Finite Group Databasebeta

← Group #13138936

Character table — Group #13138936

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order12223446668888121212122424242424242424336666663666121212121212121224242424242424242424242424242424224466668888121212122424242424242424244466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-11-111-1-111-1-1
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-11-1-111-1-111
χ9222222222222222222222222222-1-1-1222-1-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002002-1-10000-1-1
χ10222222222222222222222222222-1-1-1222-1-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-200-211000011
χ1122222222222222222222222222-1222-1-1-12-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000000000022000-1-1-1-100
χ1222222222222222222222222222-1222-1-1-12-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000000000000-2-2000111100
χ132222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-1222-1-1-1-1-12-1-1-12-1-1-1-2-2-2-2111111111111000000000000000000000000200-2-1-1000011
χ142222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-1222-1-1-1-1-12-1-1-12-1-1-1-2-2-2-2111111111111000000000000000000000000-2002110000-1-1
χ152222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1222-1-1-12-1-1-1-1-12-1-1-12-1-11111-2-2-2-21111111100000000000000000000000002-2000-1-11100
χ162222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1222-1-1-12-1-1-1-1-12-1-1-12-1-11111-2-2-2-2111111110000000000000000000000000-2200011-1-100
χ1722222-2-22220000-2-2-2-200000000222222222222-2-2-2-2-2-2-2-2000000000000000022-2-222220000-2-2-2-200000000000000000000
χ1822222-2-22220000-2-2-2-200000000222222222222-2-2-2-2-2-2-2-20000000000000000-2-222-2-2-2-20000222200000000000000000000
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χ292-2-222-22-2-222-2-22-2-22222-2-2-2-22222-2-22-2-222-2-22-2-2-2-222222-2-222-2-2222-2-2-2-222000000000000000000000000000000000000
χ302-2-222-22-2-222-2-22-2-22222-2-2-2-2222-1112-2-2-1-111-1-21112-1-1-12-2-22-111-1-1-11111-1-10000000000000000000000000000−i3i30000−i3i3
χ312-2-222-22-2-222-2-22-2-22222-2-2-2-2222-1112-2-2-1-111-1-21112-1-1-12-2-22-111-1-1-11111-1-10000000000000000000000000000i3−i30000i3−i3
χ322-2-222-22-2-222-2-22-2-22222-2-2-2-222-12-2-2-1112-111-11-211-12-1-1-111-12-2-22-1-11111-1-10000000000000000000000000000003−33−300
χ332-2-222-22-2-222-2-22-2-22222-2-2-2-222-12-2-2-1112-111-11-211-12-1-1-111-12-2-22-1-11111-1-1000000000000000000000000000000−33−3300
χ342-2-222-22-2-22-222-2-2-222-2-22222-2-222-2-22-2-222-2-22-2-2-2-22222-222-2-222-2-2-22222-2-2000000000000000000000000000000000000
χ352-2-222-22-2-22-222-2-2-222-2-22222-2-22-1112-2-2-1-111-1-21112-1-1-1-222-21-1-1111-1-1-1-1110000000000000000000000000000−i3i30000i3−i3
χ362-2-222-22-2-22-222-2-2-222-2-22222-2-22-1112-2-2-1-111-1-21112-1-1-1-222-21-1-1111-1-1-1-1110000000000000000000000000000i3−i30000−i3i3
χ372-2-222-22-2-22-222-2-2-222-2-22222-2-2-12-2-2-1112-111-11-211-12-1-11-1-11-222-211-1-1-1-1110000000000000000000000000000003−3−3300
χ382-2-222-22-2-22-222-2-2-222-2-22222-2-2-12-2-2-1112-111-11-211-12-1-11-1-11-222-211-1-1-1-111000000000000000000000000000000−333−300
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χ8066-6-6-300-3333i23i2−3i2−3i233−3333−33−3ζ5−3ζ7−3ζ13−3ζ23−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ233ζ5+3ζ73ζ13+3ζ2300000000000000000000000000000000000000−2i2ii3−i3i3−i322−2−2ii−i−iζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ8166-6-6-300-3333i23i2−3i2−3i2−3333−3333−3ζ13−3ζ23−3ζ5−3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ73ζ13+3ζ233ζ5+3ζ7000000000000000000000000000000000000002i−2ii3−i3i3−i3−2−222−i−iii−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7000000000000
χ8266-6-6-300-3333i23i2−3i2−3i2−3333−3333−3ζ13−3ζ23−3ζ5−3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ73ζ13+3ζ233ζ5+3ζ700000000000000000000000000000000000000−2i2i−i3i3−i3i322−2−2ii−i−iζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ836-66-6-3003-33−3i23i2−3i23i233−33−33333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ70000000000000000000000000000000000002-200-1-111−i2i2−i2i23−33−3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ846-66-6-3003-33−3i23i2−3i23i233−33−33333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ7000000000000000000000000000000000000-220011-1-1i2−i2i2−i2−33−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ856-66-6-3003-33−3i23i2−3i23i2−333333−333ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ230000000000000000000000000000000000002-200-1-111−i2i2−i2i2−33−33ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ866-66-6-3003-33−3i23i2−3i23i2−333333−333ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ23000000000000000000000000000000000000-220011-1-1i2−i2i2−i23−33−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ876-66-6-3003-333i2−3i23i2−3i233−33−3333−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ70000000000000000000000000000000000002-200-1-111i2−i2i2−i23−33−3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ886-66-6-3003-333i2−3i23i2−3i233−33−3333−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7000000000000000000000000000000000000-220011-1-1−i2i2−i2i2−33−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ896-66-6-3003-333i2−3i23i2−3i2−333333−33−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ230000000000000000000000000000000000002-200-1-111i2−i2i2−i2−33−33−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ906-66-6-3003-333i2−3i23i2−3i2−333333−33−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ23000000000000000000000000000000000000-220011-1-1−i2i2−i2i23−33−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ916-6-66-36-633-30000-3-33333−33−3333−333333−330000000000000000000000000000000000000000−i3i3i3−i3−2i2i2i−2i−i3i3i3−i3ii−i−i−i−iii000000000000
χ926-6-66-36-633-30000-3-33333−33−3333−333333−330000000000000000000000000000000000000000i3−i3−i3i32i−2i−2i2ii3−i3−i3i3−i−iiiii−i−i000000000000
χ936-6-66-36-633-30000-3-333−333333−3333−33−33330000000000000000000000000000000000000000−i3i3i3−i32i−2i−2i2i−i3i3i3−i3−i−iiiii−i−i000000000000
χ946-6-66-36-633-30000-3-333−333333−3333−33−33330000000000000000000000000000000000000000i3−i3−i3i3−2i2i2i−2ii3−i3−i3i3ii−i−i−i−iii000000000000
χ956-6-66-3-6633-36-6-6633-3-3-3-33333-3-30000000000000000000000000000000000000000−i3i3i3−i30000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3000000000000
χ966-6-66-3-6633-36-6-6633-3-3-3-33333-3-30000000000000000000000000000000000000000i3−i3−i3i30000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3000000000000
χ976-6-66-3-6633-3-666-633-3-333-3-3-3-3330000000000000000000000000000000000000000−i3i3i3−i30000i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000
χ986-6-66-3-6633-3-666-633-3-333-3-3-3-3330000000000000000000000000000000000000000i3−i3−i3i30000−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000

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