Finite Group Databasebeta

← Group #14281229

Character table — Group #14281229

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222444444444444444888888888888888888881010101010101010101020202020202020242424242424242424244040404040404040404040406060606060606060120120
order12222234466645661010101010101012121212152020202030303030303030606060606060606022444412121212266661212241010101020202020888824242424242424248888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111ii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1
χ611111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii11
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i11
χ91111111-1-1111-11111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i-11
χ101111111-1-1111-11111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii-11
χ111111111-1-1111-11111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-11111i−ii−iii−i−iii−i−i−i−iii−i−iii1-1
χ121111111-1-1111-11111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-11111−ii−ii−i−iii−i−iiiii−i−iii−i−i1-1
χ131111111-1-1111-11111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1111-1
χ141111111-1-1111-11111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-1-111-1-1-11111-1-1-1-11111-1-11-1
χ151111111-1-1111-11111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-1-11
χ161111111-1-1111-11111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1-1-11111-111-1-1-11111-1-111-1-1-1-111-11
χ17222222-122-1-1-122-1-12222222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-100000000002222-1-1-1-1-1-1-1-10000000000
χ18222222-122-1-1-122-1-12222222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-10000000000-2-2-2-2111111110000000000
χ19222222-122-1-1-122-1-12222222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-211111100000000002i2i−2i−2i−i−i−i−iiiii0000000000
χ20222222-122-1-1-122-1-12222222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-21111110000000000−2i−2i2i2iiiii−i−i−i−i0000000000
χ21222222-1-2-2-1-1-1-22-1-122222221111-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-211112-1-1-1-11100000000002i−2i2i−2i−i−iii−i−iii0000000000
χ22222222-1-2-2-1-1-1-22-1-122222221111-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-211112-1-1-1-1110000000000−2i2i−2i2iii−i−iii−i−i0000000000
χ23222222-1-2-2-1-1-1-22-1-122222221111-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-1-1-1-1-21111-1-100000000002-2-22-1-11111-1-10000000000
χ24222222-1-2-2-1-1-1-22-1-122222221111-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-1-1-1-1-21111-1-10000000000-222-211-1-1-1-1110000000000
χ252222-2-2222222-22-2-22-2-2-2-22222-2-2222-2-222-2-2-2-222222-2-2-2-222-2-222-2-2-2-2-222-2-22200000000000000000000000000000000
χ262222-2-2222222-22-2-22-2-2-2-22222-2-2222-2-222-2-2-2-222222-2-2-2-2-2-222-2-222222-2-222-2-200000000000000000000000000000000
χ272222-2-22-2-222222-2-22-2-2-2-222-2-2222-2-22222-2-2-2-22-2-2-2-222222222-2-22222-222-2-2-2-200000000000000000000000000000000
χ282222-2-22-2-222222-2-22-2-2-2-222-2-2222-2-22222-2-2-2-22-2-2-2-22222-2-2-2-222-2-2-2-22-2-2222200000000000000000000000000000000
χ292222-2-2-122-1-1-1-22112-2-2-2-222-1-111-122-2-2-1-11111-1-1-1-1-1111122-2-2221111-2-1-111-1-1000000000000003−33−33−33−30000000000
χ302222-2-2-122-1-1-1-22112-2-2-2-222-1-111-122-2-2-1-11111-1-1-1-1-1111122-2-2221111-2-1-111-1-100000000000000−33−33−33−330000000000
χ312222-2-2-122-1-1-1-22112-2-2-2-222-1-111-122-2-2-1-11111-1-1-1-1-11111-2-222-2-2-1-1-1-1211-1-11100000000000000−i3i3−i3i3i3−i3i3−i30000000000
χ322222-2-2-122-1-1-1-22112-2-2-2-222-1-111-122-2-2-1-11111-1-1-1-1-11111-2-222-2-2-1-1-1-1211-1-11100000000000000i3−i3i3−i3−i3i3−i3i30000000000
χ332222-2-2-1-2-2-1-1-122112-2-2-2-22211-1-1-1-2-222-1-11111-11111-1-1-1-12222-2-2-1-1-1-1-2-1-1111100000000000000−i3i3i3−i3−i3i3i3−i30000000000
χ342222-2-2-1-2-2-1-1-122112-2-2-2-22211-1-1-1-2-222-1-11111-11111-1-1-1-12222-2-2-1-1-1-1-2-1-1111100000000000000i3−i3−i3i3i3−i3−i3i30000000000
χ352222-2-2-1-2-2-1-1-122112-2-2-2-22211-1-1-1-2-222-1-11111-11111-1-1-1-1-2-2-2-2221111211-1-1-1-1000000000000003−3−33−333−30000000000
χ362222-2-2-1-2-2-1-1-122112-2-2-2-22211-1-1-1-2-222-1-11111-11111-1-1-1-1-2-2-2-2221111211-1-1-1-100000000000000−333−33−3−330000000000
χ3722-2-22-22002-2-2022-2-222-2-2-220000200002-222-2-2-200000000002i−2i2i−2i2i2i−2i−2i000002i−2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1090000
χ3822-2-22-22002-2-2022-2-222-2-2-220000200002-222-2-2-200000000002i−2i2i−2i2i2i−2i−2i000002i−2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000
χ3922-2-22-22002-2-2022-2-222-2-2-220000200002-222-2-2-20000000000−2i2i−2i2i−2i−2i2i2i00000−2i2i000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000
χ4022-2-22-22002-2-2022-2-222-2-2-220000200002-222-2-2-20000000000−2i2i−2i2i−2i−2i2i2i00000−2i2i0000000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1190000
χ4122-2-2-222002-2-202-22-2-2-222-220000200002-2-2-222-200000000002i−2i−2i2i2i2i−2i−2i00000−2i2i00000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900
χ4222-2-2-222002-2-202-22-2-2-222-220000200002-2-2-222-200000000002i−2i−2i2i2i2i−2i−2i00000−2i2i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ11900002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900
χ4322-2-2-222002-2-202-22-2-2-222-220000200002-2-2-222-20000000000−2i2i2i−2i−2i−2i2i2i000002i−2i0000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900
χ4422-2-2-222002-2-202-22-2-2-222-220000200002-2-2-222-20000000000−2i2i2i−2i−2i−2i2i2i000002i−2i00000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ11900
χ454444444444444-144-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000044-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444444-144-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000-4-4111111110000000000000000000000
χ474444444-4-4444-4-144-1-1-1-1-1-1-1-4-4-4-4-11111-1-1-1-1-1-1-111111111000000000000000004-4-1-1-1-111110000000000000000000000
χ484444444-4-4444-4-144-1-1-1-1-1-1-1-4-4-4-4-11111-1-1-1-1-1-1-11111111100000000000000000-441111-1-1-1-10000000000000000000000
χ494444-4-4444444-4-1-4-4-11111-1-144-4-4-1-1-111-1-11111-1-1-1-1-111110000000000000000000−5−555−5−5550000000000000000000000
χ504444-4-4444444-4-1-4-4-11111-1-144-4-4-1-1-111-1-11111-1-1-1-1-11111000000000000000000055−5−555−5−50000000000000000000000
χ514444-4-44-4-44444-1-4-4-11111-1-1-4-444-111-1-1-1-11111-11111-1-1-1-10000000000000000000−5−55555−5−50000000000000000000000
χ524444-4-44-4-44444-1-4-4-11111-1-1-4-444-111-1-1-1-11111-11111-1-1-1-1000000000000000000055−5−5−5−5550000000000000000000000
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χ684-44-400-24i−4i2-22040040000-4-4−2i2i00-24i−4i002-200002−2i−2i2i2i0000000000−2323−23230002i3−2i30000000000000000000000000000000000
χ694-44-400-2−4i4i2-22040040000-4-42i−2i00-2−4i4i002-2000022i2i−2i−2i000000000023−2323−230002i3−2i30000000000000000000000000000000000
χ704-44-400-2−4i4i2-22040040000-4-42i−2i00-2−4i4i002-2000022i2i−2i−2i0000000000−2323−2323000−2i32i30000000000000000000000000000000000
χ714-4-4400400-4-440400-400004-4000040000-4-400004000000004-40000000004-4000000000000000000000000000000000000
χ724-4-4400400-4-440400-400004-4000040000-4-40000400000000-44000000000-44000000000000000000000000000000000000
χ734-4-4400-20022-20400-400004-400−2i32i3-20000220000-20000−2i32i3−2i32i34-40000−2i32i32i3−2i30-22000000000000000000000000000000000000
χ744-4-4400-20022-20400-400004-400−2i32i3-20000220000-20000−2i32i3−2i32i3-4400002i3−2i3−2i32i302-2000000000000000000000000000000000000
χ754-4-4400-20022-20400-400004-4002i3−2i3-20000220000-200002i3−2i32i3−2i34-400002i3−2i3−2i32i30-22000000000000000000000000000000000000
χ764-4-4400-20022-20400-400004-4002i3−2i3-20000220000-200002i3−2i32i3−2i3-440000−2i32i32i3−2i302-2000000000000000000000000000000000000
χ77888888-488-4-4-48-2-4-4-2-2-2-2-2-2-2-4-4-4-41-2-2-2-21111111111111110000000000000000000000000000000000000000000000000
χ78888888-4-8-8-4-4-4-8-2-4-4-2-2-2-2-2-2-24444122221111111-1-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000
χ798888-8-8-488-4-4-4-8-244-22222-2-2-4-4441-2-22211-1-1-1-111111-1-1-1-10000000000000000000000000000000000000000000000000
χ808888-8-8-4-8-8-4-4-48-244-22222-2-244-4-4122-2-211-1-1-1-11-1-1-1-111110000000000000000000000000000000000000000000000000
χ8188-8-88-88008-8-80-28-82-2-2222-20000-20000-22-2-2222000000000000000000000000000000000000000000000000000000000
χ8288-8-88-8-400-4440-2-442-2-2222-20000100001-111-1-1-1−1515−1515−151515−150000000000000000000000000000000000000000000000000
χ8388-8-88-8-400-4440-2-442-2-2222-20000100001-111-1-1-115−1515−1515−15−15150000000000000000000000000000000000000000000000000
χ8488-8-8-888008-8-80-2-88222-2-22-20000-20000-2222-2-22000000000000000000000000000000000000000000000000000000000
χ8588-8-8-88-400-4440-24-4222-2-22-20000100001-1-1-111-1−1515−151515−15−15150000000000000000000000000000000000000000000000000
χ8688-8-8-88-400-4440-24-4222-2-22-20000100001-1-1-111-115−1515−15−151515−150000000000000000000000000000000000000000000000000
χ878-88-800-48i−8i4-440-200-2−2525−252522−4i4i001−2i2i−2i52i5-115−55−5-1ii−i−ii5i5−i5−i50000000000000000000000000000000000000000000000000
χ888-88-800-48i−8i4-440-200-225−2525−2522−4i4i001−2i2i2i5−2i5-11−55−55-1ii−i−i−i5−i5i5i50000000000000000000000000000000000000000000000000
χ898-88-800-4−8i8i4-440-200-2−2525−2525224i−4i0012i−2i2i5−2i5-115−55−5-1−i−iii−i5−i5i5i50000000000000000000000000000000000000000000000000
χ908-88-800-4−8i8i4-440-200-225−2525−25224i−4i0012i−2i−2i52i5-11−55−55-1−i−iiii5i5−i5−i50000000000000000000000000000000000000000000000000
χ918-8-8800800-8-880-2002−252525−25-220000-2000022−252525−25-2000000000000000000000000000000000000000000000000000000000
χ928-8-8800800-8-880-200225−25−2525-220000-200002225−25−2525-2000000000000000000000000000000000000000000000000000000000
χ938-8-8800-40044-40-2002−252525−25-2200−4i34i310000-1-15−5−551i15−i15−i15i15i3−i3i3−i30000000000000000000000000000000000000000000000000
χ948-8-8800-40044-40-2002−252525−25-22004i3−4i310000-1-15−5−551−i15i15i15−i15−i3i3−i3i30000000000000000000000000000000000000000000000000
χ958-8-8800-40044-40-200225−25−2525-2200−4i34i310000-1-1−555−51−i15i15i15−i15i3−i3i3−i30000000000000000000000000000000000000000000000000
χ968-8-8800-40044-40-200225−25−2525-22004i3−4i310000-1-1−555−51i15−i15−i15i15−i3i3−i3i30000000000000000000000000000000000000000000000000

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