Finite Group Databasebeta

← Group #13138752

Character table — Group #13138752

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order12223446668888121212122424242424242424336666663666121212121212121224242424242424242424242424242424444488881212121212121212242424242424242444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222-12-122-1-1-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000220000-1-1-1-1
χ10222222222222222222222222222-12-122-1-1-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-200001111
χ1122222222222222222222222222-12-12-1-122-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000000000002200-1-1-1-10000
χ1222222222222222222222222222-12-12-1-122-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000000000-2-20011110000
χ132222222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-122-1-1-1-1-1-12-1-1-12-1-1-1-2-2-2-2111111111111000000000000000000000000002-20000-1-111
χ142222222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-122-1-1-1-1-1-12-1-1-12-1-1-1-2-2-2-211111111111100000000000000000000000000-22000011-1-1
χ152222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-12-1-122-1-1-1-1-12-1-1-12-1-11111-2-2-2-2111111110000000000000000000000002-200-1-1110000
χ162222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-12-1-122-1-1-1-1-12-1-1-12-1-11111-2-2-2-211111111000000000000000000000000-220011-1-10000
χ1722222-2-22220000-2-2-2-200000000222222222222-2-2-2-2-2-2-2-2000000000000000022-2-200002222-2-2-2-200000000000000000000
χ1822222-2-22220000-2-2-2-200000000222222222222-2-2-2-2-2-2-2-20000000000000000-2-2220000-2-2-2-2222200000000000000000000
χ1922-2-222-22-2-222-2-222-2-22222-2-2-2-22222-2-2-2-22-2-22-2-2-2-2222222-2-222-2-22222-2-2-2-2000000000000000000000000000000000000
χ2022-2-222-22-2-222-2-222-2-22222-2-2-2-22-12-1-2-211-111-1-21112-1-1-122-2-2-1-111-1-1-1-11111000000000000000000000000000000003−33−3
χ2122-2-222-22-2-222-2-222-2-22222-2-2-2-22-12-1-2-211-111-1-21112-1-1-122-2-2-1-111-1-1-1-1111100000000000000000000000000000000−33−33
χ2222-2-222-22-2-222-2-222-2-22222-2-2-2-2-12-1211-2-2-111-11-211-12-1-1-1-11122-2-2-1-1-1-1111100000000000000000000000000003−33−30000
χ2322-2-222-22-2-222-2-222-2-22222-2-2-2-2-12-1211-2-2-111-11-211-12-1-1-1-11122-2-2-1-1-1-111110000000000000000000000000000−33−330000
χ2422-2-222-22-2-2-2-22222-2-2-2-2-2-222222222-2-2-2-22-2-22-2-2-2-22222-2-222-2-222-2-2-2-22222000000000000000000000000000000000000
χ2522-2-222-22-2-2-2-22222-2-2-2-2-2-222222-12-1-2-211-111-1-21112-1-1-1-2-22211-1-11111-1-1-1-1000000000000000000000000000000003−3−33
χ2622-2-222-22-2-2-2-22222-2-2-2-2-2-222222-12-1-2-211-111-1-21112-1-1-1-2-22211-1-11111-1-1-1-100000000000000000000000000000000−333−3
χ2722-2-222-22-2-2-2-22222-2-2-2-2-2-22222-12-1211-2-2-111-11-211-12-1-111-1-1-2-2221111-1-1-1-100000000000000000000000000003−3−330000
χ2822-2-222-22-2-2-2-22222-2-2-2-2-2-22222-12-1211-2-2-111-11-211-12-1-111-1-1-2-2221111-1-1-1-10000000000000000000000000000−333−30000
χ2922-2-22-222-2-20000-2-222000000002222-2-2-2-22-2-222222-2-2-2-20000000000000000000022-2-2000000002222-2-2-2-2000000000000
χ3022-2-22-222-2-20000-2-222000000002222-2-2-2-22-2-222222-2-2-2-200000000000000000000-2-22200000000-2-2-2-22222000000000000
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χ332-22-2200-22-2i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i222-2-22-22-222-2-200000000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2002-2i2−i2i2−i2000022-2-2i2i2−i2−i2i2i2−i2−i2000000000000
χ342-22-2200-22-2i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i222-2-22-22-222-2-200000000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200-22−i2i2−i2i20000-2-222−i2−i2i2i2−i2−i2i2i2000000000000
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χ3944444444444444444444444444-2-2-2-2-2-2-2-21111-2-211-2-211-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000
χ404444444444-4-4-4-44444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-21111-2-211-2-21122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ4144444-4-44440000-4-4-4-4000000004-24-244-2-2-2-2-2-2-4222-42220000000000000000000000000000000000000000000000000000
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χ4344444-4-44440000-4-4-4-400000000-2-2-2-2-2-2-2-2111122-1-122-1-1000000003i−3i3i−3i3i−3i3i−3i000000000000000000000000000000000000
χ4444444-4-44440000-4-4-4-400000000-2-2-2-2-2-2-2-2111122-1-122-1-100000000−3i3i−3i3i−3i3i−3i3i000000000000000000000000000000000000
χ4544-4-444-44-4-444-4-444-4-44444-4-4-4-4-2-2-2-222221-1-1122-1-1-2-211-2-222-2-2221111-1-1-1-1000000000000000000000000000000000000
χ4644-4-444-44-4-4-4-44444-4-4-4-4-4-44444-2-2-2-222221-1-1122-1-1-2-21122-2-222-2-2-1-1-1-11111000000000000000000000000000000000000
χ4744-4-44-444-4-40000-4-444000000004-24-2-4-422-222-24-2-2-2-42220000000000000000000000000000000000000000000000000000
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χ856-66-6-3003-33−3i23i2−3i23i2−3333−33333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ7000000000000000000000000000000000000002-2−i2i2−i2i2−333−3-1-111ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ866-66-6-3003-33−3i23i2−3i23i2−3333−33333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ700000000000000000000000000000000000000-22i2−i2i2−i23−3−3311-1-1−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ876-66-6-3003-333i2−3i23i2−3i233−3333−33−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ23000000000000000000000000000000000000002-2i2−i2i2−i23−3−33-1-111−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ886-66-6-3003-333i2−3i23i2−3i233−3333−33−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ2300000000000000000000000000000000000000-22−i2i2−i2i2−333−311-1-1ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ896-66-6-3003-333i2−3i23i2−3i2−3333−3333−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7000000000000000000000000000000000000002-2i2−i2i2−i2−333−3-1-111−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ906-66-6-3003-333i2−3i23i2−3i2−3333−3333−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ700000000000000000000000000000000000000-22−i2i2−i2i23−3−3311-1-1ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ916-6-66-30033-3−3i23i23i2−3i233−33−33333ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ23−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ230000000000000000000000000000000000002-200−i2i2i2−i2-1-111−333−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ926-6-66-30033-3−3i23i23i2−3i233−33−33333ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ23−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ23000000000000000000000000000000000000-2200i2−i2−i2i211-1-13−3−33−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ936-6-66-30033-3−3i23i23i2−3i2−333333−333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ70000000000000000000000000000000000002-200−i2i2i2−i2-1-1113−3−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ946-6-66-30033-3−3i23i23i2−3i2−333333−333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7000000000000000000000000000000000000-2200i2−i2−i2i211-1-1−333−3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ956-6-66-30033-33i2−3i2−3i23i233−33−3333−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ233ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ230000000000000000000000000000000000002-200i2−i2−i2i2-1-111−333−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ966-6-66-30033-33i2−3i2−3i23i233−33−3333−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ233ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ23000000000000000000000000000000000000-2200−i2i2i2−i211-1-13−3−33ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ976-6-66-30033-33i2−3i2−3i23i2−333333−33−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ73ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ70000000000000000000000000000000000002-200i2−i2−i2i2-1-1113−3−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ986-6-66-30033-33i2−3i2−3i23i2−333333−33−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ73ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ7000000000000000000000000000000000000-2200−i2i2i2−i211-1-1−333−3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.