Finite Group Databasebeta

← Group #14304641

Character table — Group #14304641

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222244444444444444444444555588888888888888888888888810101010101016161616161616161616161620202020202020204040404040406060606060606060120120120120
order122234466658810101012121515242424243030303030302222441212121220204040404060606060120120120120120120120120446666202020206060606060606060881212242424244412121212444488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iii−i−ii−ii−i
χ6111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−i−iii−ii−ii
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111i−ii−iii−i−i−ii−ii
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−ii−ii−i−iiii−ii−i
χ911111111111-1-11111111-1-1-1-111111111111-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-11-111-1-11111-1-1-1-1-1-111
χ1011111111111-1-11111111-1-1-1-111111111111-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-11-111-1-1-1-1-1-1111111-1-1
χ1111111111111-1-11111111-1-1-1-11111111111-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-111-1-1-1-1-11-1-1111111-1-1-1-111-1-1
χ1211111111111-1-11111111-1-1-1-11111111111-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-111-1-1-1-1-11-1-111-1-1-1-11111-1-111
χ1311111111111-1-11111111-1-1-1-1111111-1-1-1-11-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-11-1-111i−ii−i−i−iii−iii−i
χ1411111111111-1-11111111-1-1-1-1111111-1-1-1-11-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-11-1-111−ii−iiii−i−ii−i−ii
χ1511111111111-1-11111111-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111111-111-1-1i−ii−i−i−iiii−i−ii
χ1611111111111-1-11111111-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111111-111-1-1−ii−iiii−i−i−iii−i
χ1722222-2-2222200222-2-22200002222222222000000-2-20000-2-2-2-200000000-2-2222200000000000000-2-2000000000022-2-200000000
χ1822222-2-2222200222-2-22200002222222222000000-2-20000-2-2-2-200000000-2-2222200000000000000-2-20000000000-2-22200000000
χ1922222-2-2222200222-2-2220000222222-2-2-2-2000000-2-20000-2-2-2-20000000022-2-2-2-2000000000000002200000000002i−2i−2i2i00000000
χ2022222-2-2222200222-2-2220000222222-2-2-2-2000000-2-20000-2-2-2-20000000022-2-2-2-200000000000000220000000000−2i2i2i−2i00000000
χ212222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000
χ222222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-21111222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-1-1-1-2-21111000000000000
χ232222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-211112222-1-1-1-1-1-1-1-1-2-2111111-2-21111000000000000
χ242222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111222222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2-2-211111111-2-211111122-1-1-1-1000000000000
χ252222-122-1-1-12-2-2222-1-1-1-11111-1-1-1-1-1-122222-2-1-11122-2-2-2-2-1-1-1-11111111122-1-1-1-122-2-2-1-1-1-11111-2-2-1-111112-2-1-111000000000000
χ262222-122-1-1-12-2-2222-1-1-1-11111-1-1-1-1-1-12222-2211-1-122-2-2-2-2-1-1-1-11111111122-1-1-1-1-2-2221111-1-1-1-1-2-2-1-11111-2211-1-1000000000000
χ272222-122-1-1-12-2-2222-1-1-1-11111-1-1-1-1-1-1-2-2-2-22-2-1-11122-2-2-2-2-1-1-1-111111111-2-2111122-2-2-1-1-1-111112211-1-1-1-1-2211-1-1000000000000
χ282222-122-1-1-12-2-2222-1-1-1-11111-1-1-1-1-1-1-2-2-2-2-2211-1-122-2-2-2-2-1-1-1-111111111-2-21111-2-2221111-1-1-1-12211-1-1-1-12-2-1-111000000000000
χ292-2-2222-2-2-2222i−2i-2-222-2222i2i−2i−2i-2-2-2-2222-22-20000002-22i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i-2222-2-20000000000002i−2i2-22i2i−2i−2i000000000000000000
χ302-2-2222-2-2-2222i−2i-2-222-2222i2i−2i−2i-2-2-2-222-22-220000002-22i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i2-2-2-222000000000000−2i2i-22−2i−2i2i2i000000000000000000
χ312-2-2222-2-2-222−2i2i-2-222-222−2i−2i2i2i-2-2-2-2222-22-20000002-2−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i-2222-2-2000000000000−2i2i2-2−2i−2i2i2i000000000000000000
χ322-2-2222-2-2-222−2i2i-2-222-222−2i−2i2i2i-2-2-2-222-22-220000002-2−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i2-2-2-2220000000000002i−2i-222i2i−2i−2i000000000000000000
χ332-2-222-22-2-22200-2-22-22220000-2-2-2-2222-22-2000000-220000-2-222000000002-222-2-200000000000000-22000000000000002i−2i2i−2i0000
χ342-2-222-22-2-22200-2-22-22220000-2-2-2-2222-22-2000000-220000-2-222000000002-222-2-200000000000000-2200000000000000−2i2i−2i2i0000
χ352-2-222-22-2-22200-2-22-22220000-2-2-2-222-22-22000000-220000-2-22200000000-22-2-222000000000000002-2000000000000002-2-220000
χ362-2-222-22-2-22200-2-22-22220000-2-2-2-222-22-22000000-220000-2-22200000000-22-2-222000000000000002-200000000000000-222-20000
χ372-2-22-12-211-122i−2i-2-22-11-1-1−i−iii1111-1-12-22-2003−3−i3i32-22i2i−2i−2i-1-111−i−i−i−iiiii-22-1-111000033−3−3−i3−i3i3i32i−2i-11−i−iii003−3−i3i3000000000000
χ382-2-22-12-211-122i−2i-2-22-11-1-1−i−iii1111-1-12-22-200−33i3−i32-22i2i−2i−2i-1-111−i−i−i−iiiii-22-1-1110000−3−333i3i3−i3−i32i−2i-11−i−iii00−33i3−i3000000000000
χ392-2-22-12-211-122i−2i-2-22-11-1-1−i−iii1111-1-1-22-22003−3−i3i32-22i2i−2i−2i-1-111−i−i−i−iiiii2-211-1-1000033−3−3−i3−i3i3i3−2i2i1-1ii−i−i00−33i3−i3000000000000
χ402-2-22-12-211-122i−2i-2-22-11-1-1−i−iii1111-1-1-22-2200−33i3−i32-22i2i−2i−2i-1-111−i−i−i−iiiii2-211-1-10000−3−333i3i3−i3−i3−2i2i1-1ii−i−i003−3−i3i3000000000000
χ412-2-22-12-211-12−2i2i-2-22-11-1-1ii−i−i1111-1-12-22-2003−3i3−i32-2−2i−2i2i2i-1-111iiii−i−i−i−i-22-1-111000033−3−3i3i3−i3−i3−2i2i-11ii−i−i003−3i3−i3000000000000
χ422-2-22-12-211-12−2i2i-2-22-11-1-1ii−i−i1111-1-12-22-200−33−i3i32-2−2i−2i2i2i-1-111iiii−i−i−i−i-22-1-1110000−3−333−i3−i3i3i3−2i2i-11ii−i−i00−33−i3i3000000000000
χ432-2-22-12-211-12−2i2i-2-22-11-1-1ii−i−i1111-1-1-22-22003−3i3−i32-2−2i−2i2i2i-1-111iiii−i−i−i−i2-211-1-1000033−3−3i3i3−i3−i32i−2i1-1−i−iii00−33−i3i3000000000000
χ442-2-22-12-211-12−2i2i-2-22-11-1-1ii−i−i1111-1-1-22-2200−33−i3i32-2−2i−2i2i2i-1-111iiii−i−i−i−i2-211-1-10000−3−333−i3−i3i3i32i−2i1-1−i−iii003−3i3−i3000000000000
χ454444444444-144-1-1-144-1-14444-1-1-1-1-1-10000444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-144-1-1-144-1-14444-1-1-1-1-1-10000-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000011111111111100000000000000000000000000
χ474444444444-1-4-4-1-1-144-1-1-4-4-4-4-1-1-1-1-1-100004-444-4-4-1-11111-1-1-1-111111111000000-1-111-1-1-1-1111100000000000000000000000000
χ484444444444-1-4-4-1-1-144-1-1-4-4-4-4-1-1-1-1-1-10000-44-4-444-1-11111-1-1-1-11111111100000011-1-11111-1-1-1-100000000000000000000000000
χ494444-244-2-2-2-144-1-1-1-2-21−i1521+i152-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i152000044-2-2-2-2-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i152000000-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200000000000000000000000000
χ504444-244-2-2-2-144-1-1-1-2-21−i1521+i152-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1520000-4-42222-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1520000001111−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i15200000000000000000000000000
χ514444-244-2-2-2-144-1-1-1-2-21+i1521−i152-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i152000044-2-2-2-2-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i152000000-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200000000000000000000000000
χ524444-244-2-2-2-144-1-1-1-2-21+i1521−i152-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1520000-4-42222-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1520000001111−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i15200000000000000000000000000
χ534444-244-2-2-2-1-4-4-1-1-1-2-21−i1521+i15222221−i1521+i1521−i1521+i1521−i1521+i15200004-4-2-222-1-111111−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152000000-1-1111−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i15200000000000000000000000000
χ544444-244-2-2-2-1-4-4-1-1-1-2-21−i1521+i15222221−i1521+i1521−i1521+i1521−i1521+i1520000-4422-2-2-1-111111−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i15200000011-1-1−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i15200000000000000000000000000
χ554444-244-2-2-2-1-4-4-1-1-1-2-21+i1521−i15222221+i1521−i1521+i1521−i1521+i1521−i15200004-4-2-222-1-111111+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152000000-1-1111+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i15200000000000000000000000000
χ564444-244-2-2-2-1-4-4-1-1-1-2-21+i1521−i15222221+i1521−i1521+i1521−i1521+i1521−i1520000-4422-2-2-1-111111+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i15200000011-1-1−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i15200000000000000000000000000
χ574444-2-4-4-2-2-240044422-2-20000-2-2-2-2-2-24444000000-4-40000222200000000-4-4-2-2-2-200000000000000220000000000000000000000
χ584444-2-4-4-2-2-240044422-2-20000-2-2-2-2-2-2-4-4-4-4000000-4-4000022220000000044222200000000000000-2-20000000000000000000000
χ5944-4-44004-4-44004-4-40044000044-4-4-4-44-4-44000000000000000000000000004-44-400000000000000000000000000000000000000
χ6044-4-44004-4-44004-4-40044000044-4-4-4-4-444-400000000000000000000000000-44-4400000000000000000000000000000000000000
χ6144-4-4-200-2224004-4-400-2-2−i6i6−i6i6-2-222224-4-440000000000000000−i6i6−i6i6−i6i6−i6i600-22-220000000000000000−i6i6−i6i6000000000000000000
χ6244-4-4-200-2224004-4-400-2-2−i6i6−i6i6-2-22222-444-40000000000000000−i6i6−i6i6−i6i6−i6i6002-22-20000000000000000i6−i6i6−i6000000000000000000
χ6344-4-4-200-2224004-4-400-2-2i6−i6i6−i6-2-222224-4-440000000000000000i6−i6i6−i6i6−i6i6−i600-22-220000000000000000i6−i6i6−i6000000000000000000
χ6444-4-4-200-2224004-4-400-2-2i6−i6i6−i6-2-22222-444-40000000000000000i6−i6i6−i6i6−i6i6−i6002-22-20000000000000000−i6i6−i6i6000000000000000000
χ654-44-4400-44-4400-44-400440000-4-444-4-444-4-4000000000000000000000000004-4-4400000000000000000000000000000000000000
χ664-44-4400-44-4400-44-400440000-4-444-4-4-4-44400000000000000000000000000-444-400000000000000000000000000000000000000
χ674-44-4-2002-22400-44-400-2-26−6−6622-2-22244-4-400000000000000006−66−6−66−6600-222-200000000000000006−6−66000000000000000000
χ684-44-4-2002-22400-44-400-2-26−6−6622-2-222-4-44400000000000000006−66−6−66−66002-2-220000000000000000−666−6000000000000000000
χ694-44-4-2002-22400-44-400-2-2−666−622-2-22244-4-40000000000000000−66−666−66−600-222-20000000000000000−666−6000000000000000000
χ704-44-4-2002-22400-44-400-2-2−666−622-2-222-4-4440000000000000000−66−666−66−6002-2-2200000000000000006−6−66000000000000000000
χ714-4-4444-4-4-44-14i−4i11-14-4-1-14i4i−4i−4i1111-1-10000000000-11−i−iii-1-111−i−i−i−iiiii000000−i5i5−55−i5i5i5−i5−555−500000000000000000000000000
χ724-4-4444-4-4-44-14i−4i11-14-4-1-14i4i−4i−4i1111-1-10000000000-11−i−iii-1-111−i−i−i−iiiii000000i5−i55−5i5−i5−i5i55−5−5500000000000000000000000000
χ734-4-4444-4-4-44-1−4i4i11-14-4-1-1−4i−4i4i4i1111-1-10000000000-11ii−i−i-1-111iiii−i−i−i−i000000−i5i55−5−i5i5i5−i55−5−5500000000000000000000000000
χ744-4-4444-4-4-44-1−4i4i11-14-4-1-1−4i−4i4i4i1111-1-10000000000-11ii−i−i-1-111iiii−i−i−i−i000000i5−i5−55i5−i5−i5i5−555−500000000000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.