Finite Group Databasebeta

← Group #13051953

Character table — Group #13051953

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122244446666777781212121212121414141414142424242428282828282828282828282828282828282828285656565656565656
order1222224447141414336641414282828286666661428282822446666661212121212121212121244121212121212
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1
χ31111111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ41111111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111-1-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321−i321−i32-1-1−1−i32−1+i321+i321+i321−i321−i32
χ51111111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ61111111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111-1-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321+i321+i32-1-1−1+i32−1−i321−i321−i321+i321+i32
χ71111111-1-111111111-111-1-1-1-11111111-1-1111111111111-1-11-1-11111-1-1-1-1-1-1-1-1
χ81111111-1-111111111-111-1-1-1-11111111-1-11-1-1-1-111-1-1-1-11-1-11-1-1-1-1-1-111-1-11111
χ91111111-1-11111−1−i32−1+i32−1−i32−1+i32-111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321+i321−i321−i32
χ101111111-1-11111−1−i32−1+i32−1−i32−1+i32-111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-11-1-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321+i321−i321−i32111+i321−i32−1−i32−1−i32−1+i32−1+i32
χ111111111-1-11111−1+i32−1−i32−1+i32−1−i32-111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321−i321+i321+i32
χ121111111-1-11111−1+i32−1−i32−1+i32−1−i32-111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-11-1-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321−i321+i321+i32111−i321+i32−1+i32−1+i32−1−i32−1−i32
χ1311111-1-11111111111-1111111111111-1-1-1-11-11-1-1-11-11-1-111-1111-11-11-1-1-11-11-1
χ1411111-1-11111111111-1111111111111-1-1-1-1-11-11-1-1-11-11-111-111-11-11-11-1-1-11-11
χ1511111-1-1111111−1−i32−1+i32−1−i32−1+i32-1111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-11-11-11+i321−i32−1−i321+i32−1+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i321-11+i321−i32−1−i321+i32−1+i321−i32
χ1611111-1-1111111−1−i32−1+i32−1−i32−1+i32-1111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-11-111+i321−i321+i32−1−i321−i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i321+i32−1−i321−i32−1+i32-111+i321−i321+i32−1−i321−i32−1+i32
χ1711111-1-1111111−1+i32−1−i32−1+i32−1−i32-1111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-11-11-11−i321+i32−1+i321−i32−1−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i321-11−i321+i32−1+i321−i32−1−i321+i32
χ1811111-1-1111111−1+i32−1−i32−1+i32−1−i32-1111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-11-111−i321+i321−i32−1+i321+i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i321−i32−1+i321+i32−1−i32-111−i321+i321−i32−1+i321+i32−1−i32
χ1911111-1-1-1-111111111111-1-1-1-1111111-111-11-11-1-1-11-11-1-1-1-1-1-1-11-11-1-1111-11-11
χ2011111-1-1-1-111111111111-1-1-1-1111111-111-1-11-11-1-1-11-11-1-1-1-1-1-1-11-111-1111-11-1
χ2111111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-111-11-11-11+i321−i32−1−i321+i32−1+i321−i321+i321+i321+i321−i321−i321−i32−1−i321+i32−1+i321−i32-11−1−i32−1+i321+i32−1−i321−i32−1+i32
χ2211111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-111-1-11-111+i321−i321+i32−1−i321−i32−1+i321+i321+i321+i321−i321−i321−i321+i32−1−i321−i32−1+i321-1−1−i32−1+i32−1−i321+i32−1+i321−i32
χ2311111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-111-11-11-11−i321+i32−1+i321−i32−1−i321+i321−i321−i321−i321+i321+i321+i32−1+i321−i32−1−i321+i32-11−1+i32−1−i321−i32−1+i321+i32−1−i32
χ2411111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-111-1-11-111−i321+i321−i32−1+i321+i32−1−i321−i321−i321−i321+i321+i321+i321−i32−1+i321+i32−1−i321-1−1+i32−1−i32−1+i321−i32−1−i321+i32
χ25222-2-22-200222222220-2-200002-2-22-2-2200-20000220000-200-200000000000000
χ26222-2-22-2002222−1−i3−1+i3−1−i3−1+i30-2-20000−1−i31+i31+i3−1+i31−i31−i3200-20000−1−i3−1+i300001+i3001−i300000000000000
χ27222-2-22-2002222−1+i3−1−i3−1+i3−1−i30-2-20000−1+i31−i31−i3−1−i31+i31+i3200-20000−1+i3−1−i300001−i3001+i300000000000000
χ28222-2-2-2200222222220-2-200002-2-22-2-2-20020000-2-20000200200000000000000
χ29222-2-2-22002222−1−i3−1+i3−1−i3−1+i30-2-20000−1−i31+i31+i3−1+i31−i31−i3-200200001+i31−i30000−1−i300−1+i300000000000000
χ30222-2-2-22002222−1+i3−1−i3−1+i3−1−i30-2-20000−1+i31−i31−i3−1−i31+i31+i3-200200001−i31+i30000−1+i300−1−i300000000000000
χ3122-22-200002-2-22222202-20000-22-2-22-20000020-20002020000000-20-200000000
χ3222-22-200002-2-22222202-20000-22-2-22-200000-202000-20-2000000020200000000
χ3322-22-200002-2-22−1−i3−1+i3−1−i3−1+i302-200001+i3−1−i31+i31−i3−1+i31−i30000020-2000−1−i30−1+i300000001+i301−i300000000
χ3422-22-200002-2-22−1−i3−1+i3−1−i3−1+i302-200001+i3−1−i31+i31−i3−1+i31−i300000-2020001+i301−i30000000−1−i30−1+i300000000
χ3522-22-200002-2-22−1+i3−1−i3−1+i3−1−i302-200001−i3−1+i31−i31+i3−1−i31+i30000020-2000−1+i30−1−i300000001−i301+i300000000
χ3622-22-200002-2-22−1+i3−1−i3−1+i3−1−i302-200001−i3−1+i31−i31+i3−1−i31+i300000-2020001−i301+i30000000−1+i30−1−i300000000
χ3722-2-2200002-2-2222220-220000-2-22-2-22000020-20002020000000-20-2000000000
χ3822-2-2200002-2-2222220-220000-2-22-2-220000-202000-20-20000000202000000000
χ3922-2-2200002-2-22−1−i3−1+i3−1−i3−1+i30-2200001+i31+i3−1−i31−i31−i3−1+i3000020-2000−1−i30−1+i300000001+i301−i3000000000
χ4022-2-2200002-2-22−1−i3−1+i3−1−i3−1+i30-2200001+i31+i3−1−i31−i31−i3−1+i30000-2020001+i301−i30000000−1−i30−1+i3000000000
χ4122-2-2200002-2-22−1+i3−1−i3−1+i3−1−i30-2200001−i31−i3−1+i31+i31+i3−1−i3000020-2000−1+i30−1−i300000001−i301+i3000000000
χ4222-2-2200002-2-22−1+i3−1−i3−1+i3−1−i30-2200001−i31−i3−1+i31+i31+i3−1−i30000-2020001−i301+i30000000−1+i30−1−i3000000000
χ434-4000002i−2i400-444-4-40002i2i−2i−2i0000000000000000000002i−2i02i−2i000000000000
χ444-4000002i−2i400-4−2−2i3−2+2i32+2i32−2i30002i2i−2i−2i0000000000000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ8302ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79000000000000
χ454-4000002i−2i400-4−2+2i3−2−2i32−2i32+2i30002i2i−2i−2i0000000000000000000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ7902ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83000000000000
χ464-400000−2i2i400-444-4-4000−2i−2i2i2i000000000000000000000−2i2i0−2i2i000000000000
χ474-400000−2i2i400-4−2−2i3−2+2i32+2i32−2i3000−2i−2i2i2i000000000000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ830−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79000000000000
χ484-400000−2i2i400-4−2+2i3−2−2i32−2i32+2i3000−2i−2i2i2i000000000000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ790−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83000000000000
χ49666666666-1-1-1-100006-1-1-1-1-1-1000000-1-1-1-10000000000000000000000000000
χ506666666-6-6-1-1-1-10000-6-1-11111000000-111-10000000000000000000000000000
χ5166666-6-666-1-1-1-10000-6-1-1-1-1-1-100000011110000000000000000000000000000
χ5266666-6-6-6-6-1-1-1-100006-1-111110000001-1-110000000000000000000000000000
χ53666-6-66-600-1-1-1-10000011−i7i7−i7i7000000-1−i7i710000000000000000000000000000
χ54666-6-66-600-1-1-1-10000011i7−i7i7−i7000000-1i7−i710000000000000000000000000000
χ55666-6-6-6600-1-1-1-10000011−i7i7−i7i70000001i7−i7-10000000000000000000000000000
χ56666-6-6-6600-1-1-1-10000011i7−i7i7−i70000001−i7i7-10000000000000000000000000000
χ571212-1212-120000-222-200000-22000000000000000000000000000000000000000000
χ581212-12-12120000-222-2000002-2000000000000000000000000000000000000000000
χ5912-12000006i−6i-2−2i72i7200000002ζ11+2ζ23+2ζ43+2ζ67+2ζ71+2ζ792ζ19+2ζ31+2ζ47+2ζ55+2ζ59+2ζ83−2ζ11−2ζ23−2ζ43−2ζ67−2ζ71−2ζ79−2ζ19−2ζ31−2ζ47−2ζ55−2ζ59−2ζ8300000000000000000000000000000000000000
χ6012-12000006i−6i-22i7−2i7200000002ζ19+2ζ31+2ζ47+2ζ55+2ζ59+2ζ832ζ11+2ζ23+2ζ43+2ζ67+2ζ71+2ζ79−2ζ19−2ζ31−2ζ47−2ζ55−2ζ59−2ζ83−2ζ11−2ζ23−2ζ43−2ζ67−2ζ71−2ζ7900000000000000000000000000000000000000
χ6112-1200000−6i6i-2−2i72i720000000−2ζ11−2ζ23−2ζ43−2ζ67−2ζ71−2ζ79−2ζ19−2ζ31−2ζ47−2ζ55−2ζ59−2ζ832ζ11+2ζ23+2ζ43+2ζ67+2ζ71+2ζ792ζ19+2ζ31+2ζ47+2ζ55+2ζ59+2ζ8300000000000000000000000000000000000000
χ6212-1200000−6i6i-22i7−2i720000000−2ζ19−2ζ31−2ζ47−2ζ55−2ζ59−2ζ83−2ζ11−2ζ23−2ζ43−2ζ67−2ζ71−2ζ792ζ19+2ζ31+2ζ47+2ζ55+2ζ59+2ζ832ζ11+2ζ23+2ζ43+2ζ67+2ζ71+2ζ7900000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.