Finite Group Databasebeta

← Group #14417987

Character table — Group #14417987

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1122244444455888101010101010101010101012121616161620202020202020202020202024244860606060606011222444444558881010101010101010101010121216161616202020202020202020202020242448606060606060
order12346256610124415203028888121224242424281030306046881212242424242424404010444888226462106610124430203028888121224242424281030306046881212242424242424404010444888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-11-1-111111111111111111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-11-1-1
χ411111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-11111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-111
χ511111111111-1-1111-1ii−i−i-1-1ii−i−i111111-1-1i−i-1-1iii−i−i−i111-1i−i-1i−i11111111111-1-1111-1ii−i−i-1-1ii−i−i111111-1-1i−i-1-1iii−i−i−i111-1i−i-1i−i
χ611111111111-1-1111-1ii−i−i-1-1ii−i−i-1-11111-1-1i−i-1-1iii−i−i−i-1-1-11−ii1−ii11111111111-1-1111-1ii−i−i-1-1ii−i−i-1-11111-1-1i−i-1-1iii−i−i−i-1-1-11−ii1−ii
χ711111111111-1-1111-1−i−iii-1-1−i−iii111111-1-1−ii-1-1−i−i−iiii111-1−ii-1−ii11111111111-1-1111-1−i−iii-1-1−i−iii111111-1-1−ii-1-1−i−i−iiii111-1−ii-1−ii
χ811111111111-1-1111-1−i−iii-1-1−i−iii-1-11111-1-1−ii-1-1−i−i−iiii-1-1-11i−i1i−i11111111111-1-1111-1−i−iii-1-1−i−iii-1-11111-1-1−ii-1-1−i−i−iiii-1-1-11i−i1i−i
χ911111-11-1-11111111111111111111-1-1-1-11-11-1-1-1-11-1-11-1-1-1-111-1-1-11111111-11-1-11111111111111111111-1-1-1-11-11-1-1-1-11-1-11-1-1-1-111-1-1-111
χ1011111-11-1-1111111111111111111-11-1-1-11-11-1-1-1-11-1-11-1-111-1-1111-1-111111-11-1-1111111111111111111-11-1-1-11-11-1-1-1-11-1-11-1-111-1-1111-1-1
χ1111111-11-1-111111111-1-1-1-111-1-1-1-11-1-1-1-11-1111-1-1-111-111-1-11111-1-1-111111-11-1-111111111-1-1-1-111-1-1-1-11-1-1-1-11-1111-1-1-111-111-1-11111-1-1-1
χ1211111-11-1-111111111-1-1-1-111-1-1-1-1-11-1-1-11-1111-1-1-111-11111-1-1-1-111111111-11-1-111111111-1-1-1-111-1-1-1-1-11-1-1-11-1111-1-1-111-11111-1-1-1-1111
χ1311111-11-1-111-1-1111-1ii−i−i-1-1ii−i−i1-1-1-1-111-1−ii11i−i−i−iii-1-11-1−ii1i−i11111-11-1-111-1-1111-1ii−i−i-1-1ii−i−i1-1-1-1-111-1−ii11i−i−i−iii-1-11-1−ii1i−i
χ1411111-11-1-111-1-1111-1ii−i−i-1-1ii−i−i-11-1-1-111-1−ii11i−i−i−iii11-11i−i-1−ii11111-11-1-111-1-1111-1ii−i−i-1-1ii−i−i-11-1-1-111-1−ii11i−i−i−iii11-11i−i-1−ii
χ1511111-11-1-111-1-1111-1−i−iii-1-1−i−iii1-1-1-1-111-1i−i11−iiii−i−i-1-11-1i−i1−ii11111-11-1-111-1-1111-1−i−iii-1-1−i−iii1-1-1-1-111-1i−i11−iiii−i−i-1-11-1i−i1−ii
χ1611111-11-1-111-1-1111-1−i−iii-1-1−i−iii-11-1-1-111-1i−i11−iiii−i−i11-11−ii-1i−i11111-11-1-111-1-1111-1−i−iii-1-1−i−iii-11-1-1-111-1i−i11−iiii−i−i11-11−ii-1i−i
χ17222-2202002-2222-22-22-22-222222200000-20-20000-200-200000000000222-2202002-2222-22-22-22-222222200000-20-20000-200-200000000000
χ18222-2202002-2222-22-2-22-2222-2-2-2-200000-20-20000200200000000000222-2202002-2222-22-2-22-2222-2-2-2-200000-20-20000200200000000000
χ19222-2202002-2-2-22-2222i−2i−2i2i-2-22i2i−2i−2i00000-2020000−2i002i00000000000222-2202002-2-2-22-2222i−2i−2i2i-2-22i2i−2i−2i00000-2020000−2i002i00000000000
χ20222-2202002-2-2-22-222−2i2i2i−2i-2-2−2i−2i2i2i00000-20200002i00−2i00000000000222-2202002-2-2-22-222−2i2i2i−2i-2-2−2i−2i2i2i00000-20200002i00−2i00000000000
χ2122-12-122-1-12-122-12-122222-1-1-1-1-1-1002-1-1-12-122-1-1-1-1-1-1-1-100000000022-12-122-1-12-122-12-122222-1-1-1-1-1-1002-1-1-12-122-1-1-1-1-1-1-1-1000000000
χ2222-12-122-1-12-122-12-12-2-2-2-2-1-11111002-1-1-12-1-2-2-1-111111100000000022-12-122-1-12-122-12-12-2-2-2-2-1-11111002-1-1-12-1-2-2-1-1111111000000000
χ2322-12-122-1-12-1-2-2-12-1-22i2i−2i−2i11−i−iii002-1-1-1-212i−2i11−i−i−iiii00000000022-12-122-1-12-1-2-2-12-1-22i2i−2i−2i11−i−iii002-1-1-1-212i−2i11−i−i−iiii000000000
χ2422-12-122-1-12-1-2-2-12-1-2−2i−2i2i2i11ii−i−i002-1-1-1-21−2i2i11iii−i−i−i00000000022-12-122-1-12-1-2-2-12-1-2−2i−2i2i2i11ii−i−i002-1-1-1-21−2i2i11iii−i−i−i000000000
χ2522-12-1-22112-122-12-122222-1-1-1-1-1-100-211-1-2-1-2-211-111-11100000000022-12-1-22112-122-12-122222-1-1-1-1-1-100-211-1-2-1-2-211-111-111000000000
χ2622-12-1-22112-122-12-12-2-2-2-2-1-1111100-211-1-2-122111-1-11-1-100000000022-12-1-22112-122-12-12-2-2-2-2-1-1111100-211-1-2-122111-1-11-1-1000000000
χ2722-12-1-22112-1-2-2-12-1-22i2i−2i−2i11−i−iii00-211-121−2i2i-1-1−iiii−i−i00000000022-12-1-22112-1-2-2-12-1-22i2i−2i−2i11−i−iii00-211-121−2i2i-1-1−iiii−i−i000000000
χ2822-12-1-22112-1-2-2-12-1-2−2i−2i2i2i11ii−i−i00-211-1212i−2i-1-1i−i−i−iii00000000022-12-1-22112-1-2-2-12-1-2−2i−2i2i2i11ii−i−i00-211-1212i−2i-1-1i−i−i−iii000000000
χ2922-1-2-102−i3i32122-1-2-1-22-22-2-1-1-1-1-1-1000−i3i310100−i3i31−i3i31−i3i300000000022-1-2-102−i3i32122-1-2-1-22-22-2-1-1-1-1-1-1000−i3i310100−i3i31−i3i31−i3i3000000000
χ3022-1-2-102−i3i32122-1-2-1-2-22-22-1-11111000−i3i310100−i3i3-1i3−i3-1i3−i300000000022-1-2-102−i3i32122-1-2-1-2-22-22-1-11111000−i3i310100−i3i3-1i3−i3-1i3−i3000000000
χ3122-1-2-102−i3i321-2-2-1-2-122i−2i−2i2i11−i−iii000−i3i310-100i3−i3i3−3−i−3300000000022-1-2-102−i3i321-2-2-1-2-122i−2i−2i2i11−i−iii000−i3i310-100i3−i3i3−3−i−33000000000
χ3222-1-2-102−i3i321-2-2-1-2-12−2i2i2i−2i11ii−i−i000−i3i310-100i3−i3−i−33i3−300000000022-1-2-102−i3i321-2-2-1-2-12−2i2i2i−2i11ii−i−i000−i3i310-100i3−i3−i−33i3−3000000000
χ3322-1-2-102i3−i32122-1-2-1-22-22-2-1-1-1-1-1-1000i3−i310100i3−i31i3−i31i3−i300000000022-1-2-102i3−i32122-1-2-1-22-22-2-1-1-1-1-1-1000i3−i310100i3−i31i3−i31i3−i3000000000
χ3422-1-2-102i3−i32122-1-2-1-2-22-22-1-11111000i3−i310100i3−i3-1−i3i3-1−i3i300000000022-1-2-102i3−i32122-1-2-1-2-22-22-1-11111000i3−i310100i3−i3-1−i3i3-1−i3i3000000000
χ3522-1-2-102i3−i321-2-2-1-2-122i−2i−2i2i11−i−iii000i3−i310-100−i3i3i−33−i3−300000000022-1-2-102i3−i321-2-2-1-2-122i−2i−2i2i11−i−iii000i3−i310-100−i3i3i−33−i3−3000000000
χ3622-1-2-102i3−i321-2-2-1-2-12−2i2i2i−2i11ii−i−i000i3−i310-100−i3i3−i3−3i−3300000000022-1-2-102i3−i321-2-2-1-2-12−2i2i2i−2i11ii−i−i000i3−i310-100−i3i3−i3−3i−33000000000
χ37444444-144-1400-1-1-10000000000044-1-1-1-1000000000000-1-1-1000000444444-144-1400-1-1-10000000000044-1-1-1-1000000000000-1-1-1000000
χ38444444-144-1400-1-1-100000000000-4-4-1-1-1-1000000000000111000000444444-144-1400-1-1-100000000000-4-4-1-1-1-1000000000000111000000
χ3944444-4-1-4-4-1400-1-1-1000000000004-4111-100000000000011-100000044444-4-1-4-4-1400-1-1-1000000000004-4111-100000000000011-1000000
χ4044444-4-1-4-4-1400-1-1-100000000000-44111-1000000000000-1-1100000044444-4-1-4-4-1400-1-1-100000000000-44111-1000000000000-1-11000000
χ414-440-40400-404i−4i40-4000004i−4i00000000000000000000000000000004-440-40400-404i−4i40-4000004i−4i0000000000000000000000000000000
χ424-440-40400-40−4i4i40-400000−4i4i00000000000000000000000000000004-440-40400-40−4i4i40-400000−4i4i0000000000000000000000000000000
χ434-4-2020400-404i−4i-20200000−2i2i2ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1192ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1090000000000000000000000000004-4-2020400-404i−4i-20200000−2i2i2ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1192ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ109000000000000000000000000000
χ444-4-2020400-404i−4i-20200000−2i2i−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1192ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1092ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ1090000000000000000000000000004-4-2020400-404i−4i-20200000−2i2i−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1192ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1092ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109000000000000000000000000000
χ454-4-2020400-40−4i4i-202000002i−2i2ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1092ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1190000000000000000000000000004-4-2020400-40−4i4i-202000002i−2i2ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1092ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ119000000000000000000000000000
χ464-4-2020400-40−4i4i-202000002i−2i−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1092ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1192ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ1190000000000000000000000000004-4-2020400-40−4i4i-202000002i−2i−2ζ13+2ζ29−2ζ37+2ζ53−2ζ61+2ζ77+2ζ101−2ζ1092ζ13−2ζ29+2ζ37−2ζ53+2ζ61−2ζ77−2ζ101+2ζ109−2ζ7+2ζ23−2ζ31+2ζ47+2ζ71−2ζ79−2ζ103+2ζ1192ζ7−2ζ23+2ζ31−2ζ47−2ζ71+2ζ79+2ζ103−2ζ119000000000000000000000000000
χ47888-880-200-2-800-22-200000000000000002000000000000000000000888-880-200-2-800-22-200000000000000002000000000000000000000
χ4888-48-48-2-4-4-2-4001-210000000000000-211100000000000000000000088-48-48-2-4-4-2-4001-210000000000000-2111000000000000000000000
χ4988-48-4-8-244-2-4001-2100000000000002-1-1100000000000000000000088-48-4-8-244-2-4001-2100000000000002-1-11000000000000000000000
χ5088-4-8-40-2−4i34i3-240012100000000000000i3−i3-100000000000000000000088-4-8-40-2−4i34i3-240012100000000000000i3−i3-1000000000000000000000
χ5188-4-8-40-24i3−4i3-240012100000000000000−i3i3-100000000000000000000088-4-8-40-24i3−4i3-240012100000000000000−i3i3-1000000000000000000000
χ528-880-80-2002000-2020000000000000000000000000000010−1000000008-880-80-2002000-2020000000000000000000000000000010−100000000
χ538-880-80-2002000-20200000000000000000000000000000−101000000008-880-80-2002000-20200000000000000000000000000000−10100000000
χ5416-16-8080-400400020-20000000000000000000000000000000000000016-16-8080-400400020-200000000000000000000000000000000000000
χ55111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ56111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111
χ5711111111111111111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-111
χ5811111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-11111111111-1-11-1-1
χ5911111111111-1-1111-1ii−i−i-1-1ii−i−i111111-1-1i−i-1-1iii−i−i−i111-1i−i-1i−i-1-1-1-1-1-1-1-1-1-1-111-1-1-11−i−iii11−i−iii-1-1-1-1-1-111−ii11−i−i−iiii-1-1-11−ii1−ii
χ6011111111111-1-1111-1ii−i−i-1-1ii−i−i-1-11111-1-1i−i-1-1iii−i−i−i-1-1-11−ii1−ii-1-1-1-1-1-1-1-1-1-1-111-1-1-11−i−iii11−i−iii11-1-1-1-111−ii11−i−i−iiii111-1i−i-1i−i
χ6111111111111-1-1111-1−i−iii-1-1−i−iii111111-1-1−ii-1-1−i−i−iiii111-1−ii-1−ii-1-1-1-1-1-1-1-1-1-1-111-1-1-11ii−i−i11ii−i−i-1-1-1-1-1-111i−i11iii−i−i−i-1-1-11i−i1i−i
χ6211111111111-1-1111-1−i−iii-1-1−i−iii-1-11111-1-1−ii-1-1−i−i−iiii-1-1-11i−i1i−i-1-1-1-1-1-1-1-1-1-1-111-1-1-11ii−i−i11ii−i−i11-1-1-1-111i−i11iii−i−i−i111-1−ii-1−ii
χ6311111-11-1-11111111111111111111-1-1-1-11-11-1-1-1-11-1-11-1-1-1-111-1-1-111-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11111-111-11111-1-1111-1-1
χ6411111-11-1-1111111111111111111-11-1-1-11-11-1-1-1-11-1-11-1-111-1-1111-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-11111-111-111-1-111-1-1-111
χ6511111-11-1-111111111-1-1-1-111-1-1-1-11-1-1-1-11-1111-1-1-111-111-1-11111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-11111-1-11111-11111-11-1-1-1111-1-11-1-111-1-1-1-1111
χ6611111-11-1-111111111-1-1-1-111-1-1-1-1-11-1-1-11-1111-1-1-111-11111-1-1-1-1111-1-1-1-1-11-111-1-1-1-1-1-1-1-11111-1-111111-1111-11-1-1-1111-1-11-1-1-1-11111-1-1-1
χ6711111-11-1-111-1-1111-1ii−i−i-1-1ii−i−i1-1-1-1-111-1−ii11i−i−i−iii-1-11-1−ii1i−i-1-1-1-1-11-111-1-111-1-1-11−i−iii11−i−iii-11111-1-11i−i-1-1−iiii−i−i11-11i−i-1−ii
χ6811111-11-1-111-1-1111-1ii−i−i-1-1ii−i−i-11-1-1-111-1−ii11i−i−i−iii11-11i−i-1−ii-1-1-1-1-11-111-1-111-1-1-11−i−iii11−i−iii1-1111-1-11i−i-1-1−iiii−i−i-1-11-1−ii1i−i
χ6911111-11-1-111-1-1111-1−i−iii-1-1−i−iii1-1-1-1-111-1i−i11−iiii−i−i-1-11-1i−i1−ii-1-1-1-1-11-111-1-111-1-1-11ii−i−i11ii−i−i-11111-1-11−ii-1-1i−i−i−iii11-11−ii-1i−i
χ7011111-11-1-111-1-1111-1−i−iii-1-1−i−iii-11-1-1-111-1i−i11−iiii−i−i11-11−ii-1i−i-1-1-1-1-11-111-1-111-1-1-11ii−i−i11ii−i−i1-1111-1-11−ii-1-1i−i−i−iii-1-11-1i−i1−ii
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χ1068-880-80-2002000-2020000000000000000000000000000010−100000000-88-8080200-200020-200000000000000000000000000000−10100000000
χ1078-880-80-2002000-20200000000000000000000000000000−10100000000-88-8080200-200020-20000000000000000000000000000010−100000000
χ10816-16-8080-400400020-200000000000000000000000000000000000000-161680-80400-4000-20200000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.