Finite Group Databasebeta

← Group #13140042

Character table — Group #13140042

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order1222223444466666661212121212121212336666663666666666661212121212121212121212121212121288888888242424242424242424242424242424242244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ51111-1-111-1-1111-1-1-1-1111-1-1-1-111111111111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ61111-1-111-1-1111-1-1-1-1111-1-1-1-111111111111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111-1-111-1-1111-1-1-1-1111-1-1-1-111111111111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ81111-1-111-1-1111-1-1-1-1111-1-1-1-111111111111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222-12-12-12-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1000000000000000000000000020200-1-100-1-1
χ10222222222222222222222222222-12-12-12-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000000000000000000000000-20-200110011
χ1122222222222222222222222222-12-12-12-12-1-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000000000000000000000002020-1-100-1-100
χ1222222222222222222222222222-12-12-12-12-1-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1000000000000000000000000-20-2011001100
χ132222222-2-2-2-22222222-2-2-2-2-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ142222222-2-2-2-22222222-2-2-2-2-2-2-2-22-12-12-12-1-122-1-1-1-1-1-1-1-1-1-2-211-2-21111111111000000000000000000000000000000−i3i300−i3i3
χ152222222-2-2-2-22222222-2-2-2-2-2-2-2-22-12-12-12-1-122-1-1-1-1-1-1-1-1-1-2-211-2-21111111111000000000000000000000000000000i3−i300i3−i3
χ162222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-12-12-12-1-1-122-1-1-1-1-1-1-111-2-211-2-2111111110000000000000000000000000000−i3i300−i3i300
χ172222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-12-12-12-1-1-122-1-1-1-1-1-1-111-2-211-2-2111111110000000000000000000000000000i3−i300i3−i300
χ182222-2-222-2-2222-2-2-2-2222-2-2-2-2222-12-12-12-1-1-2-211-1-11111-122-1-1-2-211-1-1-1-11111000000000000000000000000020-200-1-10011
χ192222-2-222-2-2222-2-2-2-2222-2-2-2-2222-12-12-12-1-1-2-211-1-11111-122-1-1-2-211-1-1-1-111110000000000000000000000000-202001100-1-1
χ202222-2-222-2-2222-2-2-2-2222-2-2-2-222-12-12-12-12-111-2-2-1-11111-1-1-12211-2-2-1-1-1-1111100000000000000000000000020-20-1-1001100
χ212222-2-222-2-2222-2-2-2-2222-2-2-2-222-12-12-12-12-111-2-2-1-11111-1-1-12211-2-2-1-1-1-11111000000000000000000000000-20201100-1-100
χ222222-2-22-222-222-2-2-2-22-2-22222-2-2222222222-2-2-2-222-2-2-2-22-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ232222-2-22-222-222-2-2-2-22-2-22222-2-22-12-12-12-1-1-2-211-1-11111-1-2-21122-1-11111-1-1-1-1000000000000000000000000000000−i3i300i3−i3
χ242222-2-22-222-222-2-2-2-22-2-22222-2-22-12-12-12-1-1-2-211-1-11111-1-2-21122-1-11111-1-1-1-1000000000000000000000000000000i3−i300−i3i3
χ252222-2-22-222-222-2-2-2-22-2-22222-2-2-12-12-12-12-111-2-2-1-11111-111-2-2-1-1221111-1-1-1-10000000000000000000000000000−i3i300i3−i300
χ262222-2-22-222-222-2-2-2-22-2-22222-2-2-12-12-12-12-111-2-2-1-11111-111-2-2-1-1221111-1-1-1-10000000000000000000000000000i3−i300−i3i300
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χ312-22-2002200-2-2-200002220000-2-222-2-222-2-220000-2-2000022-22-2000022-2-2000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i000000000000
χ322-22-2002200-2-2-200002220000-2-222-2-222-2-220000-2-2000022-22-2000022-2-200000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i000000000000
χ332-22-2002-2002-2-200002-2-200002222-2-222-2-220000-2-200002-22-220000-2-22200002-22-2000022-2-222-2-200000000000000000000
χ342-22-2002-2002-2-200002-2-200002222-2-222-2-220000-2-200002-22-220000-2-2220000-22-220000-2-222-2-22200000000000000000000
χ352-2-222-220000-2222-2-2-20000000022-2-2-2-22222-22-2-2222-2-2-200000000000000002−2−222−2−2222−2−2−2−22222−2−2−2−222000000000000
χ362-2-222-220000-2222-2-2-20000000022-2-2-2-22222-22-2-2222-2-2-20000000000000000−222−2−222−2−2−22222−2−2−2−22222−2−2000000000000
χ372-2-22-2220000-22-2-222-20000000022-2-2-2-2222-22-22-22-2-222-200000000000000002−2−22−222−222−2−2−2−222−2−22222−2−2000000000000
χ382-2-22-2220000-22-2-222-20000000022-2-2-2-2222-22-22-22-2-222-20000000000000000−222−22−2−22−2−22222−2−222−2−2−2−222000000000000
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χ404444444-4-4-4-44444444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-21-2-2-2-2111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ414444-4-444-4-4444-4-4-4-4444-4-4-4-444-2-2-2-2-2-2-2-21222211-1-1-1-11-2-2-2-222221111-1-1-1-1000000000000000000000000000000000000
χ424444-4-44-444-444-4-4-4-44-4-44444-4-4-2-2-2-2-2-2-2-21222211-1-1-1-112222-2-2-2-2-1-1-1-11111000000000000000000000000000000000000
χ4344-4-400404i−4i04-40000-4004i4i−4i−4i004-24-2-42-42-20000-220000200004i−4i−2i2i0000−2i−2i2i2i000000000000000000000000000000000000
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χ4644-4-400404i−4i04-40000-4004i4i−4i−4i00-2-2-2-22222100001-1-33-33-10000−2i2i−2i2i−3i3i−3i3iii−i−i000000000000000000000000000000000000
χ4744-4-40040−4i4i04-40000-400−4i−4i4i4i004-24-2-42-42-20000-22000020000−4i4i2i−2i00002i2i−2i−2i000000000000000000000000000000000000
χ4844-4-40040−4i4i04-40000-400−4i−4i4i4i00-24-242-42-4-20000-220000200002i−2i−4i4i00002i2i−2i−2i000000000000000000000000000000000000
χ4944-4-40040−4i4i04-40000-400−4i−4i4i4i00-2-2-2-22222100001-13-33-3-100002i−2i2i−2i−3i3i−3i3i−i−iii000000000000000000000000000000000000
χ5044-4-40040−4i4i04-40000-400−4i−4i4i4i00-2-2-2-22222100001-1-33-33-100002i−2i2i−2i3i−3i3i−3i−i−iii000000000000000000000000000000000000
χ514-44-4004400-4-4-400004440000-4-44-2-424-2-42-20000220000-24-4-220000-2-2220000000000000000000000000000000000000000
χ524-44-4004400-4-4-400004440000-4-4-242-4-242-4-20000220000-2-224-40000-2-2220000000000000000000000000000000000000000
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χ664-4-44-4440000-44-4-444-400000000-2-22222-2-212-22-2-11-1-111-100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000
χ67666666-36666-3-3-3-3-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ68666666-36666-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3000000000000000000000000000000000000-2-2-2-2-2-2-2-21111111111111111000000000000
χ69666666-3-6-6-6-6-3-3-3-3-3-3-333333333000000000000000000000000000000000000000000003−33−33−33−33−33−33−33−3000000000000
χ70666666-3-6-6-6-6-3-3-3-3-3-3-33333333300000000000000000000000000000000000000000000−33−33−33−33−33−33−33−33000000000000
χ716666-6-6-36-6-66-3-33333-3-3-33333-3-30000000000000000000000000000000000002222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ726666-6-6-36-6-66-3-33333-3-3-33333-3-3000000000000000000000000000000000000-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
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χ926-6-666-6-300003-3-3-333333−3333−33−3333−3333000000000000000000000000000000000000−222−2−222−2−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
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χ946-6-666-6-300003-3-3-3333−3333−333333−3333−33000000000000000000000000000000000000−222−2−222−2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ956-6-66-66-300003-333-3-3333−33−333333−33−33330000000000000000000000000000000000002−2−22−222−2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ966-6-66-66-300003-333-3-3333−33−333333−33−3333000000000000000000000000000000000000−222−22−2−22−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ976-6-66-66-300003-333-3-33−333333−33−333333−330000000000000000000000000000000000002−2−22−222−2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ986-6-66-66-300003-333-3-33−333333−33−333333−33000000000000000000000000000000000000−222−22−2−22−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000

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