χ252222-2-2-2-22222-2-2-2-22-222-2-22-12-1-122-1-2-2-2-21111-1-1-1-1-1-11122-2-21111-1-1-1-1111122-2-20000000020-200000-1-1-1-1000000111100000000
χ262222-2-2-2-22222-2-2-2-22-222-2-22-12-1-122-1-2-2-2-21111-1-1-1-1-1-11122-2-21111-1-1-1-11111-2-22200000000-202000001111000000-1-1-1-100000000
χ272222-2-2-2-22222-2-2-2-22-222-2-2-12-122-1-121111-2-2-2-2-1-1-1-122-2-2-1-1111111-1-1-1-111110000000022-2-200002-20000000000000000-1-111-1-111
χ282222-2-2-2-22222-2-2-2-22-222-2-2-12-122-1-121111-2-2-2-2-1-1-1-122-2-2-1-1111111-1-1-1-1111100000000-2-2220000-22000000000000000011-1-111-1-1
χ292222-2-2-2-22222-2-2-2-2-22-2-2222-12-1-122-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-122-2-200000000-20200000-1-11100000011-1-100000000
χ302222-2-2-2-22222-2-2-2-2-22-2-2222-12-1-122-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-1-2-2220000000020-20000011-1-1000000-1-11100000000
χ312222-2-2-2-22222-2-2-2-2-22-2-222-12-122-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-10000000022-2-20000-220000000000000000-1-11111-1-1
χ322222-2-2-2-22222-2-2-2-2-22-2-222-12-122-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-100000000-2-22200002-2000000000000000011-1-1-1-111
χ3322-2-222-2-222-2-222-2-2000000222-2-2-2-2222-2-222-2-222-2-20000000022-2-20000000000002i−2i2i−2i00000000000000002i−2i2i−2i00000000000000
χ3422-2-222-2-222-2-222-2-2000000222-2-2-2-2222-2-222-2-222-2-20000000022-2-2000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i00000000000000
χ3522-2-2-2-22222-2-2-2-222000000222-2-2-2-22-2-222-2-22222-2-200000000-2-2220000000000002i−2i−2i2i00000000000000002i−2i−2i2i00000000000000
χ3622-2-2-2-22222-2-2-2-222000000222-2-2-2-22-2-222-2-22222-2-200000000-2-222000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i00000000000000
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χ392-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-2-112-212i−2i2i−2i−ii−ii-11-11−i3i33−30000−ii−ii−i3−i3i3i333−3−32-22i−2i0000000000000000-11−i3i3000000−ii3−300000000
χ402-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-2-112-212i−2i2i−2i−ii−ii-11-11−i3i33−30000−ii−ii−i3−i3i3i333−3−3-22−2i2i00000000000000001-1i3−i3000000i−i−3300000000
χ412-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-2-112-212i−2i2i−2i−ii−ii-11-11i3−i3−330000−ii−iii3i3−i3−i3−3−3332-22i−2i0000000000000000-11i3−i3000000−ii−3300000000
χ422-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-2-112-212i−2i2i−2i−ii−ii-11-11i3−i3−330000−ii−iii3i3−i3−i3−3−333-22−2i2i00000000000000001-1−i3i3000000i−i3−300000000
χ432-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i000000002-2−2i2i00000000000000002-200000000−2i2i0000000000
χ442-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i00000000-222i−2i0000000000000000-22000000002i−2i0000000000
χ452-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-2-112-21−2i2i−2i2ii−ii−i-11-11−i3i3−330000i−ii−i−i3−i3i3i3−3−3332-2−2i2i0000000000000000-11−i3i3000000i−i−3300000000
χ462-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-2-112-21−2i2i−2i2ii−ii−i-11-11−i3i3−330000i−ii−i−i3−i3i3i3−3−333-222i−2i00000000000000001-1i3−i3000000−ii3−300000000
χ472-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-2-112-21−2i2i−2i2ii−ii−i-11-11i3−i33−30000i−ii−ii3i3−i3−i333−3−32-2−2i2i0000000000000000-11i3−i3000000i−i3−300000000
χ482-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-2-112-21−2i2i−2i2ii−ii−i-11-11i3−i33−30000i−ii−ii3i3−i3−i333−3−3-222i−2i00000000000000001-1−i3i3000000−ii−3300000000
χ492-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-2-22-22-22i−2i−2i2i2i−2i−2i2i2-2-22000000002i−2i−2i2i00000000000000002-22i−2i00000000000000000000002-22i−2i0000
χ502-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-2-22-22-22i−2i−2i2i2i−2i−2i2i2-2-22000000002i−2i−2i2i0000000000000000-22−2i2i0000000000000000000000-22−2i2i0000
χ512-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-221-1-2−iii−i2i−2i−2i2i-111-100003−3−i3i3−iii−i3−33−3−i3i3−i3i3000000002-22i−2i0000000000000000000000-11−ii3−3−i3i3
χ522-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-221-1-2−iii−i2i−2i−2i2i-111-100003−3−i3i3−iii−i3−33−3−i3i3−i3i300000000-22−2i2i00000000000000000000001-1i−i−33i3−i3
χ532-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-221-1-2−iii−i2i−2i−2i2i-111-10000−33i3−i3−iii−i−33−33i3−i3i3−i3000000002-22i−2i0000000000000000000000-11−ii−33i3−i3
χ542-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-121-221-1-2−iii−i2i−2i−2i2i-111-10000−33i3−i3−iii−i−33−33i3−i3i3−i300000000-22−2i2i00000000000000000000001-1i−i3−3−i3i3
χ552-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-2-22-22-2−2i2i2i−2i−2i2i2i−2i2-2-2200000000−2i2i2i−2i00000000000000002-2−2i2i00000000000000000000002-2−2i2i0000
χ562-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-2-22-22-2−2i2i2i−2i−2i2i2i−2i2-2-2200000000−2i2i2i−2i0000000000000000-222i−2i0000000000000000000000-222i−2i0000
χ572-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-221-1-2i−i−ii−2i2i2i−2i-111-100003−3i3−i3i−i−ii3−33−3i3−i3i3−i3000000002-2−2i2i0000000000000000000000-11i−i3−3i3−i3
χ582-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-221-1-2i−i−ii−2i2i2i−2i-111-100003−3i3−i3i−i−ii3−33−3i3−i3i3−i300000000-222i−2i00000000000000000000001-1−ii−33−i3i3
χ592-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-121-221-1-2i−i−ii−2i2i2i−2i-111-10000−33−i3i3i−i−ii−33−33−i3i3−i3i3000000002-2−2i2i0000000000000000000000-11i−i−33−i3i3
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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
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χ794-4-444i−4i−4i4i4-4-444i−4i−4i4i0000004-2-42-2-4424i−4i−4i4i−2i2i2i−2i-222-200000000−2i2i2i−2i00000000000000000000000000000000000000000000000000
χ804-4-444i−4i−4i4i4-4-444i−4i−4i4i000000-2-222-22-22−2i2i2i−2i−2i2i2i−2i1-1-11000023−23−2i32i3i−i−ii−33−33i3−i3i3−i3000000000000000000000000000000000000000000
χ814-4-444i−4i−4i4i4-4-444i−4i−4i4i000000-2-222-22-22−2i2i2i−2i−2i2i2i−2i1-1-110000−23232i3−2i3i−i−ii3−33−3−i3i3−i3i3000000000000000000000000000000000000000000
χ824-4-44−4i4i4i−4i4-4-44−4i4i4i−4i0000004-2-42-2-442−4i4i4i−4i2i−2i−2i2i-222-2000000002i−2i−2i2i00000000000000000000000000000000000000000000000000
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χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000000022220000020200-1-10000-1-1-1-1-1-1000000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000-2-2-2-200000-20-200110000111111000000000000
χ8766666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000222200000-20-200110000-1-1-1-111000000000000
χ8866666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000-2-2-2-20000020200-1-100001111-1-1000000000000
χ896666-6-6-6-6-3-3-3-333336-6-3-3330000000000000000000000000000000000000000000022-2-20000020-200-1-10000-1-11111000000000000
χ906666-6-6-6-6-3-3-3-333336-6-3-33300000000000000000000000000000000000000000000-2-22200000-2020011000011-1-1-1-1000000000000
χ916666-6-6-6-6-3-3-3-33333-6633-3-30000000000000000000000000000000000000000000022-2-200000-20200110000-1-111-1-1000000000000
χ926666-6-6-6-6-3-3-3-33333-6633-3-300000000000000000000000000000000000000000000-2-2220000020-200-1-1000011-1-111000000000000
χ9366-6-666-6-6-3-333-3-3330033−3333−33000000000000000000000000000000000000000000002i−2i2i−2i0000000000−i3i30000−ii−ii−i3i3000000000000
χ9466-6-666-6-6-3-333-3-3330033−3333−3300000000000000000000000000000000000000000000−2i2i−2i2i0000000000i3−i30000i−ii−ii3−i3000000000000
χ9566-6-666-6-6-3-333-3-33300−3333−3333000000000000000000000000000000000000000000002i−2i2i−2i0000000000i3−i30000−ii−iii3−i3000000000000
χ9666-6-666-6-6-3-333-3-33300−3333−333300000000000000000000000000000000000000000000−2i2i−2i2i0000000000−i3i30000i−ii−i−i3i3000000000000
χ9766-6-6-6-666-3-33333-3-30033−33−3333000000000000000000000000000000000000000000002i−2i−2i2i0000000000−i3i30000−iii−ii3−i3000000000000
χ9866-6-6-6-666-3-33333-3-30033−33−333300000000000000000000000000000000000000000000−2i2i2i−2i0000000000i3−i30000i−i−ii−i3i3000000000000
χ9966-6-6-6-666-3-33333-3-300−333333−33000000000000000000000000000000000000000000002i−2i−2i2i0000000000i3−i30000−iii−i−i3i3000000000000
χ10066-6-6-6-666-3-33333-3-300−333333−3300000000000000000000000000000000000000000000−2i2i2i−2i0000000000−i3i30000i−i−iii3−i3000000000000
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).