Finite Group Databasebeta

← Group #11781672

Character table — Group #11781672

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222222244444444444444444444444444444444444444444444444444444444444444424242424242424242424242448484848484872727272
order12223344446666661212121234666888812121212121212121212121212121212121212121212242424242424242424242424242424242424242424242424242424242424242444881212121224242424246612128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-1
χ61111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-111
χ71111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111
χ81111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-1
χ92222222-2-22222222-2-2-2-22-2222000022-2-222-2-22222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002-20022-2-200000000000000
χ102222222-2-22222222-2-2-2-22-2222000022-2-222-2-22222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-2200-2-22200000000000000
χ11222222-222-222222222222-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000
χ12222222-222-222222222222-2222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222222222220000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-2222220000-2-222-2-222-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000002i−2i00002i2i−2i−2i0000000000
χ14222222-2-2-2-2222222-2-2-2-2222220000-2-222-2-222-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000−2i2i0000−2i−2i2i2i0000000000
χ1522222-122222-1-122-12222-12-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000
χ1622222-122222-1-122-12222-12-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-211110000
χ1722222-122222-1-122-12222-12-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111111111110000000000002-2-1-1110000
χ1822222-122222-1-122-12222-12-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111111111000000000000-2211-1-10000
χ1922222-1-222-22-1-122-12222-1-2-1-1-122-2-21111-2-2-2-211111111-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000−i3i3−i3i30000
χ2022222-1-222-22-1-122-12222-1-2-1-1-122-2-21111-2-2-2-211111111-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000i3−i3i3−i30000
χ2122222-1-222-22-1-122-12222-1-2-1-1-1-2-2221111-2-2-2-211111111-1-1-1-1-1-1-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000−i3i3i3−i30000
χ2222222-1-222-22-1-122-12222-1-2-1-1-1-2-2221111-2-2-2-211111111-1-1-1-1-1-1-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000i3−i3−i3i30000
χ232222-122222-122-1-12-1-1-1-1-12-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ242222-122222-122-1-12-1-1-1-1-12-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ252222-122222-122-1-12-1-1-1-1-12-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-111111111-2-2-2-211111111-2-2-2-21111111122-2-2-1-1-1-111110000000000
χ262222-122222-122-1-12-1-1-1-1-12-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-111111111-2-2-2-211111111-2-2-2-211111111-2-2221111-1-1-1-10000000000
χ272222-122-2-22-122-1-121111-1-2-1-1-1000022-2-2-1-111-1-1-1-11111-2-2111133−3−333−3−300003333−3−3−3−300003333−3−3−3−32-200-1-1113−33−30000000000
χ282222-122-2-22-122-1-121111-1-2-1-1-1000022-2-2-1-111-1-1-1-11111-2-2111133−3−333−3−300003333−3−3−3−300003333−3−3−3−3-220011-1-1−33−330000000000
χ292222-122-2-22-122-1-121111-1-2-1-1-1000022-2-2-1-111-1-1-1-11111-2-21111−3−333−3−3330000−3−3−3−333330000−3−3−3−333332-200-1-111−33−330000000000
χ302222-122-2-22-122-1-121111-1-2-1-1-1000022-2-2-1-111-1-1-1-11111-2-21111−3−333−3−3330000−3−3−3−333330000−3−3−3−33333-220011-1-13−33−30000000000
χ312222-12-222-2-122-1-12-1-1-1-1-1-2-1-1-122-2-2-2-2-2-211111111111122-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000−i3i3−i3i3−i3i3i3−i30000000000
χ322222-12-222-2-122-1-12-1-1-1-1-1-2-1-1-122-2-2-2-2-2-211111111111122-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000i3−i3i3−i3i3−i3−i3i30000000000
χ332222-12-222-2-122-1-12-1-1-1-1-1-2-1-1-1-2-222-2-2-2-211111111111122-1-1-1-11111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-10000−i3i3−i3i3i3−i3−i3i30000000000
χ342222-12-222-2-122-1-12-1-1-1-1-1-2-1-1-1-2-222-2-2-2-211111111111122-1-1-1-11111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-10000i3−i3i3−i3−i3i3i3−i30000000000
χ352222-12-2-2-2-2-122-1-121111-12-1-1-10000-2-22211-1-11111-1-1-1-1-2-2111133−3−3−3−33300003333−3−3−3−30000−3−3−3−33333002i−2i−i3i3i3−i3−i−iii0000000000
χ362222-12-2-2-2-2-122-1-121111-12-1-1-10000-2-22211-1-11111-1-1-1-1-2-2111133−3−3−3−33300003333−3−3−3−30000−3−3−3−3333300−2i2ii3−i3−i3i3ii−i−i0000000000
χ372222-12-2-2-2-2-122-1-121111-12-1-1-10000-2-22211-1-11111-1-1-1-1-2-21111−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3002i−2ii3−i3−i3i3−i−iii0000000000
χ382222-12-2-2-2-2-122-1-121111-12-1-1-10000-2-22211-1-11111-1-1-1-1-2-21111−3−33333−3−30000−3−3−3−3333300003333−3−3−3−300−2i2i−i3i3i3−i3ii−i−i0000000000
χ392-2-222202-202-2-2-2-2222-2-2202-2-22-20000000000000000002-222-2-22-22-2000022-2-222-2-222-2-2000000000000000000000000000000−i2i2−i2i2
χ402-2-222202-202-2-2-2-2222-2-2202-2-22-20000000000000000002-222-2-22-22-2000022-2-222-2-222-2-2000000000000000000000000000000i2−i2i2−i2
χ412-2-222202-202-2-2-2-2222-2-2202-2-2-220000000000000000002-222-2-2-22-220000-2-222-2-222-2-222000000000000000000000000000000−i2i2i2−i2
χ422-2-222202-202-2-2-2-2222-2-2202-2-2-220000000000000000002-222-2-2-22-220000-2-222-2-222-2-222000000000000000000000000000000i2−i2−i2i2
χ4344444-24-4-444-2-244-2-4-4-4-4-2-4-2-2-20000-2-22244-4-4-2-2-2-22222222222000000000000000000000000000000000000000000000000000000
χ4444444-2-4-4-4-44-2-244-2-4-4-4-4-24-2-2-2000022-2-2-4-4442222-2-2-2-2222222000000000000000000000000000000000000000000000000000000
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χ464444-2-24444-2-2-2-2-2-2-2-2-2-214111-4-4-4-4-2-2-2-2-2-2-2-211111111-2-21111222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000000000
χ474444-2-24-4-44-2-2-2-2-2-222221-41110000-2-222-2-2221111-1-1-1-122-1-1-1-12323−23−232323−23−230000−3−3−3−333330000−3−3−3−333330000000000000000000000
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χ494444-2-2-444-4-2-2-2-2-2-2-2-2-2-21-411144-4-422222222-1-1-1-1-1-1-1-1-2-21111-2-2-2-22222-2-2-2-2111111112222-1-1-1-1-1-1-1-10000000000000000000000
χ504444-2-2-444-4-2-2-2-2-2-2-2-2-2-21-4111-4-44422222222-1-1-1-1-1-1-1-1-2-211112222-2-2-2-22222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000000000
χ514444-2-2-4-4-4-4-2-2-2-2-2-2222214111000022-2-222-2-2-1-1-1-1111122-1-1-1-12323−23−23−23−2323230000−3−3−3−3333300003333−3−3−3−30000000000000000000000
χ524444-2-2-4-4-4-4-2-2-2-2-2-2222214111000022-2-222-2-2-1-1-1-1111122-1-1-1-1−23−2323232323−23−2300003333−3−3−3−30000−3−3−3−333330000000000000000000000
χ5344-4-4440000-44-44-4-4000040-44-400−2i22i200000000000000000000000000−2i22i2−2i22i2000000000000−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i20000000000000000000000
χ5444-4-4440000-44-44-4-4000040-44-4002i2−2i2000000000000000000000000002i2−2i22i2−2i20000000000002i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i20000000000000000000000
χ5544-4-44-20000-4-224-420000-202-2200−2i22i200−2i32i300000000−2i3−2i32i32i30000000000−2i22i2−2i22i26−66−66−66−66−66−6i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000000000
χ5644-4-44-20000-4-224-420000-202-2200−2i22i2002i3−2i3000000002i32i3−2i3−2i30000000000−2i22i2−2i22i2−66−66−66−66−66−66i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000000000
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χ6344-4-4-2-200002-22-22223−2323−2310-11-100−2i22i200−2i32i300003i3i−3i−3ii3i3−i3−i300−33−3300002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ236−66−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ230000000000000000000000
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χ6644-4-4-2-200002-22-22223−2323−2310-11-1002i2−2i2002i3−2i30000−3i−3i3i3i−i3−i3i3i300−33−330000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ236−66−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ230000000000000000000000
χ6744-4-4-2-200002-22-222−2323−232310-11-100−2i22i200−2i32i30000−3i−3i3i3ii3i3−i3−i3003−33−300002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ76−66−6ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ70000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.