Finite Group Databasebeta

← Group #11782072

Character table — Group #11782072

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222222244444444444444444444444444444444444444444444444444444444444444424242424242424242424242448484848484872727272
order122233444466666612121212346668888121212121212121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424246688121224242424246612128888
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
χ51111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-111-1-111-1-1
χ61111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11-1-111-1-111
χ71111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-111-1-1-1-111
χ81111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-1-11111-1-1
χ92222222-2-22222222-2-2-2-22-222200002222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002-22200-2-200000000000000
χ102222222-2-22222222-2-2-2-22-222200002222-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-22-2-2002200000000000000
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
χ13222222-2-2-2-2222222-2-2-2-2222220000-2-2-2-22222-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000002i−2i002i2i−2i−2i0000000000
χ14222222-2-2-2-2222222-2-2-2-2222220000-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000−2i2i00−2i−2i2i2i0000000000
χ1522222-1222222-1-12-12222-12-1-1-1222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000
χ1622222-1222222-1-12-12222-12-1-1-1222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-211110000
χ1722222-1222222-1-12-12222-12-1-1-1-2-2-2-222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111111111110000000000002-2-1-1110000
χ1822222-1222222-1-12-12222-12-1-1-1-2-2-2-222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111111111000000000000-2211-1-10000
χ1922222-1-222-222-1-12-12222-1-2-1-1-122-2-2-2-211-2-21111111111-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000−i3i3−i3i30000
χ2022222-1-222-222-1-12-12222-1-2-1-1-122-2-2-2-211-2-21111111111-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000i3−i3i3−i30000
χ2122222-1-222-222-1-12-12222-1-2-1-1-1-2-222-2-211-2-21111111111-1-1-1-1-1-1-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000−i3i3i3−i30000
χ2222222-1-222-222-1-12-12222-1-2-1-1-1-2-222-2-211-2-21111111111-1-1-1-1-1-1-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000i3−i3−i3i30000
χ232222-122222-1-122-12-1-1-1-1-12-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10000000000
χ242222-122222-1-122-12-1-1-1-1-12-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-211-2-21111110000000000
χ252222-122222-1-122-12-1-1-1-1-12-1-1-1-2-2-2-2-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-111111111-2-2-2-211111111-2-2-2-21111111122-1-1-2-2-1-111110000000000
χ262222-122222-1-122-12-1-1-1-1-12-1-1-1-2-2-2-2-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-111111111-2-2-2-211111111-2-2-2-211111111-2-2112211-1-1-1-10000000000
χ272222-122-2-22-1-122-121111-1-2-1-1-10000-1-12211-2-2-1-1-1-11111-2-2111133−3−333−3−300003333−3−3−3−300003333−3−3−3−32-2-1-100113−33−30000000000
χ282222-122-2-22-1-122-121111-1-2-1-1-10000-1-12211-2-2-1-1-1-11111-2-2111133−3−333−3−300003333−3−3−3−300003333−3−3−3−3-221100-1-1−33−330000000000
χ292222-122-2-22-1-122-121111-1-2-1-1-10000-1-12211-2-2-1-1-1-11111-2-21111−3−333−3−3330000−3−3−3−333330000−3−3−3−333332-2-1-10011−33−330000000000
χ302222-122-2-22-1-122-121111-1-2-1-1-10000-1-12211-2-2-1-1-1-11111-2-21111−3−333−3−3330000−3−3−3−333330000−3−3−3−33333-221100-1-13−33−30000000000
χ312222-12-222-2-1-122-12-1-1-1-1-1-2-1-1-122-2-211-2-211-2-21111111122-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-21111111100−i3i300−i3i3−i3i3i3−i30000000000
χ322222-12-222-2-1-122-12-1-1-1-1-1-2-1-1-122-2-211-2-211-2-21111111122-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-21111111100i3−i300i3−i3i3−i3−i3i30000000000
χ332222-12-222-2-1-122-12-1-1-1-1-1-2-1-1-1-2-22211-2-211-2-21111111122-1-1-1-11111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-100−i3i300−i3i3i3−i3−i3i30000000000
χ342222-12-222-2-1-122-12-1-1-1-1-1-2-1-1-1-2-22211-2-211-2-21111111122-1-1-1-11111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-100i3−i300i3−i3−i3i3i3−i30000000000
χ352222-12-2-2-2-2-1-122-121111-12-1-1-1000011-2-2-1-1221111-1-1-1-1-2-2111133−3−3−3−33300003333−3−3−3−30000−3−3−3−3333300−i3i32i−2ii3−i3−i−iii0000000000
χ362222-12-2-2-2-2-1-122-121111-12-1-1-1000011-2-2-1-1221111-1-1-1-1-2-2111133−3−3−3−33300003333−3−3−3−30000−3−3−3−3333300i3−i3−2i2i−i3i3ii−i−i0000000000
χ372222-12-2-2-2-2-1-122-121111-12-1-1-1000011-2-2-1-1221111-1-1-1-1-2-21111−3−33333−3−30000−3−3−3−3333300003333−3−3−3−300−i3i3−2i2ii3−i3ii−i−i0000000000
χ382222-12-2-2-2-2-1-122-121111-12-1-1-1000011-2-2-1-1221111-1-1-1-1-2-21111−3−33333−3−30000−3−3−3−3333300003333−3−3−3−300i3−i32i−2i−i3i3−i−iii0000000000
χ392-22-22202-20-2-22-22-222-2-2202-2-2002i−2i00000000000000002-222-2-200002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000002−2−i2i2
χ402-22-22202-20-2-22-22-222-2-2202-2-2002i−2i00000000000000002-222-2-200002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000−22i2−i2
χ412-22-22202-20-2-22-22-222-2-2202-2-200−2i2i00000000000000002-222-2-20000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000002−2i2−i2
χ422-22-22202-20-2-22-22-222-2-2202-2-200−2i2i00000000000000002-222-2-20000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000−22−i2i2
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χ474444-2-24-4-44-2-2-2-2-2-222221-41110000-2-2-2-222221111-1-1-1-122-1-1-1-12323−23−232323−23−230000−3−3−3−333330000−3−3−3−333330000000000000000000000
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χ524444-2-2-4-4-4-4-2-2-2-2-2-222221411100002222-2-2-2-2-1-1-1-1111122-1-1-1-1−23−2323232323−23−2300003333−3−3−3−30000−3−3−3−333330000000000000000000000
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χ6944-4-4-2-2-4004-222-222−2323−232310-11-100002-22-223−2300-1-111−3−333003−33−30000000066−6−6ζ5−ζ7+2ζ13−2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ232ζ5−2ζ7+ζ13−ζ23−66−66−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ230000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.