Finite Group Databasebeta

← Group #72242880

Character table — Group #72242880

Order 3456.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size189121818182436324273654545472108432364872727296144432364872727296144189121818182436324273654545472108432364872727296144432364872727296144
order1322488642622488643366122424612336612242461226224886426224886466661224246126666122424612
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111-1-11-111111-1-11-111111-1-11-111111-1-11-111111-1-11-111111-1-11-111111-1-11-111111-1-11-1
χ3111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1
χ4111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11
χ52220-200002220-200002220-200002220-200002220-200002220-200002220-200002220-20000
χ622-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i200
χ722-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i200
χ88-102000-108-102000-108-102000-108-102000-108-102000-108-102000-108-102000-108-102000-10
χ98-10-2000108-10-2000108-10-2000108-10-2000108-10-2000108-10-2000108-10-2000108-10-200010
χ10111111111111111111−1+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−i32−1−i32−1−i32111111111111111111−1+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−i32−1−i32−1−i32
χ1111111-1-11-111111-1-11-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i3211111-1-11-111111-1-11-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32
χ12111-1111-1-1111-1111-1-1−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i32111-1111-1-1111-1111-1-1−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i32
χ13111-11-1-1-11111-11-1-1-11−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32111-11-1-1-11111-11-1-1-11−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32
χ142220-200002220-20000−1+i3−1+i3−1+i301−i30000−1−i3−1−i3−1−i301+i300002220-200002220-20000−1+i3−1+i3−1+i301−i30000−1−i3−1−i3−1−i301+i30000
χ1522-200i2−i20022-200i2−i200−1+i3−1+i31−i300−ζ5−ζ23ζ5+ζ2300−1−i3−1−i31+i300−ζ7−ζ13ζ7+ζ130022-200i2−i20022-200i2−i200−1+i3−1+i31−i300−ζ5−ζ23ζ5+ζ2300−1−i3−1−i31+i300−ζ7−ζ13ζ7+ζ1300
χ1622-200−i2i20022-200−i2i200−1+i3−1+i31−i300ζ5+ζ23−ζ5−ζ2300−1−i3−1−i31+i300ζ7+ζ13−ζ7−ζ130022-200−i2i20022-200−i2i200−1+i3−1+i31−i300ζ5+ζ23−ζ5−ζ2300−1−i3−1−i31+i300ζ7+ζ13−ζ7−ζ1300
χ178-102000-108-102000-10−4+4i31−i320−1+i30001−i320−4−4i31+i320−1−i30001+i3208-102000-108-102000-10−4+4i31−i320−1+i30001−i320−4−4i31+i320−1−i30001+i320
χ188-10-2000108-10-200010−4+4i31−i3201−i3000−1+i320−4−4i31+i3201+i3000−1−i3208-10-2000108-10-200010−4+4i31−i3201−i3000−1+i320−4−4i31+i3201+i3000−1−i320
χ19111111111111111111−1−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+i32−1+i32−1+i32111111111111111111−1−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+i32−1+i32−1+i32
χ2011111-1-11-111111-1-11-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i3211111-1-11-111111-1-11-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32
χ21111-1111-1-1111-1111-1-1−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i32111-1111-1-1111-1111-1-1−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i32
χ22111-11-1-1-11111-11-1-1-11−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32111-11-1-1-11111-11-1-1-11−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32
χ232220-200002220-20000−1−i3−1−i3−1−i301+i30000−1+i3−1+i3−1+i301−i300002220-200002220-20000−1−i3−1−i3−1−i301+i30000−1+i3−1+i3−1+i301−i30000
χ2422-200i2−i20022-200i2−i200−1−i3−1−i31+i300−ζ7−ζ13ζ7+ζ1300−1+i3−1+i31−i300−ζ5−ζ23ζ5+ζ230022-200i2−i20022-200i2−i200−1−i3−1−i31+i300−ζ7−ζ13ζ7+ζ1300−1+i3−1+i31−i300−ζ5−ζ23ζ5+ζ2300
χ2522-200−i2i20022-200−i2i200−1−i3−1−i31+i300ζ7+ζ13−ζ7−ζ1300−1+i3−1+i31−i300ζ5+ζ23−ζ5−ζ230022-200−i2i20022-200−i2i200−1−i3−1−i31+i300ζ7+ζ13−ζ7−ζ1300−1+i3−1+i31−i300ζ5+ζ23−ζ5−ζ2300
χ268-102000-108-102000-10−4−4i31+i320−1−i30001+i320−4+4i31−i320−1+i30001−i3208-102000-108-102000-10−4−4i31+i320−1−i30001+i320−4+4i31−i320−1+i30001−i320
χ278-10-2000108-10-200010−4−4i31+i3201+i3000−1−i320−4+4i31−i3201−i3000−1+i3208-10-2000108-10-200010−4−4i31+i3201+i3000−1−i320−4+4i31−i3201−i3000−1+i320
χ28333333333-1-1-1-1-1-1-1-1-1000000000000000000333333333-1-1-1-1-1-1-1-1-1000000000000000000
χ2933333-3-33-3-1-1-1-1-111-1100000000000000000033333-3-33-3-1-1-1-1-111-11000000000000000000
χ30333-3333-3-3-1-1-11-1-1-111000000000000000000333-3333-3-3-1-1-11-1-1-111000000000000000000
χ31333-33-3-3-33-1-1-11-1111-1000000000000000000333-33-3-3-33-1-1-11-1111-1000000000000000000
χ326660-60000-2-2-20200000000000000000000006660-60000-2-2-2020000000000000000000000
χ3366-6003i2−3i200-2-2200−i2i20000000000000000000066-6003i2−3i200-2-2200−i2i200000000000000000000
χ3466-600−3i23i200-2-2200i2−i20000000000000000000066-600−3i23i200-2-2200i2−i200000000000000000000
χ3524-306000-30-810-20001000000000000000000024-306000-30-810-200010000000000000000000
χ3624-30-600030-8102000-1000000000000000000024-30-600030-8102000-10000000000000000000
χ37111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3811111-1-11-111111-1-11-111111-1-11-111111-1-11-1-1-1-1-1-111-11-1-1-1-1-111-11-1-1-1-1-111-11-1-1-1-1-111-11
χ39111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1-1-1-11-1-1-111-1-1-11-1-1-111-1-1-11-1-1-111-1-1-11-1-1-111
χ40111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11-1-1-11-1111-1-1-1-11-1111-1-1-1-11-1111-1-1-1-11-1111-1
χ412220-200002220-200002220-200002220-20000-2-2-2020000-2-2-2020000-2-2-2020000-2-2-2020000
χ4222-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i200-2-2200−i2i200-2-2200−i2i200-2-2200−i2i200-2-2200−i2i200
χ4322-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i200-2-2200i2−i200-2-2200i2−i200-2-2200i2−i200-2-2200i2−i200
χ448-102000-108-102000-108-102000-108-102000-10-810-200010-810-200010-810-200010-810-200010
χ458-10-2000108-10-2000108-10-2000108-10-200010-8102000-10-8102000-10-8102000-10-8102000-10
χ46111111111111111111−1+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−i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32
χ4711111-1-11-111111-1-11-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32-1-1-1-1-111-11-1-1-1-1-111-111−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ48111-1111-1-1111-1111-1-1−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i32-1-1-11-1-1-111-1-1-11-1-1-1111−i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i321+i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32
χ49111-11-1-1-11111-11-1-1-11−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32-1-1-11-1111-1-1-1-11-1111-11−i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321+i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i32
χ502220-200002220-20000−1+i3−1+i3−1+i301−i30000−1−i3−1−i3−1−i301+i30000-2-2-2020000-2-2-20200001−i31−i31−i30−1+i300001+i31+i31+i30−1−i30000
χ5122-200i2−i20022-200i2−i200−1+i3−1+i31−i300−ζ5−ζ23ζ5+ζ2300−1−i3−1−i31+i300−ζ7−ζ13ζ7+ζ1300-2-2200−i2i200-2-2200−i2i2001−i31−i3−1+i300ζ5+ζ23−ζ5−ζ23001+i31+i3−1−i300ζ7+ζ13−ζ7−ζ1300
χ5222-200−i2i20022-200−i2i200−1+i3−1+i31−i300ζ5+ζ23−ζ5−ζ2300−1−i3−1−i31+i300ζ7+ζ13−ζ7−ζ1300-2-2200i2−i200-2-2200i2−i2001−i31−i3−1+i300−ζ5−ζ23ζ5+ζ23001+i31+i3−1−i300−ζ7−ζ13ζ7+ζ1300
χ538-102000-108-102000-10−4+4i31−i320−1+i30001−i320−4−4i31+i320−1−i30001+i320-810-200010-810-2000104−4i3−1+i3201−i3000−1+i3204+4i3−1−i3201+i3000−1−i320
χ548-10-2000108-10-200010−4+4i31−i3201−i3000−1+i320−4−4i31+i3201+i3000−1−i320-8102000-10-8102000-104−4i3−1+i320−1+i30001−i3204+4i3−1−i320−1−i30001+i320
χ55111111111111111111−1−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+i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32
χ5611111-1-11-111111-1-11-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32-1-1-1-1-111-11-1-1-1-1-111-111+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ57111-1111-1-1111-1111-1-1−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i32-1-1-11-1-1-111-1-1-11-1-1-1111+i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i321−i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32
χ58111-11-1-1-11111-11-1-1-11−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32-1-1-11-1111-1-1-1-11-1111-11+i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321−i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i32
χ592220-200002220-20000−1−i3−1−i3−1−i301+i30000−1+i3−1+i3−1+i301−i30000-2-2-2020000-2-2-20200001+i31+i31+i30−1−i300001−i31−i31−i30−1+i30000
χ6022-200i2−i20022-200i2−i200−1−i3−1−i31+i300−ζ7−ζ13ζ7+ζ1300−1+i3−1+i31−i300−ζ5−ζ23ζ5+ζ2300-2-2200−i2i200-2-2200−i2i2001+i31+i3−1−i300ζ7+ζ13−ζ7−ζ13001−i31−i3−1+i300ζ5+ζ23−ζ5−ζ2300
χ6122-200−i2i20022-200−i2i200−1−i3−1−i31+i300ζ7+ζ13−ζ7−ζ1300−1+i3−1+i31−i300ζ5+ζ23−ζ5−ζ2300-2-2200i2−i200-2-2200i2−i2001+i31+i3−1−i300−ζ7−ζ13ζ7+ζ13001−i31−i3−1+i300−ζ5−ζ23ζ5+ζ2300
χ628-102000-108-102000-10−4−4i31+i320−1−i30001+i320−4+4i31−i320−1+i30001−i320-810-200010-810-2000104+4i3−1−i3201+i3000−1−i3204−4i3−1+i3201−i3000−1+i320
χ638-10-2000108-10-200010−4−4i31+i3201+i3000−1−i320−4+4i31−i3201−i3000−1+i320-8102000-10-8102000-104+4i3−1−i320−1−i30001+i3204−4i3−1+i320−1+i30001−i320
χ64333333333-1-1-1-1-1-1-1-1-1000000000000000000-3-3-3-3-3-3-3-3-3111111111000000000000000000
χ6533333-3-33-3-1-1-1-1-111-11000000000000000000-3-3-3-3-333-3311111-1-11-1000000000000000000
χ66333-3333-3-3-1-1-11-1-1-111000000000000000000-3-3-33-3-3-333111-1111-1-1000000000000000000
χ67333-33-3-3-33-1-1-11-1111-1000000000000000000-3-3-33-3333-3111-11-1-1-11000000000000000000
χ686660-60000-2-2-2020000000000000000000000-6-6-60600002220-20000000000000000000000
χ6966-6003i2−3i200-2-2200−i2i200000000000000000000-6-6600−3i23i20022-200i2−i200000000000000000000
χ7066-600−3i23i200-2-2200i2−i200000000000000000000-6-66003i2−3i20022-200−i2i200000000000000000000
χ7124-306000-30-810-200010000000000000000000-2430-6000308-102000-10000000000000000000
χ7224-30-600030-8102000-10000000000000000000-24306000-308-10-200010000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.