Finite Group Databasebeta

← Group #13180385

Character table — Group #13180385

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112889916181818242436363636363636363648481128899161818182424363636363636363636484811288991618181824243636363636363636364848
order12436221244422444448888663612366612121212661212121212242424246636123666121212126612121212122424242466
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ311111111111-1-111111-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-111111111111-1-111111-1-1-1-1-1-1
χ411111111111-1-11-1-1-1-11111-1-111111111111-1-11-1-1-1-11111-1-111111111111-1-11-1-1-1-11111-1-1
χ511-11111-1-1111-1-111-1-111-1-11-111-11111-1-1111-1-111-1-111-1-11-111-11111-1-1111-1-111-1-111-1-11-1
χ611-11111-1-1111-1-1-1-111-1-1111-111-11111-1-1111-1-1-1-111-1-1111-111-11111-1-1111-1-1-1-111-1-1111-1
χ711-11111-1-111-11-111-1-1-1-111-1111-11111-1-111-11-111-1-1-1-111-1111-11111-1-111-11-111-1-1-1-111-11
χ811-11111-1-111-11-1-1-11111-1-1-1111-11111-1-111-11-1-1-11111-1-1-1111-11111-1-111-11-1-1-11111-1-1-11
χ9222222222-2-200-20000000000222222222-2-200-20000000000222222222-2-200-20000000000
χ1022222-2-22-2000000000i2−i2i2−i20022222-2-22-2000000000i2−i2i2−i20022222-2-22-2000000000i2−i2i2−i200
χ1122222-2-22-2000000000−i2i2−i2i20022222-2-22-2000000000−i2i2−i2i20022222-2-22-2000000000−i2i2−i2i200
χ1222-22222-2-2-2-2002000000000022-22222-2-2-2-2002000000000022-22222-2-2-2-20020000000000
χ1322-222-2-2-22000000000i2−i2−i2i20022-222-2-2-22000000000i2−i2−i2i20022-222-2-2-22000000000i2−i2−i2i200
χ1422-222-2-2-22000000000−i2i2i2−i20022-222-2-2-22000000000−i2i2i2−i20022-222-2-2-22000000000−i2i2i2−i200
χ152-202-22-2002-2000002i−2i0000002-202-22-2002-2000002i−2i0000002-202-22-2002-2000002i−2i000000
χ162-202-22-2002-200000−2i2i0000002-202-22-2002-200000−2i2i0000002-202-22-2002-200000−2i2i000000
χ172-202-22-200-220002-2000000002-202-22-200-220002-2000000002-202-22-200-220002-200000000
χ182-202-22-200-22000-22000000002-202-22-200-22000-22000000002-202-22-200-22000-2200000000
χ194-404-4-44000000000000000004-404-4-44000000000000000004-404-4-4400000000000000000
χ20888-1-100-100022000000000-1-1888-1-100-100022000000000-1-1888-1-100-100022000000000-1-1
χ21888-1-100-1000-2-200000000011888-1-100-1000-2-200000000011888-1-100-1000-2-200000000011
χ2288-8-1-10010002-2000000000-1188-8-1-10010002-2000000000-1188-8-1-10010002-2000000000-11
χ2388-8-1-1001000-220000000001-188-8-1-1001000-220000000001-188-8-1-1001000-220000000001-1
χ2416-160-22000000000000000000016-160-22000000000000000000016-160-220000000000000000000
χ25111111111111111111111111−1+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+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ2611111111111111-1-1-1-1-1-1-1-111−1+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+i321−i321−i321−i321−i321−i321−i321−i321−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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ2711111111111-1-111111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32
χ2811111111111-1-11-1-1-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ2911-11111-1-1111-1-111-1-111-1-11-1−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32
χ3011-11111-1-1111-1-1-1-111-1-1111-1−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32
χ3111-11111-1-111-11-111-1-1-1-111-11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ3211-11111-1-111-11-1-1-11111-1-1-11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32
χ33222222222-2-200-20000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3001−i30000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3001+i30000000000
χ3422222-2-22-2000000000i2−i2i2−i200−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i3000000000−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ2300−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i3000000000−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ1300
χ3522222-2-22-2000000000−i2i2−i2i200−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i3000000000ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ2300−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i3000000000ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ1300
χ3622-22222-2-2-2-20020000000000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i300−1+i30000000000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i300−1−i30000000000
χ3722-222-2-2-22000000000i2−i2−i2i200−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i3−1+i3000000000−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ2300−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i3−1−i3000000000−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ1300
χ3822-222-2-2-22000000000−i2i2i2−i200−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i3−1+i3000000000ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ2300−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i3−1−i3000000000ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ1300
χ392-202-22-2002-2000002i−2i000000−1+i31−i30−1+i31−i3−1+i31−i300−1+i31−i3000002ζ14−2ζ14000000−1−i31+i30−1−i31+i3−1−i31+i300−1−i31+i3000002ζ22−2ζ22000000
χ402-202-22-2002-200000−2i2i000000−1+i31−i30−1+i31−i3−1+i31−i300−1+i31−i300000−2ζ142ζ14000000−1−i31+i30−1−i31+i3−1−i31+i300−1−i31+i300000−2ζ222ζ22000000
χ412-202-22-200-220002-200000000−1+i31−i30−1+i31−i3−1+i31−i3001−i3−1+i3000−1+i31−i300000000−1−i31+i30−1−i31+i3−1−i31+i3001+i3−1−i3000−1−i31+i300000000
χ422-202-22-200-22000-2200000000−1+i31−i30−1+i31−i3−1+i31−i3001−i3−1+i30001−i3−1+i300000000−1−i31+i30−1−i31+i3−1−i31+i3001+i3−1−i30001+i3−1−i300000000
χ434-404-4-4400000000000000000−2+2i32−2i30−2+2i32−2i32−2i3−2+2i300000000000000000−2−2i32+2i30−2−2i32+2i32+2i3−2−2i300000000000000000
χ44888-1-100-100022000000000-1-1−4+4i3−4+4i3−4+4i31−i321−i32001−i32000−1+i3−1+i30000000001−i321−i32−4−4i3−4−4i3−4−4i31+i321+i32001+i32000−1−i3−1−i30000000001+i321+i32
χ45888-1-100-1000-2-200000000011−4+4i3−4+4i3−4+4i31−i321−i32001−i320001−i31−i3000000000−1+i32−1+i32−4−4i3−4−4i3−4−4i31+i321+i32001+i320001+i31+i3000000000−1−i32−1−i32
χ4688-8-1-10010002-2000000000-11−4+4i3−4+4i34−4i31−i321−i3200−1+i32000−1+i31−i30000000001−i32−1+i32−4−4i3−4−4i34+4i31+i321+i3200−1−i32000−1−i31+i30000000001+i32−1−i32
χ4788-8-1-1001000-220000000001-1−4+4i3−4+4i34−4i31−i321−i3200−1+i320001−i3−1+i3000000000−1+i321−i32−4−4i3−4−4i34+4i31+i321+i3200−1−i320001+i3−1−i3000000000−1−i321+i32
χ4816-160-220000000000000000000−8+8i38−8i301−i3−1+i30000000000000000000−8−8i38+8i301+i3−1−i30000000000000000000
χ49111111111111111111111111−1−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−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ5011111111111111-1-1-1-1-1-1-1-111−1−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−i321+i321+i321+i321+i321+i321+i321+i321+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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ5111111111111-1-111111-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32
χ5211111111111-1-11-1-1-1-11111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ5311-11111-1-1111-1-111-1-111-1-11-1−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32
χ5411-11111-1-1111-1-1-1-111-1-1111-1−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32
χ5511-11111-1-111-11-111-1-1-1-111-11−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ5611-11111-1-111-11-1-1-11111-1-1-11−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32
χ57222222222-2-200-20000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3001+i30000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3001−i30000000000
χ5822222-2-22-2000000000i2−i2i2−i200−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i3000000000−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ1300−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i3000000000−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ2300
χ5922222-2-22-2000000000−i2i2−i2i200−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i3000000000ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ1300−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i3000000000ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ2300
χ6022-22222-2-2-2-20020000000000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i300−1−i30000000000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i300−1+i30000000000
χ6122-222-2-2-22000000000i2−i2−i2i200−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i3−1−i3000000000−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ1300−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i3−1+i3000000000−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ2300
χ6222-222-2-2-22000000000−i2i2i2−i200−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i3−1−i3000000000ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ1300−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i3−1+i3000000000ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ2300
χ632-202-22-2002-2000002i−2i000000−1−i31+i30−1−i31+i3−1−i31+i300−1−i31+i3000002ζ22−2ζ22000000−1+i31−i30−1+i31−i3−1+i31−i300−1+i31−i3000002ζ14−2ζ14000000
χ642-202-22-2002-200000−2i2i000000−1−i31+i30−1−i31+i3−1−i31+i300−1−i31+i300000−2ζ222ζ22000000−1+i31−i30−1+i31−i3−1+i31−i300−1+i31−i300000−2ζ142ζ14000000
χ652-202-22-200-220002-200000000−1−i31+i30−1−i31+i3−1−i31+i3001+i3−1−i3000−1−i31+i300000000−1+i31−i30−1+i31−i3−1+i31−i3001−i3−1+i3000−1+i31−i300000000
χ662-202-22-200-22000-2200000000−1−i31+i30−1−i31+i3−1−i31+i3001+i3−1−i30001+i3−1−i300000000−1+i31−i30−1+i31−i3−1+i31−i3001−i3−1+i30001−i3−1+i300000000
χ674-404-4-4400000000000000000−2−2i32+2i30−2−2i32+2i32+2i3−2−2i300000000000000000−2+2i32−2i30−2+2i32−2i32−2i3−2+2i300000000000000000
χ68888-1-100-100022000000000-1-1−4−4i3−4−4i3−4−4i31+i321+i32001+i32000−1−i3−1−i30000000001+i321+i32−4+4i3−4+4i3−4+4i31−i321−i32001−i32000−1+i3−1+i30000000001−i321−i32
χ69888-1-100-1000-2-200000000011−4−4i3−4−4i3−4−4i31+i321+i32001+i320001+i31+i3000000000−1−i32−1−i32−4+4i3−4+4i3−4+4i31−i321−i32001−i320001−i31−i3000000000−1+i32−1+i32
χ7088-8-1-10010002-2000000000-11−4−4i3−4−4i34+4i31+i321+i3200−1−i32000−1−i31+i30000000001+i32−1−i32−4+4i3−4+4i34−4i31−i321−i3200−1+i32000−1+i31−i30000000001−i32−1+i32
χ7188-8-1-1001000-220000000001-1−4−4i3−4−4i34+4i31+i321+i3200−1−i320001+i3−1−i3000000000−1−i321+i32−4+4i3−4+4i34−4i31−i321−i3200−1+i320001−i3−1+i3000000000−1+i321−i32
χ7216-160-220000000000000000000−8−8i38+8i301+i3−1−i30000000000000000000−8+8i38−8i301−i3−1+i30000000000000000000

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