Finite Group Databasebeta

← Group #14314289

Character table — Group #14314289

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222222244444444444558888888888888888888888101010101010101010202020202020202424404040404040404040404040484848486060606060606060120120
order1223446668858101212202024242424441015203030304040404060606060120120120120120120120120224881212121266824242424248888242424242424242410102020161616161616161624
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
χ51111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−iiiii−i−i−i−i1111iiii−i−i−i−i-1-1
χ61111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii−i−i−i−iiiii1111−i−i−i−iiiii-1-1
χ71111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1−i−i−i−iiiii11
χ81111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1iiii−i−i−i−i11
χ911-11-11-1-11-1-1111-11-1-111-1-111-111-1-1111-1-1-1-1111111-1-1-1-11-1-1-1-111-1-11-1111-1-11-1i−ii−iii−i−iii−i−i11-1-1ii−i−iii−i−i-11
χ1011-11-11-1-11-1-1111-11-1-111-1-111-111-1-1111-1-1-1-1111111-1-1-1-11-1-1-1-111-1-11-1111-1-11-1−ii−ii−i−iii−i−iii11-1-1−i−iii−i−iii-11
χ1111-11-11-1-11-1-1111-11-1-111-1-111-111-1-1111-1-1-1-1111111-1-1-1-11-1-1-1-111-1-11-1111-1-1-11i−ii−iii−i−iii−i−i-1-111−i−iii−i−iii1-1
χ1211-11-11-1-11-1-1111-11-1-111-1-111-111-1-1111-1-1-1-1111111-1-1-1-11-1-1-1-111-1-11-1111-1-1-11−ii−ii−i−iii−i−iii-1-111ii−i−iii−i−i1-1
χ1311-11-11-1-11-1-1111-11-1-111-1-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-1-11111-1-111-11-1-1-1111-11-1-1111-1-1-1-11111-1-111-1-1-1-1111-1
χ1411-11-11-1-11-1-1111-11-1-111-1-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-1-11111-1-111-11-1-1-1111-1-111-1-1-11111-1-111-1-1-1-11111-1-11-1
χ1511-11-11-1-11-1-1111-11-1-111-1-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-1-11111-1-111-11-1-1-111-111-1-1111-1-1-1-111-1-111-1-11111-1-1-11
χ1611-11-11-1-11-1-1111-11-1-111-1-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-1-11111-1-111-11-1-1-111-11-111-1-1-11111-1-1-1-11111-1-1-1-111-11
χ17222222222-2-22-222222-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2222-2-2222222-2-2-2-2-20000000000000000000000000000
χ18222222222-2-22-222222-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2222220000000000000000000000000000
χ192222-2-222200202-2-2-2-200002222-22220000-2-2-2-200000000-2-22002222-2-2000000000000000000000002−22−22−22−200
χ202222-2-222200202-2-2-2-200002222-22220000-2-2-2-200000000-2-22002222-2-200000000000000000000000−22−22−22−2200
χ212222-2-222200202-2-2-2-20000-2-222-22220000-2-2-2-20000000022-200-2-2-2-22200000000000000000000000−i2i2−i2i2i2−i2i2−i200
χ222222-2-222200202-2-2-2-20000-2-222-22220000-2-2-2-20000000022-200-2-2-2-22200000000000000000000000i2−i2i2−i2−i2i2−i2i200
χ23222-122-1-1-122222-1-122-1-1-1-1222-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-12-1-1-1-1002222-1-1-1-1-1-1-1-100000000000000
χ24222-122-1-1-122222-1-122-1-1-1-1222-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-12-1-1-1-100-2-2-2-21111111100000000000000
χ25222-122-1-1-122222-1-122-1-1-1-1-2-22-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2111111-21111002i2i−2i−2i−i−i−i−iiiii00000000000000
χ26222-122-1-1-122222-1-122-1-1-1-1-2-22-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2111111-2111100−2i−2i2i2iiiii−i−i−i−i00000000000000
χ27222-122-1-1-1-2-22-22-1-1221111222-12-1-1-1-2-2-2-2-1-1-1-111111111222-2-2-1-1-1-1-1-1-21111000000−i3i3−i3i3−i3i3−i3i300000000000000
χ28222-122-1-1-1-2-22-22-1-1221111222-12-1-1-1-2-2-2-2-1-1-1-111111111222-2-2-1-1-1-1-1-1-21111000000i3−i3i3−i3i3−i3i3−i300000000000000
χ29222-122-1-1-1-2-22-22-1-1221111-2-22-12-1-1-1-2-2-2-2-1-1-1-111111111-2-2-2221111112-1-1-1-10000003−33−3−33−3300000000000000
χ30222-122-1-1-1-2-22-22-1-1221111-2-22-12-1-1-1-2-2-2-2-1-1-1-111111111-2-2-2221111112-1-1-1-1000000−33−333−33−300000000000000
χ3122-222-2-2-22002022-222000022-22-2-2-22000022-2-200000000-22-20022-2-2-2200000000000000000000000−i2i2i2−i2−i2i2i2−i200
χ3222-222-2-2-22002022-222000022-22-2-2-22000022-2-200000000-22-20022-2-2-2200000000000000000000000i2−i2−i2i2i2−i2−i2i200
χ3322-222-2-2-22002022-2220000-2-2-22-2-2-22000022-2-2000000002-2200-2-2222-2000000000000000000000002−2−22−222−200
χ3422-222-2-2-22002022-2220000-2-2-22-2-2-22000022-2-2000000002-2200-2-2222-200000000000000000000000−222−22−2−2200
χ3522-22-22-2-22222-22-22-2-2-2-22222-222-2-22-2-222-2-222-2-2-2-222222-2-22222-2-22-2-2-2-2220000000000000000000000000000
χ3622-22-22-2-22222-22-22-2-2-2-222-2-2-222-2-22-2-222-2-222-2-2-2-22222-222-2-2-2-222-22222-2-20000000000000000000000000000
χ3722-2-1-2211-1222-221-1-2-211-1-122-2-1211-1-2-22211-1-11111-1-1-1-12-2-222-1-111-11-211-1-10000003−3−333−3−3300000000000000
χ3822-2-1-2211-1222-221-1-2-211-1-122-2-1211-1-2-22211-1-11111-1-1-1-12-2-222-1-111-11-211-1-1000000−333−3−333−300000000000000
χ3922-2-1-2211-1222-221-1-2-211-1-1-2-2-2-1211-1-2-22211-1-11111-1-1-1-1-222-2-211-1-11-12-1-111000000−i3i3i3−i3i3−i3−i3i300000000000000
χ4022-2-1-2211-1222-221-1-2-211-1-1-2-2-2-1211-1-2-22211-1-11111-1-1-1-1-222-2-211-1-11-12-1-111000000i3−i3−i3i3−i3i3i3−i300000000000000
χ4122-2-1-2211-1-2-22221-1-2-2-1-11122-2-1211-122-2-211-1-1-1-1-1-111112-2-2-2-2-1-111-112-1-111002i−2i2i−2i−i−iii−i−iii00000000000000
χ4222-2-1-2211-1-2-22221-1-2-2-1-11122-2-1211-122-2-211-1-1-1-1-1-111112-2-2-2-2-1-111-112-1-11100−2i2i−2i2iii−i−iii−i−i00000000000000
χ4322-2-1-2211-1-2-22221-1-2-2-1-111-2-2-2-1211-122-2-211-1-1-1-1-1-11111-2222211-1-11-1-211-1-1002-2-22-1-11111-1-100000000000000
χ4422-2-1-2211-1-2-22221-1-2-2-1-111-2-2-2-1211-122-2-211-1-1-1-1-1-11111-2222211-1-11-1-211-1-100-222-211-1-1-1-11100000000000000
χ4544444444444-14-144-1-1444400-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000044000000000000-1-1-1-10000000000
χ4644444444444-14-144-1-1444400-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-4-400000000000011110000000000
χ47444444444-4-4-1-4-144-1-1-4-4-4-400-1-1-1-1-1-11111-1-1-1-111111111000000000000000000000000000000−55−550000000000
χ48444444444-4-4-1-4-144-1-1-4-4-4-400-1-1-1-1-1-11111-1-1-1-1111111110000000000000000000000000000005−55−50000000000
χ49444-2-4-4-2-2-20040422-4-40000444-2-4-2-2-20000222200000000-4-4400-2-2-2-222000000000000000000000000000000000
χ50444-2-4-4-2-2-20040422-4-40000-4-44-2-4-2-2-2000022220000000044-4002222-2-2000000000000000000000000000000000
χ5144-44-44-4-4444-1-4-1-4411-4-444001-1-111-111-1-111-1-11111-1-1-1-1000000000000000000000000000000−555−50000000000
χ5244-44-44-4-4444-1-4-1-4411-4-444001-1-111-111-1-111-1-11111-1-1-1-10000000000000000000000000000005−5−550000000000
χ5344-44-44-4-44-4-4-14-1-441144-4-4001-1-111-1-1-11111-1-1-1-1-1-1111100000000000000004-4000000000000-1-1110000000000
χ5444-44-44-4-44-4-4-14-1-441144-4-4001-1-111-1-1-11111-1-1-1-1-1-111110000000000000000-4400000000000011-1-10000000000
χ5544-4-24-422-200404-2244000044-4-2-422-20000-2-22200000000-44-400-2-2222-2000000000000000000000000000000000
χ5644-4-24-422-200404-22440000-4-4-4-2-422-20000-2-222000000004-440022-2-2-22000000000000000000000000000000000
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χ654-40-2002i3−2i32−2i22i240-40000−66i2−i24i−4i0-202i3−2i3200−2i22i20000−6−666i2i2−i2−i200022−22−2i2i−2323000i6−i6−220000000000000000000000000000
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χ888-80-4004i3−4i34−4i24i2-202002i5−2i5−26262i2−2i200010−i3i3-1−1010i2−i2−i5i5−1515ζ7−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+ζ10100000000000000000000000000000000000000000000
χ898-80-4004i3−4i344i2−4i2-20200−2i52i526−26−2i22i200010−i3i3-1−1010−i2i2i5−i515−15−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−ζ11900000000000000000000000000000000000000000000
χ908-80-4004i3−4i344i2−4i2-202002i5−2i526−26−2i22i200010−i3i3-110−10−i2i2−i5i5−1515−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−ζ10100000000000000000000000000000000000000000000

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