Finite Group Databasebeta

← Group #13160245

Character table — Group #13160245

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1122222222222224444444444444444444444466668888888888888121212121212121212121212121212121616161616161616161616161618181818242727363636364848484854545472144216
order123333346666688333366661212121212242424242424242424241616161641212121224242424242424244848484848484848484848484848484812121212121212121212121212161616164444848484812121212288262
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111-1-1-1-1111-1-1-1
χ4111111111111111111111111111111111111111111-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-11111-1-1-1-1-1-1-111-1
χ611111111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11
χ711111111111111111111111111111111111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-11
χ811111111111111111111111111111111111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1
χ92222222222222-2-22222222222222-2-2-2-2-2-2-2-2-2-2000002222-2-2-2-2-2-2-2-2000000000000000000000000000000000022000000002-2-2000
χ102222222222222-2-22222222222222-2-2-2-2-2-2-2-2-2-2000002222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-200000000-222000
χ112222222-2222220022222222-2-2-2-2-2000000000022−2−20-2-2-2-20000000022222222−2−2−2−2−2−2−2−2000000000000022−2−202222−2−20000-200000
χ122222222-2222220022222222-2-2-2-2-2000000000022−2−20-2-2-2-20000000022222222−2−2−2−2−2−2−2−20000000000000−2−2220-2-2−2−2220000200000
χ132222222-2222220022222222-2-2-2-2-20000000000−2−2220-2-2-2-200000000−2−2−2−2−2−2−2−222222222000000000000022−2−20-2-222−2−20000200000
χ142222222-2222220022222222-2-2-2-2-20000000000−2−2220-2-2-2-200000000−2−2−2−2−2−2−2−2222222220000000000000−2−222022−2−2220000-200000
χ15222222-12-1222222-1-1-1-1-1-1-1-1-1222222222222-1-100002-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-12222-1-1-1-1-1-1-1-12222000-1-1-1-100000002-10
χ16222222-12-1222222-1-1-1-1-1-1-1-1-1222222222222-1-100002-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-12222-1-1-1-1-1-1-1-1-2-2-2-200011110000000-210
χ17222222-12-1222222-1-1-1-1-1-1-1-1-1222222222222-1-10000-2-1-1-1-1-1-1-1-1-1-1-1-100000000000000001-2-2-2-2111111112222000-1-1-1-10000000-210
χ18222222-12-1222222-1-1-1-1-1-1-1-1-1222222222222-1-10000-2-1-1-1-1-1-1-1-1-1-1-1-100000000000000001-2-2-2-211111111-2-2-2-2000111100000002-10
χ19222-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122222222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1000020000002-1-1-1000000
χ20222-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1222222-22-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111-2-21111110000-2000000-2111000000
χ21222-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122-2-2-2-222-1-1-122-1-1-1-1-1-1-2-2111111-2-211111122-1-1-122-1-1-1-1-1-10000-2000000-2111000000
χ22222-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122-2-2-2-2-22-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111-2-2111-2-2111111000020000002-1-1-1000000
χ2322-12-1-1222-12-1-122-12-1-1-12-1-12-12-1-1-1-122-1-1-1-12222222-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-1-100002000000-12-1-1000000
χ2422-12-1-1222-12-1-122-12-1-1-12-1-12-12-1-1-1-122-1-1-1-1222222-2-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-21-21111-2-211110000-20000001-211000000
χ2522-12-1-1222-12-1-122-12-1-1-12-1-12-12-1-1-1-122-1-1-1-122-2-2-2-22-12-1-1-1-122-1-1-1-111-2-2111111-2-211112-12-1-1-1-122-1-1-1-10000-20000001-211000000
χ2622-12-1-1222-12-1-122-12-1-1-12-1-12-12-1-1-1-122-1-1-1-122-2-2-2-2-2-12-1-1-1-122-1-1-1-111-2-2111111-2-21111-21-21111-2-2111100002000000-12-1-1000000
χ2722-1-12-1222-1-12-122-1-12-1-1-12-12-1-12-1-1-1-1-122-1-12222222-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-12-1-12-1-1-1-1-122-1-100002000000-1-12-1000000
χ2822-1-12-1222-1-12-122-1-12-1-1-12-12-1-12-1-1-1-1-122-1-1222222-2-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-211-211111-2-2110000-200000011-21000000
χ2922-1-12-1222-1-12-122-1-12-1-1-12-12-1-12-1-1-1-1-122-1-122-2-2-2-22-1-12-1-1-1-1-122-1-11111-2-2111111-2-2112-1-12-1-1-1-1-122-1-10000-200000011-21000000
χ3022-1-12-1222-1-12-122-1-12-1-1-12-12-1-12-1-1-1-1-122-1-122-2-2-2-2-2-1-12-1-1-1-1-122-1-11111-2-2111111-2-211-211-211111-2-21100002000000-1-12-1000000
χ3122-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-12-1-1-1-1-1-1222222222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-12-1-1-1-1-1-12200002000000-1-1-12000000
χ3222-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-12-1-1-1-1-1-122222222-2-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-2111-2111111-2-20000-2000000111-2000000
χ3322-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-12-1-1-1-1-1-12222-2-2-2-22-1-1-12-1-1-1-1-1-122111111-2-2111111-2-22-1-1-12-1-1-1-1-1-1220000-2000000111-2000000
χ3422-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-12-1-1-1-1-1-12222-2-2-2-2-2-1-1-12-1-1-1-1-1-122111111-2-2111111-2-2-2111-2111111-2-200002000000-1-1-12000000
χ352-2222220-2-2-2-2-22−22222-2-2-2-2000002−22−22−22−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000002−22−22−22−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000000000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ702i−2iζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000i2−i2000
χ362-2222220-2-2-2-2-22−22222-2-2-2-2000002−22−22−22−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000002−22−22−22−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000000000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70−2i2i−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000−i2i2000
χ372-2222220-2-2-2-2-22−22222-2-2-2-2000002−22−22−22−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000002−22−22−22−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000000000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70−2i2iζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000−i2i2000
χ382-2222220-2-2-2-2-22−22222-2-2-2-2000002−22−22−22−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000002−22−22−22−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000000000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ702i−2i−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000i2−i2000
χ392-2222220-2-2-2-2-2−222222-2-2-2-200000−22−22−22−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000−22−22−22−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000000000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ502i−2iζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000−i2i2000
χ402-2222220-2-2-2-2-2−222222-2-2-2-200000−22−22−22−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000−22−22−22−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000000000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50−2i2i−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000i2−i2000
χ412-2222220-2-2-2-2-2−222222-2-2-2-200000−22−22−22−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000−22−22−22−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000000000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50−2i2iζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000i2−i2000
χ422-2222220-2-2-2-2-2−222222-2-2-2-200000−22−22−22−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000−22−22−22−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000000000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ502i−2i−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000−i2i2000
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χ744-44444-202-4-4-4-422−22-2-2-2-222220000022−2222−2222−2222−22−22000000000−22−22−22−22000000000000000000000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
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χ764-44444-202-4-4-4-4−2222-2-2-2-2222200000−2222−2222−2222−22222−20000000002−22−22−22−2000000000000000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ774-44444-202-4-4-4-4−2222-2-2-2-2222200000−2222−2222−2222−22222−20000000002−22−22−22−200000000000000000000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.