Finite Group Databasebeta

← Group #14304755

Character table — Group #14304755

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444445555888888888888888888888810101010101020202020202020202424404040404040404040404040484848486060606060606060120120
order122234466658810101012122424242422221520203030304040404060606060120120120120120120120120446666881212242424242444441212121212121212101020204444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111i−ii−iiiii−i−i−i−i1111i−ii−iii−i−i-1-1
χ61111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−ii−ii−i−i−i−iiiii1111−ii−ii−i−iii-1-1
χ71111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iiiii−i−i−i−i-1-1-1-1−ii−ii−i−iii11
χ81111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−i−i−i−iiiii-1-1-1-1i−ii−iii−i−i11
χ911111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11-111-1-111-1-111-1-111-1-11111-1-1-1-11-1
χ1011111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11-1-1-111-1-111-1-11111-1-1-1-1-1-111111-1
χ1111111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1111-1-111-1-111-1-1-1-111-1-1-1-11111-11
χ1211111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-11-1-111-1-111-1-111-1-1111111-1-1-1-1-11
χ1311111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1i−i−iiii−i−i−i−iii11-1-1i−ii−i−i−iii-11
χ1411111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1−iii−i−i−iiiii−i−i11-1-1−ii−iiii−i−i-11
χ1511111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11i−i−iiii−i−i−i−iii-1-111−ii−iiii−i−i1-1
χ1611111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11−iii−i−i−iiiii−i−i-1-111i−ii−i−i−iii1-1
χ1722222-2-2222200222-2-2000022222-2-22220000-2-2-2-200000000-2-2222200-2-2000000000000000000000022-2-2000000
χ1822222-2-2222200222-2-2000022222-2-22220000-2-2-2-200000000-2-2222200-2-20000000000000000000000-2-222000000
χ1922222-2-2222200222-2-20000-2-2-2-22-2-22220000-2-2-2-20000000022-2-2-2-2002200000000000000000000002i−2i−2i2i000000
χ2022222-2-2222200222-2-20000-2-2-2-22-2-22220000-2-2-2-20000000022-2-2-2-200220000000000000000000000−2i2i2i−2i000000
χ212222-122-1-1-1222222-1-1-1-1-1-12222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1002222-1-1-1-1-1-1-1-100000000000000
χ222222-122-1-1-1222222-1-1-1-1-1-12222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-100-2-2-2-21111111100000000000000
χ232222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2111111002i−2i2i−2i−i−i−i−iiiii00000000000000
χ242222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-211111100−2i2i−2i2iiiii−i−i−i−i00000000000000
χ252222-122-1-1-12-2-2222-1-111112222-122-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-1-2-2-1-111110022-2-2-1-111-1-11100000000000000
χ262222-122-1-1-12-2-2222-1-111112222-122-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-1-2-2-1-1111100-2-22211-1-111-1-100000000000000
χ272222-122-1-1-12-2-2222-1-11111-2-2-2-2-122-1-1-1-2-2-2-2-1-1-1-111111111-2-211112211-1-1-1-1002i−2i−2i2i−i−iiiii−i−i00000000000000
χ282222-122-1-1-12-2-2222-1-11111-2-2-2-2-122-1-1-1-2-2-2-2-1-1-1-111111111-2-211112211-1-1-1-100−2i2i2i−2iii−i−i−i−iii00000000000000
χ292-22-222-2-2-2222i−2i-22-22-22i2i−2i−2i22-2-222-2-2-222i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i-222-22-22i−2i2-22i2i−2i−2i0000000000000000000000000000
χ302-22-222-2-2-2222i−2i-22-22-22i2i−2i−2i-2-22222-2-2-222i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i2-2-22-22−2i2i-22−2i−2i2i2i0000000000000000000000000000
χ312-22-222-2-2-222−2i2i-22-22-2−2i−2i2i2i22-2-222-2-2-22−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i-222-22-2−2i2i2-2−2i−2i2i2i0000000000000000000000000000
χ322-22-222-2-2-222−2i2i-22-22-2−2i−2i2i2i-2-22222-2-2-22−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i2-2-22-222i−2i-222i2i−2i−2i0000000000000000000000000000
χ332-22-22-22-2-22200-22-2-22000022-2-22-22-2-220000-2-222000000002-22-22-200-22000000000000000000000000002i−2i2i−2i00
χ342-22-22-22-2-22200-22-2-22000022-2-22-22-2-220000-2-222000000002-22-22-200-2200000000000000000000000000−2i2i−2i2i00
χ352-22-22-22-2-22200-22-2-220000-2-2222-22-2-220000-2-22200000000-22-22-22002-2000000000000000000000000002-2-2200
χ362-22-22-22-2-22200-22-2-220000-2-2222-22-2-220000-2-22200000000-22-22-22002-200000000000000000000000000-222-200
χ372-22-2-12-211-122i−2i-22-2-11−i−iii22-2-2-12-211-12i2i−2i−2i-1-111−i−i−i−iiiii-22-11-112i−2i-11−i−iii000000−i3i33−3−i3i33−300000000000000
χ382-22-2-12-211-122i−2i-22-2-11−i−iii22-2-2-12-211-12i2i−2i−2i-1-111−i−i−i−iiiii-22-11-112i−2i-11−i−iii000000i3−i3−33i3−i3−3300000000000000
χ392-22-2-12-211-122i−2i-22-2-11−i−iii-2-222-12-211-12i2i−2i−2i-1-111−i−i−i−iiiii2-21-11-1−2i2i1-1ii−i−i0000003−3i3−i3−33−i3i300000000000000
χ402-22-2-12-211-122i−2i-22-2-11−i−iii-2-222-12-211-12i2i−2i−2i-1-111−i−i−i−iiiii2-21-11-1−2i2i1-1ii−i−i000000−33−i3i33−3i3−i300000000000000
χ412-22-2-12-211-12−2i2i-22-2-11ii−i−i22-2-2-12-211-1−2i−2i2i2i-1-111iiii−i−i−i−i-22-11-11−2i2i-11ii−i−i000000−i3i3−33−i3i3−3300000000000000
χ422-22-2-12-211-12−2i2i-22-2-11ii−i−i22-2-2-12-211-1−2i−2i2i2i-1-111iiii−i−i−i−i-22-11-11−2i2i-11ii−i−i000000i3−i33−3i3−i33−300000000000000
χ432-22-2-12-211-12−2i2i-22-2-11ii−i−i-2-222-12-211-1−2i−2i2i2i-1-111iiii−i−i−i−i2-21-11-12i−2i1-1−i−iii0000003−3−i3i3−33i3−i300000000000000
χ442-22-2-12-211-12−2i2i-22-2-11ii−i−i-2-222-12-211-1−2i−2i2i2i-1-111iiii−i−i−i−i2-21-11-12i−2i1-1−i−iii000000−33i3−i33−3−i3i300000000000000
χ454444444444-144-1-1-14444440000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000044000000000000-1-1-1-10000000000
χ464444444444-144-1-1-14444440000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000-4-400000000000011110000000000
χ474444444444-1-4-4-1-1-144-4-4-4-40000-1-1-1-1-1-11111-1-1-1-111111111000000000000004-4000000000000-1-1110000000000
χ484444444444-1-4-4-1-1-144-4-4-4-40000-1-1-1-1-1-11111-1-1-1-11111111100000000000000-4400000000000011-1-10000000000
χ494444-2-4-4-2-2-24004442200004444-2-4-4-2-2-20000222200000000-4-4-2-2-2-2002200000000000000000000000000000000
χ504444-2-4-4-2-2-2400444220000-4-4-4-4-2-4-4-2-2-2000022220000000044222200-2-200000000000000000000000000000000
χ5144-4-44004-4-44004-4-40000004-44-44004-4-400000000000000000044-4-4000000000000000000000000000000000000
χ5244-4-44004-4-44004-4-4000000-44-444004-4-4000000000000000000-4-444000000000000000000000000000000000000
χ5344-4-4-200-2224004-4-400−i6i6−i6i64-44-4-200-22200000000−i6−i6i6i6−i6−i6i6i600-2-2220000−i6i6−i6i60000000000000000000000000000
χ5444-4-4-200-2224004-4-400−i6i6−i6i6-44-44-200-22200000000−i6−i6i6i6−i6−i6i6i60022-2-20000i6−i6i6−i60000000000000000000000000000
χ5544-4-4-200-2224004-4-400i6−i6i6−i64-44-4-200-22200000000i6i6−i6−i6i6i6−i6−i600-2-2220000i6−i6i6−i60000000000000000000000000000
χ5644-4-4-200-2224004-4-400i6−i6i6−i6-44-44-200-22200000000i6i6−i6−i6i6i6−i6−i60022-2-20000−i6i6−i6i60000000000000000000000000000
χ574-44-444-4-4-44-14i−4i1-114-44i4i−4i−4i0000-1-1111-1−i−iii-1-111−i−i−i−iiiii0000000000000000000000000000−55−i5i50000000000
χ584-44-444-4-4-44-14i−4i1-114-44i4i−4i−4i0000-1-1111-1−i−iii-1-111−i−i−i−iiiii00000000000000000000000000005−5i5−i50000000000
χ594-44-444-4-4-44-1−4i4i1-114-4−4i−4i4i4i0000-1-1111-1ii−i−i-1-111iiii−i−i−i−i0000000000000000000000000000−55i5−i50000000000
χ604-44-444-4-4-44-1−4i4i1-114-4−4i−4i4i4i0000-1-1111-1ii−i−i-1-111iiii−i−i−i−i00000000000000000000000000005−5−i5i50000000000
χ614-44-4-2-4422-2400-44-42-2000044-4-4-2-4422-2000022-2-2000000004-4-22-22002-200000000000000000000000000000000
χ624-44-4-2-4422-2400-44-42-20000-4-444-2-4422-2000022-2-200000000-442-22-200-2200000000000000000000000000000000
χ634-4-44400-44-4400-4-440000004-4-44400-44-40000000000000000004-4-44000000000000000000000000000000000000
χ644-4-44400-44-4400-4-44000000-444-4400-44-4000000000000000000-444-4000000000000000000000000000000000000
χ654-4-44-2002-22400-4-44006−6−664-4-44-2002-220000000066−6−6−6−66600-222-200006−6−660000000000000000000000000000
χ664-4-44-2002-22400-4-44006−6−66-444-4-2002-220000000066−6−6−6−666002-2-220000−666−60000000000000000000000000000
χ674-4-44-2002-22400-4-4400−666−64-4-44-2002-2200000000−6−66666−6−600-222-20000−666−60000000000000000000000000000
χ684-4-44-2002-22400-4-4400−666−6-444-4-2002-2200000000−6−66666−6−6002-2-2200006−6−660000000000000000000000000000
χ6988888-8-8888-200-2-2-2-8-800000000-222-2-2-20000222200000000000000000000000000000000000000000000000000
χ708888-488-4-4-4-288-2-2-2-4-4-4-4-4-400001-2-2111-2-2-2-2111111111111000000000000000000000000000000000000000000
χ718888-488-4-4-4-2-8-8-2-2-2-4-4444400001-2-211122221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ728888-4-8-8-4-4-4-200-2-2-244000000001221110000-1-1-1-1−1515−1515−1515−1515000000000000000000000000000000000000000000
χ738888-4-8-8-4-4-4-200-2-2-244000000001221110000-1-1-1-115−1515−1515−1515−15000000000000000000000000000000000000000000
χ7488-8-88008-8-8-200-2220000000000-200-222i10−i10i10−i100000i10−i10−i10i10i10−i10−i10i10000000000000000000000000000000000000000000
χ7588-8-88008-8-8-200-2220000000000-200-222−i10i10−i10i100000−i10i10i10−i10−i10i10i10−i10000000000000000000000000000000000000000000
χ7688-8-8-400-444-200-22200−2i62i6−2i62i600001001-1-1i10−i10i10−i10−1515−1515−ζ7−ζ53+ζ61+ζ71−ζ77−ζ103+ζ109+ζ119ζ13+ζ23−ζ29−ζ31+ζ37+ζ47−ζ79−ζ101ζ7+ζ53−ζ61−ζ71+ζ77+ζ103−ζ109−ζ119−ζ13−ζ23+ζ29+ζ31−ζ37−ζ47+ζ79+ζ101−ζ7−ζ53+ζ61+ζ71−ζ77−ζ103+ζ109+ζ119ζ13+ζ23−ζ29−ζ31+ζ37+ζ47−ζ79−ζ101ζ7+ζ53−ζ61−ζ71+ζ77+ζ103−ζ109−ζ119−ζ13−ζ23+ζ29+ζ31−ζ37−ζ47+ζ79+ζ101000000000000000000000000000000000000000000
χ7788-8-8-400-444-200-22200−2i62i6−2i62i600001001-1-1−i10i10−i10i1015−1515−15ζ13+ζ23−ζ29−ζ31+ζ37+ζ47−ζ79−ζ101−ζ7−ζ53+ζ61+ζ71−ζ77−ζ103+ζ109+ζ119−ζ13−ζ23+ζ29+ζ31−ζ37−ζ47+ζ79+ζ101ζ7+ζ53−ζ61−ζ71+ζ77+ζ103−ζ109−ζ119ζ13+ζ23−ζ29−ζ31+ζ37+ζ47−ζ79−ζ101−ζ7−ζ53+ζ61+ζ71−ζ77−ζ103+ζ109+ζ119−ζ13−ζ23+ζ29+ζ31−ζ37−ζ47+ζ79+ζ101ζ7+ζ53−ζ61−ζ71+ζ77+ζ103−ζ109−ζ119000000000000000000000000000000000000000000
χ7888-8-8-400-444-200-222002i6−2i62i6−2i600001001-1-1i10−i10i10−i1015−1515−15−ζ13−ζ23+ζ29+ζ31−ζ37−ζ47+ζ79+ζ101ζ7+ζ53−ζ61−ζ71+ζ77+ζ103−ζ109−ζ119ζ13+ζ23−ζ29−ζ31+ζ37+ζ47−ζ79−ζ101−ζ7−ζ53+ζ61+ζ71−ζ77−ζ103+ζ109+ζ119−ζ13−ζ23+ζ29+ζ31−ζ37−ζ47+ζ79+ζ101ζ7+ζ53−ζ61−ζ71+ζ77+ζ103−ζ109−ζ119ζ13+ζ23−ζ29−ζ31+ζ37+ζ47−ζ79−ζ101−ζ7−ζ53+ζ61+ζ71−ζ77−ζ103+ζ109+ζ119000000000000000000000000000000000000000000
χ7988-8-8-400-444-200-222002i6−2i62i6−2i600001001-1-1−i10i10−i10i10−1515−1515ζ7+ζ53−ζ61−ζ71+ζ77+ζ103−ζ109−ζ119−ζ13−ζ23+ζ29+ζ31−ζ37−ζ47+ζ79+ζ101−ζ7−ζ53+ζ61+ζ71−ζ77−ζ103+ζ109+ζ119ζ13+ζ23−ζ29−ζ31+ζ37+ζ47−ζ79−ζ101ζ7+ζ53−ζ61−ζ71+ζ77+ζ103−ζ109−ζ119−ζ13−ζ23+ζ29+ζ31−ζ37−ζ47+ζ79+ζ101−ζ7−ζ53+ζ61+ζ71−ζ77−ζ103+ζ109+ζ119ζ13+ζ23−ζ29−ζ31+ζ37+ζ47−ζ79−ζ101000000000000000000000000000000000000000000
χ808-88-88-88-8-88-2002-22-8800000000-22-222-2000022-2-200000000000000000000000000000000000000000000000000
χ818-88-8-48-844-4-28i−8i2-22-44−4i−4i4i4i00001-22-1-11−2i−2i2i2i11-1-1iiii−i−i−i−i000000000000000000000000000000000000000000
χ828-88-8-48-844-4-2−8i8i2-22-444i4i−4i−4i00001-22-1-112i2i−2i−2i11-1-1−i−i−i−iiiii000000000000000000000000000000000000000000
χ838-88-8-4-8844-4-2002-224-40000000012-2-1-110000-1-111−i15i15−i15i15i15−i15i15−i15000000000000000000000000000000000000000000
χ848-88-8-4-8844-4-2002-224-40000000012-2-1-110000-1-111i15−i15i15−i15−i15i15−i15i15000000000000000000000000000000000000000000
χ858-8-88800-88-8-20022-20000000000-2002-2210−10−1010000010−10−1010−101010−10000000000000000000000000000000000000000000
χ868-8-88800-88-8-20022-20000000000-2002-22−101010−100000−101010−1010−10−1010000000000000000000000000000000000000000000
χ878-8-88-4004-44-20022-20026−26−26260000100-11-110−10−101015−15−1515−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101000000000000000000000000000000000000000000
χ888-8-88-4004-44-20022-20026−26−26260000100-11-1−101010−10−151515−15−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119000000000000000000000000000000000000000000
χ898-8-88-4004-44-20022-200−262626−260000100-11-110−10−1010−151515−15ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119000000000000000000000000000000000000000000
χ908-8-88-4004-44-20022-200−262626−260000100-11-1−101010−1015−15−1515ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101−ζ7+ζ53−ζ61+ζ71+ζ77−ζ103−ζ109+ζ119−ζ13+ζ23+ζ29−ζ31−ζ37+ζ47−ζ79+ζ101ζ7−ζ53+ζ61−ζ71−ζ77+ζ103+ζ109−ζ119ζ13−ζ23−ζ29+ζ31+ζ37−ζ47+ζ79−ζ101000000000000000000000000000000000000000000

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