Finite Group Databasebeta

← Group #14303449

Character table — Group #14303449

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222444444444444555588888888888888888888881010101010101212202020202020202020202020243030303040404040404040404040484848486060606060606060120
order122234466658810101012122424242422221520203030304040404060606060120120120120120120120120446666444444881212242424244444444121212121212121220202020444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11
χ3111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1
χ51111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111ii−i−i-1-1-1-1-1-1-1-11ii−i−ii−iiiii−i−i−i−i1111-1-1i−iii−i−i-1
χ61111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111−i−iii-1-1-1-1-1-1-1-11−i−iii−ii−i−i−i−iiiii1111-1-1−ii−i−iii-1
χ71111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-1-1−i−iiii−iiiii−i−i−i−i-1-1-1-111−ii−i−iii1
χ81111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-1-1ii−i−i−ii−i−i−i−iiiii-1-1-1-111i−iii−i−i1
χ911111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-11111-1-111-1-111-1-111-1-11111-1-1-1-1-1
χ1011111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-11111-1
χ1111111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-111111
χ1211111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-111-1-111-1-111-1-111-1-1-1-11
χ1311111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i11-1-11111-1ii−i−i−iiii−i−i−i−iii11-1-1-1-1i−i−i−iii1
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−i−iii11-1-11111-1−i−iiii−i−i−iiiii−i−i11-1-1-1-1−iiii−i−i1
χ1511111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i11-1-111111−i−iii−iiii−i−i−i−iii-1-11111−iiii−i−i-1
χ1611111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii11-1-111111ii−i−ii−i−i−iiiii−i−i-1-11111i−i−i−iii-1
χ1722222-2-2222200222-2-2000022222-2-22220000-2-2-2-200000000-2-2222200000000-2-20000022220000000000000000-2-200000
χ1822222-2-2222200222-2-2000022222-2-22220000-2-2-2-200000000-2-2222200000000-2-200000-2-2-2-200000000000000002200000
χ1922222-2-2222200222-2-20000-2-2-2-22-2-22220000-2-2-2-20000000022-2-2-2-20000000022000002i2i−2i−2i0000000000000000−2i2i00000
χ2022222-2-2222200222-2-20000-2-2-2-22-2-22220000-2-2-2-20000000022-2-2-2-2000000002200000−2i−2i2i2i00000000000000002i−2i00000
χ212222-122-1-1-1222222-1-1-1-1-1-12222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100222222-1-1-1-1-1-10000022-1-1-1-1-1-1-1-10000000000000
χ222222-122-1-1-1222222-1-1-1-1-1-12222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-222-1-1-1-1-1-100000-2-2111111110000000000000
χ232222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111002i2i−2i−2i-2-2111111000002i−2i−i−i−i−iiiii0000000000000
χ242222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111100−2i−2i2i2i-2-211111100000−2i2iiiii−i−i−i−i0000000000000
χ252222-122-1-1-12-2-2222-1-111112222-122-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-1002222-2-2-1-1111100000-2-2-1-111-1-1110000000000000
χ262222-122-1-1-12-2-2222-1-111112222-122-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-100-2-2-2-2-2-2-1-11111000002211-1-111-1-10000000000000
χ272222-122-1-1-12-2-2222-1-11111-2-2-2-2-122-1-1-1-2-2-2-2-1-1-1-111111111-2-21111002i2i−2i−2i2211-1-1-1-100000−2i2i−i−iiiii−i−i0000000000000
χ282222-122-1-1-12-2-2222-1-11111-2-2-2-2-122-1-1-1-2-2-2-2-1-1-1-111111111-2-2111100−2i−2i2i2i2211-1-1-1-1000002i−2iii−i−i−i−iii0000000000000
χ2922-2-222-2-2-222002-2-22-2000022-2-222-2-2-22000022-2-2000000002-22-22-2002-22-2002-2000000000002-2002-2000000000000000
χ3022-2-222-2-2-222002-2-22-2000022-2-222-2-2-22000022-2-2000000002-22-22-200-22-22002-200000000000-2200-22000000000000000
χ3122-2-222-2-2-222002-2-22-20000-2-22222-2-2-22000022-2-200000000-22-22-22002i−2i−2i2i00-22000000000002i−2i00−2i2i000000000000000
χ3222-2-222-2-2-222002-2-22-20000-2-22222-2-2-22000022-2-200000000-22-22-2200−2i2i2i−2i00-2200000000000−2i2i002i−2i000000000000000
χ3322-2-22-22-2-222002-2-2-22000022-2-22-22-2-220000-2-22200000000-222-22-22i−2i000000-2200000000000000000002i−2i002i−2i0000000
χ3422-2-22-22-2-222002-2-2-22000022-2-22-22-2-220000-2-22200000000-222-22-2−2i2i000000-220000000000000000000−2i2i00−2i2i0000000
χ3522-2-22-22-2-222002-2-2-220000-2-2222-22-2-220000-2-222000000002-2-22-222i−2i0000002-200000000000000000002i−2i00−2i2i0000000
χ3622-2-22-22-2-222002-2-2-220000-2-2222-22-2-220000-2-222000000002-2-22-22−2i2i0000002-20000000000000000000−2i2i002i−2i0000000
χ3722-2-2-12-211-12002-2-2-1133−3−322-2-2-12-211-10000-1-1113333−3−3−3−32-2-11-11002-22-200-1133−3−30000000-113−3-113−30000000000000
χ3822-2-2-12-211-12002-2-2-1133−3−322-2-2-12-211-10000-1-1113333−3−3−3−32-2-11-1100-22-2200-1133−3−300000001-1−331-1−330000000000000
χ3922-2-2-12-211-12002-2-2-1133−3−3-2-222-12-211-10000-1-1113333−3−3−3−3-221-11-1002i−2i−2i2i001-1−3−3330000000−iii3−i3i−i−i3i30000000000000
χ4022-2-2-12-211-12002-2-2-1133−3−3-2-222-12-211-10000-1-1113333−3−3−3−3-221-11-100−2i2i2i−2i001-1−3−3330000000i−i−i3i3−iii3−i30000000000000
χ4122-2-2-12-211-12002-2-2-11−3−33322-2-2-12-211-10000-1-111−3−3−3−333332-2-11-11002-22-200-11−3−3330000000-11−33-11−330000000000000
χ4222-2-2-12-211-12002-2-2-11−3−33322-2-2-12-211-10000-1-111−3−3−3−333332-2-11-1100-22-2200-11−3−33300000001-13−31-13−30000000000000
χ4322-2-2-12-211-12002-2-2-11−3−333-2-222-12-211-10000-1-111−3−3−3−33333-221-11-1002i−2i−2i2i001-133−3−30000000−ii−i3i3i−ii3−i30000000000000
χ4422-2-2-12-211-12002-2-2-11−3−333-2-222-12-211-10000-1-111−3−3−3−33333-221-11-100−2i2i2i−2i001-133−3−30000000i−ii3−i3−ii−i3i30000000000000
χ452-22-22002-2-22−i2i2-22-200−i2i2−i2i22-2-222002-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2002-2-22000000−i2i200−i2i2−i2i202-22-2000000000000000000−i2i2−i2i20
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χ472-22-22002-2-22−i2i2-22-200−i2i2−i2i2-222-22002-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i200-222-2000000i2−i200i2−i2i2−i202i−2i−2i2i0000000000000000002−2−220
χ482-22-22002-2-22−i2i2-22-200−i2i2−i2i2-222-22002-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i200-222-2000000i2−i200i2−i2i2−i20−2i2i2i−2i000000000000000000−222−20
χ492-22-22002-2-22i2−i2-22-200i2−i2i2−i22-2-222002-2-2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2002-2-22000000i2−i200i2−i2i2−i202-22-2000000000000000000i2−i2i2−i20
χ502-22-22002-2-22i2−i2-22-200i2−i2i2−i22-2-222002-2-2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2002-2-22000000i2−i200i2−i2i2−i20-22-22000000000000000000−i2i2−i2i20
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χ522-22-22002-2-22i2−i2-22-200i2−i2i2−i2-222-22002-2-2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i200-222-2000000−i2i200−i2i2−i2i20−2i2i2i−2i0000000000000000002−2−220
χ534444444444-144-1-1-14444440000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000044000000000000400000000000000-1-1-1-1000000000
χ544444444444-144-1-1-14444440000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-4-4000000000000-4000000000000001111000000000
χ554444444444-1-4-4-1-1-144-4-4-4-40000-1-1-1-1-1-11111-1-1-1-11111111100000044000000000000-400000000000000-1-111000000000
χ564444444444-1-4-4-1-1-144-4-4-4-40000-1-1-1-1-1-11111-1-1-1-111111111000000-4-400000000000040000000000000011-1-1000000000
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χ6044-4-44-44-4-44-100-111-4400000000-11-111-1−55−5511-1-1−55−55−55−55000000−4i4i000000000000000000000000000i−ii5−i5000000000
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χ918-8-88800-88-8-20022-20000000000-2002-22i10−i10−i10i100000i10−i10−i10i10i10−i10−i10i10000000000000000000000000000000000000000000000000
χ928-8-88800-88-8-20022-20000000000-2002-22−i10i10i10−i100000−i10i10i10−i10−i10i10i10−i10000000000000000000000000000000000000000000000000
χ938-8-88-4004-44-20022-200−2i62i62i6−2i60000100-11-1i10−i10−i10i10−151515−15−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−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+ζ119000000000000000000000000000000000000000000000000
χ948-8-88-4004-44-20022-200−2i62i62i6−2i60000100-11-1−i10i10i10−i1015−15−1515ζ13+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−ζ119ζ7+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−ζ101000000000000000000000000000000000000000000000000
χ958-8-88-4004-44-20022-2002i6−2i6−2i62i60000100-11-1i10−i10−i10i1015−15−1515−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−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+ζ101000000000000000000000000000000000000000000000000
χ968-8-88-4004-44-20022-2002i6−2i6−2i62i60000100-11-1−i10i10i10−i10−151515−15ζ7+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−ζ101ζ13+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−ζ119000000000000000000000000000000000000000000000000

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