Finite Group Databasebeta

← Group #13147827

Character table — Group #13147827

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order12224444366612121212441212121233666666121212121212121236661212121212121212121212121212121212121212224444444444224444666666121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ51111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1
χ61111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ71111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-1-1-111-1-1-1-111111111-1-1-1-111
χ81111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-111-1-111
χ91111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-11-111111111-1-111-1-111-1-1-1-1-1-1-1-1
χ101111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111-1-11-11-1-11111-1-111-1-111-1-11111-1-1-1-1
χ111111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-111-1-1111-1-1-1-1-1-111-1-11111-1-1-1-11111
χ121111-1-1-1-11111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1-111-1-111-1-1-1-111111111
χ131111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-11-1-111-1-111-1-1-1-11111-1-111-1-111
χ141111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-111-11-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ151111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-111-1-1-1-1-111-1-11111-1-111-1-11111-1-1
χ161111-1-1-1-11111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1-1111-1-11111-1-1-1-111-1-111-1-111-1-1
χ1722222222222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122220000000020200000-1-1-1-100000000000000-1-1-1-1
χ1822222222222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-20-2000001111000000000000001111
χ192222222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022220000020200-1-1000000000000-1-1-1-1-1-10000
χ202222222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000-20-200110000000000001111110000
χ212222222222222222-2-2-2-2-2-22-1-1-1222-12222-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-111111111222200000000-20-200000-1-11100000000000000-1-111
χ222222222222222222-2-2-2-2-2-22-1-1-1222-12222-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-111111111-2-2-2-2000000002020000011-1-10000000000000011-1-1
χ232222222222222222-2-2-2-2-2-2-1222-1-1-12-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-1111111110000222200000-20-20011000000000000-1-1-1-1110000
χ242222222222222222-2-2-2-2-2-2-1222-1-1-12-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-1111111110000-2-2-2-20000020200-1-10000000000001111-1-10000
χ252222-2-2-2-22222-2-2-2-22-222-2-22-1-1-1222-1-2-2-2-21111-1-1-1-1-1-11122-2-21111-1-1-1-1111122-2-20000000020-200000-1-1-1-1000000000000001111
χ262222-2-2-2-22222-2-2-2-22-222-2-22-1-1-1222-1-2-2-2-21111-1-1-1-1-1-11122-2-21111-1-1-1-11111-2-22200000000-20200000111100000000000000-1-1-1-1
χ272222-2-2-2-22222-2-2-2-22-222-2-2-1222-1-1-121111-2-2-2-2-1-1-1-122-2-2-1-1111111-1-1-1-11111000022-2-20000020-200-1-1000000000000-1-111110000
χ282222-2-2-2-22222-2-2-2-22-222-2-2-1222-1-1-121111-2-2-2-2-1-1-1-122-2-2-1-1111111-1-1-1-111110000-2-22200000-202001100000000000011-1-1-1-10000
χ292222-2-2-2-22222-2-2-2-2-22-2-2222-1-1-1222-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-122-2-200000000-20200000-1-1110000000000000011-1-1
χ302222-2-2-2-22222-2-2-2-2-22-2-2222-1-1-1222-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-1-2-2220000000020-20000011-1-100000000000000-1-111
χ312222-2-2-2-22222-2-2-2-2-22-2-222-1222-1-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-1000022-2-200000-2020011000000000000-1-111-1-10000
χ322222-2-2-2-22222-2-2-2-2-22-2-222-1222-1-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-10000-2-2220000020-200-1-100000000000011-1-1110000
χ3322-2-222-2-222-2-222-2-200000022-2-22-2-2222-2-222-2-222-2-20000000022-2-20000000000002i−2i2i−2i0000000000000000000000002i−2i2i−2i000000
χ3422-2-222-2-222-2-222-2-200000022-2-22-2-2222-2-222-2-222-2-20000000022-2-2000000000000−2i2i−2i2i000000000000000000000000−2i2i−2i2i000000
χ3522-2-222-2-222-2-222-2-2000000-12-2-2-1112-1-11122-2-2-1-11100003−33−3-1-11133−3−333−3−300002i−2i2i−2i0000000000−i3i3000000000000−ii−ii−i3i30000
χ3622-2-222-2-222-2-222-2-2000000-12-2-2-1112-1-11122-2-2-1-11100003−33−3-1-11133−3−333−3−30000−2i2i−2i2i0000000000i3−i3000000000000i−ii−ii3−i30000
χ3722-2-222-2-222-2-222-2-2000000-12-2-2-1112-1-11122-2-2-1-1110000−33−33-1-111−3−333−3−33300002i−2i2i−2i0000000000i3−i3000000000000−ii−iii3−i30000
χ3822-2-222-2-222-2-222-2-2000000-12-2-2-1112-1-11122-2-2-1-1110000−33−33-1-111−3−333−3−3330000−2i2i−2i2i0000000000−i3i3000000000000i−ii−i−i3i30000
χ3922-2-2-2-22222-2-2-2-22200000022-2-22-2-22-2-222-2-22222-2-200000000-2-2220000000000002i−2i−2i2i0000000000000000000000002i−2i−2i2i000000
χ4022-2-2-2-22222-2-2-2-22200000022-2-22-2-22-2-222-2-22222-2-200000000-2-222000000000000−2i2i2i−2i000000000000000000000000−2i2i2i−2i000000
χ4122-2-2-2-22222-2-2-2-222000000-12-2-2-111211-1-1-2-222-1-11100003−3−3311-1-133−3−3−3−33300002i−2i−2i2i0000000000−i3i3000000000000−iii−ii3−i30000
χ4222-2-2-2-22222-2-2-2-222000000-12-2-2-111211-1-1-2-222-1-11100003−3−3311-1-133−3−3−3−3330000−2i2i2i−2i0000000000i3−i3000000000000i−i−ii−i3i30000
χ4322-2-2-2-22222-2-2-2-222000000-12-2-2-111211-1-1-2-222-1-1110000−333−311-1-1−3−33333−3−300002i−2i−2i2i0000000000i3−i3000000000000−iii−i−i3i30000
χ4422-2-2-2-22222-2-2-2-222000000-12-2-2-111211-1-1-2-222-1-1110000−333−311-1-1−3−33333−3−30000−2i2i2i−2i0000000000−i3i3000000000000i−i−iii3−i30000
χ452-22-22i−2i2i−2i2-22-22i−2i2i−2i000000222-2-22-2-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i000000002-22i−2i00000000000000002-200000000000000002i−2i00
χ462-22-22i−2i2i−2i2-22-22i−2i2i−2i000000222-2-22-2-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i00000000-22−2i2i0000000000000000-220000000000000000−2i2i00
χ472-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-11-22-212i−2i2i−2i−ii−ii-11-11−i3i33−30000−ii−ii−i3i3−i3i33−33−32-22i−2i0000000000000000-11−i3i300000000000000−ii3−3
χ482-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-11-22-212i−2i2i−2i−ii−ii-11-11−i3i33−30000−ii−ii−i3i3−i3i33−33−3-22−2i2i00000000000000001-1i3−i300000000000000i−i−33
χ492-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-11-22-212i−2i2i−2i−ii−ii-11-11i3−i3−330000−ii−iii3−i3i3−i3−33−332-22i−2i0000000000000000-11i3−i300000000000000−ii−33
χ502-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-11-22-212i−2i2i−2i−ii−ii-11-11i3−i3−330000−ii−iii3−i3i3−i3−33−33-22−2i2i00000000000000001-1−i3i300000000000000i−i3−3
χ512-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000222-2-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i000000002-2−2i2i00000000000000002-20000000000000000−2i2i00
χ522-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000222-2-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i00000000-222i−2i0000000000000000-2200000000000000002i−2i00
χ532-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-11-22-21−2i2i−2i2ii−ii−i-11-11−i3i3−330000i−ii−i−i3i3−i3i3−33−332-2−2i2i0000000000000000-11−i3i300000000000000i−i−33
χ542-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-11-22-21−2i2i−2i2ii−ii−i-11-11−i3i3−330000i−ii−i−i3i3−i3i3−33−33-222i−2i00000000000000001-1i3−i300000000000000−ii3−3
χ552-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-11-22-21−2i2i−2i2ii−ii−i-11-11i3−i33−30000i−ii−ii3−i3i3−i33−33−32-2−2i2i0000000000000000-11i3−i300000000000000i−i3−3
χ562-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-11-22-21−2i2i−2i2ii−ii−i-11-11i3−i33−30000i−ii−ii3−i3i3−i33−33−3-222i−2i00000000000000001-1−i3i300000000000000−ii−33
χ572-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-22-2-22-22i−2i−2i2i2i−2i−2i2i2-2-22000000002i−2i−2i2i00000000000000002-22i−2i0000000000002-22i−2i00000000000000
χ582-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-22-2-22-22i−2i−2i2i2i−2i−2i2i2-2-22000000002i−2i−2i2i0000000000000000-22−2i2i000000000000-22−2i2i00000000000000
χ592-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-22-2-22-2−2i2i2i−2i−2i2i2i−2i2-2-2200000000−2i2i2i−2i00000000000000002-2−2i2i0000000000002-2−2i2i00000000000000
χ602-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-22-2-22-2−2i2i2i−2i−2i2i2i−2i2-2-2200000000−2i2i2i−2i0000000000000000-222i−2i000000000000-222i−2i00000000000000
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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
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χ784-4-444i−4i−4i4i4-4-444i−4i−4i4i000000-24-4422-2-4−2i2i2i−2i4i−4i−4i4i-222-200000000−2i2i2i−2i00000000000000000000000000000000000000000000000000
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χ814-4-44−4i4i4i−4i4-4-44−4i4i4i−4i0000004-22-2-4-442−4i4i4i−4i2i−2i−2i2i-222-2000000002i−2i−2i2i00000000000000000000000000000000000000000000000000
χ824-4-44−4i4i4i−4i4-4-44−4i4i4i−4i000000-24-4422-2-42i−2i−2i2i−4i4i4i−4i-222-2000000002i−2i−2i2i00000000000000000000000000000000000000000000000000
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χ844-4-44−4i4i4i−4i4-4-44−4i4i4i−4i000000-2-22-222-222i−2i−2i2i2i−2i−2i2i1-1-1100000000−iii−i−3i3i3i−3i-333-3000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000000000002222000022000000-1-1-1-1-1-1-1-10000000000
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χ8766666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000000022220000-2-2000000-1-1-1-111110000000000
χ8866666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000000000-2-2-2-20000220000001111-1-1-1-10000000000
χ896666-6-6-6-6-3-3-3-333336-6-3-33300000000000000000000000000000000000000000000000022-2-200002-2000000-1-111-1-1110000000000
χ906666-6-6-6-6-3-3-3-333336-6-3-333000000000000000000000000000000000000000000000000-2-2220000-2200000011-1-111-1-10000000000
χ916666-6-6-6-6-3-3-3-33333-6633-3-300000000000000000000000000000000000000000000000022-2-20000-22000000-1-11111-1-10000000000
χ926666-6-6-6-6-3-3-3-33333-6633-3-3000000000000000000000000000000000000000000000000-2-22200002-200000011-1-1-1-1110000000000
χ936-6-666i−6i−6i6i-333-3−3i3i3i−3i0033−33−3i33i30000000000000000000000000000000000000000000000002-22i−2i000000000000-11−ii3−3−i3i30000000000
χ946-6-666i−6i−6i6i-333-3−3i3i3i−3i0033−33−3i33i3000000000000000000000000000000000000000000000000-22−2i2i0000000000001-1i−i−33i3−i30000000000
χ956-6-666i−6i−6i6i-333-3−3i3i3i−3i00−33333i3−3i30000000000000000000000000000000000000000000000002-22i−2i000000000000-11−ii−33i3−i30000000000
χ966-6-666i−6i−6i6i-333-3−3i3i3i−3i00−33333i3−3i3000000000000000000000000000000000000000000000000-22−2i2i0000000000001-1i−i3−3−i3i30000000000
χ976-6-66−6i6i6i−6i-333-33i−3i−3i3i0033−333i3−3i30000000000000000000000000000000000000000000000002-2−2i2i000000000000-11i−i3−3i3−i30000000000
χ986-6-66−6i6i6i−6i-333-33i−3i−3i3i0033−333i3−3i3000000000000000000000000000000000000000000000000-222i−2i0000000000001-1−ii−33−i3i30000000000
χ996-6-66−6i6i6i−6i-333-33i−3i−3i3i00−3333−3i33i30000000000000000000000000000000000000000000000002-2−2i2i000000000000-11i−i−33−i3i30000000000
χ1006-6-66−6i6i6i−6i-333-33i−3i−3i3i00−3333−3i33i3000000000000000000000000000000000000000000000000-222i−2i0000000000001-1−ii3−3i3−i30000000000
χ1011212-12-121212-12-12-6-666-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-12-12-12-121212-6-66666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-1212-1212i−12i12i−12i-66-66−6i6i−6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-1212-12−12i12i−12i12i-66-666i−6i6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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