Finite Group Databasebeta

← Group #14304613

Character table — Group #14304613

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222224444444444555588888888888888888888881010101010101010101020202020202024243030303030303030303030303030303040404040404040404040404048484848120120
order122234466688885101010121224242424222215202030303040404040606060601201201201201201201201204466668888121224242424244444444488888888444412121212121212121010202024
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−iii−i−iiiii−i−i−i−ii−ii−iiiii−i−i−i−i1111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii−i−iii−i−i−i−iiiii−ii−ii−i−i−i−iiiii1111-1-1
χ7111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i−ii−ii−i−i−i−iiiii-1-1-1-111
χ8111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiiii−ii−iiiii−i−i−i−i-1-1-1-111
χ91111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11-1
χ101111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-11-1
χ111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-11
χ121111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-111-11
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1ii−i−iii−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii11-1-1-11
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1−i−iii−i−iiiiiii−i−i−i−i−iii−i−i−iiiii−i−i11-1-1-11
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11ii−i−iii−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-1-1111-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11−i−iii−i−iiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-1-1111-1
χ1722222-2-222200002222-2-2000022222-2-22220000-2-2-2-200000000-2-222220000-2-20000002222-2-2-2-200000000000000000000000000
χ1822222-2-222200002222-2-2000022222-2-22220000-2-2-2-200000000-2-222220000-2-2000000-2-2-2-2222200000000000000000000000000
χ1922222-2-222200002222-2-20000-2-2-2-22-2-22220000-2-2-2-20000000022-2-2-2-20000220000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ2022222-2-222200002222-2-20000-2-2-2-22-2-22220000-2-2-2-20000000022-2-2-2-2000022000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
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χ232222-122-1-1-122222222-1-1-1-1-1-1-2-2-2-2-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2-2-21111110000000000000000002i−2i2i−2i−i−i−i−iiiii000000
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χ252222-122-1-1-1-2-2-2-22222-1-111112222-122-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-1-2-2-2-2-1-1111100000000000000000022-2-2-1-111-1-111000000
χ262222-122-1-1-1-2-2-2-22222-1-111112222-122-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-1-2-2-2-2-1-11111000000000000000000-2-22211-1-111-1-1000000
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χ282222-122-1-1-1-2-2-2-22222-1-11111-2-2-2-2-122-1-1-1-2-2-2-2-1-1-1-111111111-2-21111222211-1-1-1-1000000000000000000−2i2i2i−2iii−i−i−i−iii000000
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χ392-22-222-2-2-22−2i2i−2i2i2-22-22-2−2i2i−2i2i22-2-222-2-2-22−2i2i−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i-222-2-22−2i2i−2i2i2-2−2i2i−2i2i000000000000000000000000000000000000
χ402-22-222-2-2-22−2i2i−2i2i2-22-22-2−2i2i−2i2i-2-22222-2-2-22−2i2i−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i2-2-222-22i−2i2i−2i-222i−2i2i−2i000000000000000000000000000000000000
χ412-22-22-22-2-2200002-22-2-22000022-2-22-22-2-220000-2-222000000002-22-2-220000-22000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000
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χ432-22-22-22-2-2200002-22-2-220000-2-2222-22-2-220000-2-22200000000-22-222-200002-2000000000000002-22-2-22-22000000000000000000
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χ512-22-2-12-211-1−2i2i−2i2i2-22-2-11i−ii−i-2-222-12-211-1−2i2i−2i2i-1-111ii−i−iii−i−i2-21-1-112i−2i2i−2i1-1−ii−ii00000000000000000000003−3−i3i3−33i3−i3000000
χ522-22-2-12-211-1−2i2i−2i2i2-22-2-11i−ii−i-2-222-12-211-1−2i2i−2i2i-1-111ii−i−iii−i−i2-21-1-112i−2i2i−2i1-1−ii−ii0000000000000000000000−33i3−i33−3−i3i3000000
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χ8688-8-88008-8-8−4i2−4i24i24i2-2-22200−4i2−4i24i24i20000-200-222i2i2−i2−i20000i2i2i2i2−i2−i2−i2−i20000000000000000000000000000000000000000000000000000
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χ8888-8-8-400-444−4i2−4i24i24i2-2-222002i22i2−2i2−2i200001001-1-1i2i2−i2−i2−1515−1515−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+ζ119ζ13+ζ23+ζ29+ζ31+ζ37+ζ47+ζ79+ζ101ζ7+ζ53+ζ61+ζ71+ζ77+ζ103+ζ109+ζ1190000000000000000000000000000000000000000000000000000
χ8988-8-8-400-444−4i2−4i24i24i2-2-222002i22i2−2i2−2i200001001-1-1i2i2−i2−i215−1515−15−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+ζ101ζ7+ζ53+ζ61+ζ71+ζ77+ζ103+ζ109+ζ119ζ13+ζ23+ζ29+ζ31+ζ37+ζ47+ζ79+ζ1010000000000000000000000000000000000000000000000000000
χ9088-8-8-400-4444i24i2−4i2−4i2-2-22200−2i2−2i22i22i200001001-1-1−i2−i2i2i2−1515−1515ζ13+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−ζ119−ζ13−ζ23−ζ29−ζ31−ζ37−ζ47−ζ79−ζ101−ζ7−ζ53−ζ61−ζ71−ζ77−ζ103−ζ109−ζ1190000000000000000000000000000000000000000000000000000
χ9188-8-8-400-4444i24i2−4i2−4i2-2-22200−2i2−2i22i22i200001001-1-1−i2−i2i2i215−1515−15ζ7+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−ζ101−ζ7−ζ53−ζ61−ζ71−ζ77−ζ103−ζ109−ζ119−ζ13−ζ23−ζ29−ζ31−ζ37−ζ47−ζ79−ζ1010000000000000000000000000000000000000000000000000000
χ928-88-88-88-8-880000-22-22-8800000000-22-222-2000022-2-2000000000000000000000000000000000000000000000000000000000000
χ938-88-8-48-844-48i−8i8i−8i-22-22-44−4i4i−4i4i00001-22-1-11−2i2i−2i2i11-1-1ii−i−iii−i−i0000000000000000000000000000000000000000000000000000
χ948-88-8-48-844-4−8i8i−8i8i-22-22-444i−4i4i−4i00001-22-1-112i−2i2i−2i11-1-1−i−iii−i−iii0000000000000000000000000000000000000000000000000000
χ958-88-8-4-8844-40000-22-224-40000000012-2-1-110000-1-111−i15i15i15−i15−i15i15i15−i150000000000000000000000000000000000000000000000000000
χ968-88-8-4-8844-40000-22-224-40000000012-2-1-110000-1-111i15−i15−i15i15i15−i15−i15i150000000000000000000000000000000000000000000000000000
χ978-8-88800-88-842−42−4242-222-20042−42−42420000-2002-22−222−20000−2−22222−2−20000000000000000000000000000000000000000000000000000
χ988-8-88800-88-8−424242−42-222-200−424242−420000-2002-222−2−22000022−2−2−2−2220000000000000000000000000000000000000000000000000000
χ998-8-88-4004-4442−42−4242-222-200−222222−220000100-11-1−222−2−151515−15ζ7−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+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−ζ1010000000000000000000000000000000000000000000000000000
χ1008-8-88-4004-4442−42−4242-222-200−222222−220000100-11-1−222−215−15−1515−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−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+ζ1190000000000000000000000000000000000000000000000000000
χ1018-8-88-4004-44−424242−42-222-20022−22−22220000100-11-12−2−22−151515−15−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−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+ζ1010000000000000000000000000000000000000000000000000000
χ1028-8-88-4004-44−424242−42-222-20022−22−22220000100-11-12−2−2215−15−1515ζ13−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+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−ζ1190000000000000000000000000000000000000000000000000000

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