Finite Group Databasebeta

← Group #14304756

Character table — Group #14304756

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222244444444445555888888888888888888888810101010101010101010202020202020202020202020202020202020202020202020202020202020242448484848120120120120120120
order122234466612121212588101010242424242222152020303030404040406060606012012012012012012012012044666612121212444488888812121212121212122424242424242424242424242410102020244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1i−ii−i-1-1ii−i−iiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i111111-1-1i−ii−i
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1i−ii−i-1-1ii−i−iiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-111−ii−ii
χ7111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1−ii−ii-1-1−i−iii−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii111111-1-1−ii−ii
χ8111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1−ii−ii-1-1−i−iii−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-111i−ii−i
χ9111111111111111-1-1111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-1
χ10111111111111111-1-1111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-111
χ11111111111111111-1-1111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11-1-1-111
χ12111111111111111-1-1111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1111-1-1
χ13111111111111111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i11−i−iiiiiii−i−i−i−i1111−i−i−i−iiiii1-111-1-1-11i−i−ii
χ14111111111111111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i11−i−iiiiiii−i−i−i−i1111−i−i−i−iiiii-11-1-1111-1−iii−i
χ15111111111111111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii11ii−i−i−i−i−i−iiiii1111iiii−i−i−i−i1-111-1-1-11−iii−i
χ16111111111111111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii11ii−i−i−i−i−i−iiiii1111iiii−i−i−i−i-11-1-1111-1i−i−ii
χ1722222-2-2222-2-2-2-2200222000022222-2-22220000-2-2-2-200000000-2-22222-2-2-2-222-2-200000022-2-222-2-2000000000000000000000000
χ1822222-2-2222-2-2-2-2200222000022222-2-22220000-2-2-2-200000000-2-22222-2-2-2-2-2-222000000-2-222-2-222000000000000000000000000
χ1922222-2-2222-2-2-2-22002220000-2-2-2-22-2-22220000-2-2-2-20000000022-2-2-2-222222i−2i−2i2i0000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2022222-2-2222-2-2-2-22002220000-2-2-2-22-2-22220000-2-2-2-20000000022-2-2-2-22222−2i2i2i−2i000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ212222-122-1-1-1-1-1-1-1222222-1-1-1-12222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ222222-122-1-1-1-1-1-1-1222222-1-1-1-12222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-211111111-1-1-1-111111111000000000000
χ232222-122-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111112i−2i2i−2i-2-22i2i−2i−2i−i−i−i−iiiii1111−i−i−i−iiiii000000000000
χ242222-122-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-211111111−2i2i−2i2i-2-2−2i−2i2i2iiiii−i−i−i−i1111iiii−i−i−i−i000000000000
χ252222-122-1-1-1-1-1-1-12-2-222211112222-122-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111000000000000
χ262222-122-1-1-1-1-1-1-12-2-222211112222-122-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-1-1-1-1-1-2-2-2-2-2-22222111111111111-1-1-1-1-1-1-1-1000000000000
χ272222-122-1-1-1-1-1-1-12-2-22221111-2-2-2-2-122-1-1-1-2-2-2-2-1-1-1-111111111-2-2111111112i−2i2i−2i22−2i−2i2i2i−i−i−i−iiiii-1-1-1-1iiii−i−i−i−i000000000000
χ282222-122-1-1-1-1-1-1-12-2-22221111-2-2-2-2-122-1-1-1-2-2-2-2-1-1-1-111111111-2-211111111−2i2i−2i2i222i2i−2i−2iiiii−i−i−i−i-1-1-1-1−i−i−i−iiiii000000000000
χ292222-1-2-2-1-1-1111120022233−3−32222-1-2-2-1-1-1000011113333−3−3−3−3-2-2-1-1-1-1111122-2-2000000-1-111-1-11133−3−333−3−333−3−3000000000000
χ302222-1-2-2-1-1-1111120022233−3−32222-1-2-2-1-1-1000011113333−3−3−3−3-2-2-1-1-1-11111-2-22200000011-1-111-1-133−3−3−3−333−3−333000000000000
χ312222-1-2-2-1-1-1111120022233−3−3-2-2-2-2-1-2-2-1-1-1000011113333−3−3−3−3221111-1-1-1-12i−2i−2i2i000000−i−iiiii−i−i−3−333i3i3−i3−i3−i3−i3i3i3000000000000
χ322222-1-2-2-1-1-1111120022233−3−3-2-2-2-2-1-2-2-1-1-1000011113333−3−3−3−3221111-1-1-1-1−2i2i2i−2i000000ii−i−i−i−iii−3−333−i3−i3i3i3i3i3−i3−i3000000000000
χ332222-1-2-2-1-1-11111200222−3−3332222-1-2-2-1-1-100001111−3−3−3−33333-2-2-1-1-1-1111122-2-2000000-1-111-1-111−3−333−3−333−3−333000000000000
χ342222-1-2-2-1-1-11111200222−3−3332222-1-2-2-1-1-100001111−3−3−3−33333-2-2-1-1-1-11111-2-22200000011-1-111-1-1−3−33333−3−333−3−3000000000000
χ352222-1-2-2-1-1-11111200222−3−333-2-2-2-2-1-2-2-1-1-100001111−3−3−3−33333221111-1-1-1-12i−2i−2i2i000000−i−iiiii−i−i33−3−3−i3−i3i3i3i3i3−i3−i3000000000000
χ362222-1-2-2-1-1-11111200222−3−333-2-2-2-2-1-2-2-1-1-100001111−3−3−3−33333221111-1-1-1-1−2i2i2i−2i000000ii−i−i−i−iii33−3−3i3i3−i3−i3−i3−i3i3i3000000000000
χ372-22-222-2-2-2222-2-222i−2i-22-22i−2i2i−2i2-22-222-2-2-222i2i−2i−2i22-2-22i2i−2i−2i2i2i−2i−2i-2222-2-2-2-22200002i−2i0000000000002i−2i2i−2i00000000000000000000
χ382-22-222-2-2-2222-2-222i−2i-22-22i−2i2i−2i-22-2222-2-2-222i2i−2i−2i22-2-22i2i−2i−2i2i2i−2i−2i2-2-2-22222-2-20000−2i2i000000000000−2i2i−2i2i00000000000000000000
χ392-22-222-2-2-2222-2-22−2i2i-22-2−2i2i−2i2i2-22-222-2-2-22−2i−2i2i2i22-2-2−2i−2i2i2i−2i−2i2i2i-2222-2-2-2-2220000−2i2i000000000000−2i2i−2i2i00000000000000000000
χ402-22-222-2-2-2222-2-22−2i2i-22-2−2i2i−2i2i-22-2222-2-2-22−2i−2i2i2i22-2-2−2i−2i2i2i−2i−2i2i2i2-2-2-22222-2-200002i−2i0000000000002i−2i2i−2i00000000000000000000
χ412-22-22-22-2-22-2-222200-22-200002-22-22-22-2-220000-2-222000000002-222-2-222-2-20000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ422-22-22-22-2-22-2-222200-22-200002-22-22-22-2-220000-2-222000000002-222-2-222-2-2000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ432-22-22-22-2-22-2-222200-22-20000-22-222-22-2-220000-2-22200000000-22-2-222-2-2220000002-2-220000000000002-22-2-22-22000000000000
χ442-22-22-22-2-22-2-222200-22-20000-22-222-22-2-220000-2-22200000000-22-2-222-2-222000000-222-2000000000000-22-222-22-2000000000000
χ452-22-2-12-211-1-1-11122i−2i-22-2−ii−ii2-22-2-12-211-12i2i−2i−2i-1-111−i−iii−i−iii-22-1-11111-1-100002i−2i00003−33−33−33−3−ii−ii−i3i3i3−i3−i3i3i3−i3000000000000
χ462-22-2-12-211-1-1-11122i−2i-22-2−ii−ii2-22-2-12-211-12i2i−2i−2i-1-111−i−iii−i−iii-22-1-11111-1-100002i−2i0000−33−33−33−33−ii−iii3−i3−i3i3i3−i3−i3i3000000000000
χ472-22-2-12-211-1-1-11122i−2i-22-2−ii−ii-22-22-12-211-12i2i−2i−2i-1-111−i−iii−i−iii2-211-1-1-1-1110000−2i2i0000−i3i3−i3i3i3−i3i3−i3i−ii−i−333−33−3−33000000000000
χ482-22-2-12-211-1-1-11122i−2i-22-2−ii−ii-22-22-12-211-12i2i−2i−2i-1-111−i−iii−i−iii2-211-1-1-1-1110000−2i2i0000i3−i3i3−i3−i3i3−i3i3i−ii−i3−3−33−333−3000000000000
χ492-22-2-12-211-1-1-1112−2i2i-22-2i−ii−i2-22-2-12-211-1−2i−2i2i2i-1-111ii−i−iii−i−i-22-1-11111-1-10000−2i2i00003−33−33−33−3i−ii−ii3−i3−i3i3i3−i3−i3i3000000000000
χ502-22-2-12-211-1-1-1112−2i2i-22-2i−ii−i2-22-2-12-211-1−2i−2i2i2i-1-111ii−i−iii−i−i-22-1-11111-1-10000−2i2i0000−33−33−33−33i−ii−i−i3i3i3−i3−i3i3i3−i3000000000000
χ512-22-2-12-211-1-1-1112−2i2i-22-2i−ii−i-22-22-12-211-1−2i−2i2i2i-1-111ii−i−iii−i−i2-211-1-1-1-11100002i−2i0000−i3i3−i3i3i3−i3i3−i3−ii−ii3−3−33−333−3000000000000
χ522-22-2-12-211-1-1-1112−2i2i-22-2i−ii−i-22-22-12-211-1−2i−2i2i2i-1-111ii−i−iii−i−i2-211-1-1-1-11100002i−2i0000i3−i3i3−i3−i3i3−i3i3−ii−ii−333−33−3−33000000000000
χ532-22-2-1-2211-111-1-1200-22-2−i3i3i3−i32-22-2-1-2211-1000011-1-1−i3−i3i3i3i3i3−i3−i32-2-1-111-1-1110000002i−2i2i−2i−333−3−333−3−i3i3i3−i3−ii−ii−ii−ii000000000000
χ542-22-2-1-2211-111-1-1200-22-2−i3i3i3−i32-22-2-1-2211-1000011-1-1−i3−i3i3i3i3i3−i3−i32-2-1-111-1-111000000−2i2i−2i2i3−3−333−3−33−i3i3i3−i3i−ii−ii−ii−i000000000000
χ552-22-2-1-2211-111-1-1200-22-2−i3i3i3−i3-22-22-1-2211-1000011-1-1−i3−i3i3i3i3i3−i3−i3-2211-1-111-1-10000002-2-22i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3-11-111-11-1000000000000
χ562-22-2-1-2211-111-1-1200-22-2−i3i3i3−i3-22-22-1-2211-1000011-1-1−i3−i3i3i3i3i3−i3−i3-2211-1-111-1-1000000-222-2−i3i3i3−i3i3−i3−i3i3i3−i3−i3i31-11-1-11-11000000000000
χ572-22-2-1-2211-111-1-1200-22-2i3−i3−i3i32-22-2-1-2211-1000011-1-1i3i3−i3−i3−i3−i3i3i32-2-1-111-1-1110000002i−2i2i−2i3−3−333−3−33i3−i3−i3i3−ii−ii−ii−ii000000000000
χ582-22-2-1-2211-111-1-1200-22-2i3−i3−i3i32-22-2-1-2211-1000011-1-1i3i3−i3−i3−i3−i3i3i32-2-1-111-1-111000000−2i2i−2i2i−333−3−333−3i3−i3−i3i3i−ii−ii−ii−i000000000000
χ592-22-2-1-2211-111-1-1200-22-2i3−i3−i3i3-22-22-1-2211-1000011-1-1i3i3−i3−i3−i3−i3i3i3-2211-1-111-1-10000002-2-22−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3-11-111-11-1000000000000
χ602-22-2-1-2211-111-1-1200-22-2i3−i3−i3i3-22-22-1-2211-1000011-1-1i3i3−i3−i3−i3−i3i3i3-2211-1-111-1-1000000-222-2i3−i3−i3i3−i3i3i3−i3−i3i3i3−i31-11-1-11-11000000000000
χ6144444444444444-144-1-1-144440000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000000044-1-1-1-1000000
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χ6444444444444444-1-4-4-1-1-1-4-4-4-40000-1-1-1-1-1-11111-1-1-1-1111111110000000000000000000000000000000000000000-4411-1-1000000
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χ8188888-8-8888-8-8-8-8-200-2-2-200000000-222-2-2-200002222000000000000000000000000000000000000000000000000000000000000
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χ8888-8-8-400-44443−4343−43-200-222000000001001-1-1i10−i10i10−i10−33−33−ζ7+ζ29+ζ31−ζ53−ζ77+ζ79+ζ101−ζ103ζ7−ζ29−ζ31+ζ53+ζ77−ζ79−ζ101+ζ103−ζ7+ζ29+ζ31−ζ53−ζ77+ζ79+ζ101−ζ103ζ7−ζ29−ζ31+ζ53+ζ77−ζ79−ζ101+ζ103−ζ13−ζ23−ζ37−ζ47+ζ61+ζ71+ζ109+ζ119ζ13+ζ23+ζ37+ζ47−ζ61−ζ71−ζ109−ζ119−ζ13−ζ23−ζ37−ζ47+ζ61+ζ71+ζ109+ζ119ζ13+ζ23+ζ37+ζ47−ζ61−ζ71−ζ109−ζ1190000000000000000000000000000000000000000000000000000
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χ9088-8-8-400-444−4343−4343-200-222000000001001-1-1i10−i10i10−i103−33−3−ζ13−ζ23−ζ37−ζ47+ζ61+ζ71+ζ109+ζ119ζ13+ζ23+ζ37+ζ47−ζ61−ζ71−ζ109−ζ119−ζ13−ζ23−ζ37−ζ47+ζ61+ζ71+ζ109+ζ119ζ13+ζ23+ζ37+ζ47−ζ61−ζ71−ζ109−ζ119−ζ7+ζ29+ζ31−ζ53−ζ77+ζ79+ζ101−ζ103ζ7−ζ29−ζ31+ζ53+ζ77−ζ79−ζ101+ζ103−ζ7+ζ29+ζ31−ζ53−ζ77+ζ79+ζ101−ζ103ζ7−ζ29−ζ31+ζ53+ζ77−ζ79−ζ101+ζ1030000000000000000000000000000000000000000000000000000
χ9188-8-8-400-444−4343−4343-200-222000000001001-1-1−i10i10−i10i103−33−3ζ13+ζ23+ζ37+ζ47−ζ61−ζ71−ζ109−ζ119−ζ13−ζ23−ζ37−ζ47+ζ61+ζ71+ζ109+ζ119ζ13+ζ23+ζ37+ζ47−ζ61−ζ71−ζ109−ζ119−ζ13−ζ23−ζ37−ζ47+ζ61+ζ71+ζ109+ζ119ζ7−ζ29−ζ31+ζ53+ζ77−ζ79−ζ101+ζ103−ζ7+ζ29+ζ31−ζ53−ζ77+ζ79+ζ101−ζ103ζ7−ζ29−ζ31+ζ53+ζ77−ζ79−ζ101+ζ103−ζ7+ζ29+ζ31−ζ53−ζ77+ζ79+ζ101−ζ1030000000000000000000000000000000000000000000000000000
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χ998-8-88-4004-4443−43−4343-20022-200000000100-11-110−10−1010−333−3ζ13−ζ23+ζ37−ζ47−ζ61+ζ71−ζ109+ζ119−ζ13+ζ23−ζ37+ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47+ζ61−ζ71+ζ109−ζ119ζ13−ζ23+ζ37−ζ47−ζ61+ζ71−ζ109+ζ119−ζ7−ζ29+ζ31+ζ53+ζ77+ζ79−ζ101−ζ103ζ7+ζ29−ζ31−ζ53−ζ77−ζ79+ζ101+ζ103ζ7+ζ29−ζ31−ζ53−ζ77−ζ79+ζ101+ζ103−ζ7−ζ29+ζ31+ζ53+ζ77+ζ79−ζ101−ζ1030000000000000000000000000000000000000000000000000000
χ1008-8-88-4004-4443−43−4343-20022-200000000100-11-1−101010−10−333−3−ζ13+ζ23−ζ37+ζ47+ζ61−ζ71+ζ109−ζ119ζ13−ζ23+ζ37−ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47−ζ61+ζ71−ζ109+ζ119−ζ13+ζ23−ζ37+ζ47+ζ61−ζ71+ζ109−ζ119ζ7+ζ29−ζ31−ζ53−ζ77−ζ79+ζ101+ζ103−ζ7−ζ29+ζ31+ζ53+ζ77+ζ79−ζ101−ζ103−ζ7−ζ29+ζ31+ζ53+ζ77+ζ79−ζ101−ζ103ζ7+ζ29−ζ31−ζ53−ζ77−ζ79+ζ101+ζ1030000000000000000000000000000000000000000000000000000
χ1018-8-88-4004-44−434343−43-20022-200000000100-11-110−10−10103−3−33−ζ7−ζ29+ζ31+ζ53+ζ77+ζ79−ζ101−ζ103ζ7+ζ29−ζ31−ζ53−ζ77−ζ79+ζ101+ζ103ζ7+ζ29−ζ31−ζ53−ζ77−ζ79+ζ101+ζ103−ζ7−ζ29+ζ31+ζ53+ζ77+ζ79−ζ101−ζ103ζ13−ζ23+ζ37−ζ47−ζ61+ζ71−ζ109+ζ119−ζ13+ζ23−ζ37+ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47+ζ61−ζ71+ζ109−ζ119ζ13−ζ23+ζ37−ζ47−ζ61+ζ71−ζ109+ζ1190000000000000000000000000000000000000000000000000000
χ1028-8-88-4004-44−434343−43-20022-200000000100-11-1−101010−103−3−33ζ7+ζ29−ζ31−ζ53−ζ77−ζ79+ζ101+ζ103−ζ7−ζ29+ζ31+ζ53+ζ77+ζ79−ζ101−ζ103−ζ7−ζ29+ζ31+ζ53+ζ77+ζ79−ζ101−ζ103ζ7+ζ29−ζ31−ζ53−ζ77−ζ79+ζ101+ζ103−ζ13+ζ23−ζ37+ζ47+ζ61−ζ71+ζ109−ζ119ζ13−ζ23+ζ37−ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47−ζ61+ζ71−ζ109+ζ119−ζ13+ζ23−ζ37+ζ47+ζ61−ζ71+ζ109−ζ1190000000000000000000000000000000000000000000000000000

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