Finite Group Databasebeta

← Group #11923335

Character table — Group #11923335

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size112224444444444666688888888121212121212121216161616161616161616161618182424242424242432323232363636484848484848
order12346233466812242422443366612121224446881266121212122424242424242466612121224661212228121212122424
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111-11-11111111111-1-111-11111111111111-1-11-1-11-1-111111-1-1-1-1-1-1-1-1-1
χ311111111-111-11-1-1111111111-111-111-11-1-1111-1-111-1-1-1-1-1-111-111111-111-1-11-1-111-1-1-1-1
χ411111111-111-11-1-11-11-111111-111-11-111-11111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-111-1-11111
χ5111111−1−i32−1+i321−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i321−1−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+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ6111111−1−i32−1+i321−1−i32−1+i3211111-11-1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211-1-111-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321−i3211+i321−i321−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321−i321+i321−i32
χ7111111−1−i32−1+i32-1−1−i32−1+i32-11-1-11111−1−i32−1+i321−1−i32−1+i32-1−1−i32−1+i32-111-11-1-11−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i3211-1−1−i32−1+i321−1−i32−1+i32-1−1−i32−1+i321+i321−i321-1-1−1−i32−1+i321+i321−i321+i321−i32
χ8111111−1−i32−1+i32-1−1−i32−1+i32-11-1-11-11-1−1−i32−1+i321−1−i32−1+i32-1−1−i32−1+i32-11-111-111−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-1-1-11+i321−i3211+i321−i32-1−1−i32−1+i321+i321−i32-1111+i321−i32−1−i32−1+i32−1−i32−1+i32
χ9111111−1+i32−1−i321−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i321−1+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−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ10111111−1+i32−1−i321−1+i32−1−i3211111-11-1−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211-1-111-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321+i3211−i321+i321−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321+i321−i321+i32
χ11111111−1+i32−1−i32-1−1+i32−1−i32-11-1-11111−1+i32−1−i321−1+i32−1−i32-1−1+i32−1−i32-111-11-1-11−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i3211-1−1+i32−1−i321−1+i32−1−i32-1−1+i32−1−i321−i321+i321-1-1−1+i32−1−i321−i321+i321−i321+i32
χ12111111−1+i32−1−i32-1−1+i32−1−i32-11-1-11-11-1−1+i32−1−i321−1+i32−1−i32-1−1+i32−1−i32-11-111-111−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-1-1-11−i321+i3211−i321+i32-1−1+i32−1−i321−i321+i32-1111−i321+i32−1+i32−1−i32−1+i32−1−i32
χ1311111-111111-11-1-1111111-1111111-1-111-1-11-1-11111-1-1-1-1-1-111111-111-1-1-111-11-1-1-111-1-1
χ1411111-111111-11-1-11-11-111-1111111-11-11-111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111-1111-1-111
χ1511111-111-1111111111111-111-111-1-1-1-11111-1-1-1-11111111111-111-1111-1-1-1-1-1-11-1-1-1-111
χ1611111-111-11111111-11-111-111-111-1-11111-11-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-11111-1-1
χ1711111-1−1−i32−1+i321−1−i32−1+i32-11-1-11111−1−i32−1+i32-1−1−i32−1+i321−1−i32−1+i321-1-111-1-111+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32111−1−i32−1+i32-1−1−i32−1+i32-11+i321−i32−1−i32−1+i32-11-11+i321−i32−1−i32−1+i321+i321−i32
χ1811111-1−1−i32−1+i321−1−i32−1+i32-11-1-11-11-1−1−i32−1+i32-1−1−i32−1+i321−1−i32−1+i321-11-11-1111+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-1-111+i321−i32-11+i321−i32-11+i321−i32−1−i32−1+i321-11−1−i32−1+i321+i321−i32−1−i32−1+i32
χ1911111-1−1−i32−1+i32-1−1−i32−1+i3211111111−1−i32−1+i32-1−1−i32−1+i32-1−1−i32−1+i32-1-1-1-111111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1−1−i32−1+i32-1−1−i32−1+i3211+i321−i321+i321−i32-1-111+i321−i321+i321−i32−1−i32−1+i32
χ2011111-1−1−i32−1+i32-1−1−i32−1+i3211111-11-1−1−i32−1+i32-1−1−i32−1+i32-1−1−i32−1+i32-1-11111-111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-11+i321−i32-11+i321−i3211+i321−i321+i321−i3211-1−1−i32−1+i32−1−i32−1+i321+i321−i32
χ2111111-1−1+i32−1−i321−1+i32−1−i32-11-1-11111−1+i32−1−i32-1−1+i32−1−i321−1+i32−1−i321-1-111-1-111−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32111−1+i32−1−i32-1−1+i32−1−i32-11−i321+i32−1+i32−1−i32-11-11−i321+i32−1+i32−1−i321−i321+i32
χ2211111-1−1+i32−1−i321−1+i32−1−i32-11-1-11-11-1−1+i32−1−i32-1−1+i32−1−i321−1+i32−1−i321-11-11-1111−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-1-111−i321+i32-11−i321+i32-11−i321+i32−1+i32−1−i321-11−1+i32−1−i321−i321+i32−1+i32−1−i32
χ2311111-1−1+i32−1−i32-1−1+i32−1−i3211111111−1+i32−1−i32-1−1+i32−1−i32-1−1+i32−1−i32-1-1-1-111111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1−1+i32−1−i32-1−1+i32−1−i3211−i321+i321−i321+i32-1-111−i321+i321−i321+i32−1+i32−1−i32
χ2411111-1−1+i32−1−i32-1−1+i32−1−i3211111-11-1−1+i32−1−i32-1−1+i32−1−i32-1−1+i32−1−i32-1-11111-111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-11−i321+i32-11−i321+i3211−i321+i321−i321+i3211-1−1+i32−1−i32−1+i32−1−i321−i321+i32
χ25222-220220220-200-222-2220220-2-20000-20020000-2-2000000-220220-2-200000000000000
χ26222-220220220-200-2-222220220-2-20000-20020000-2-20000002-20-2-202200000000000000
χ27222-220−1−i3−1+i30−1−i3−1+i30-200-222-2−1−i3−1+i30−1−i3−1+i301+i31−i30000-200200001+i31−i3000000-220−1−i3−1+i301+i31−i300000000000000
χ28222-220−1−i3−1+i30−1−i3−1+i30-200-2-222−1−i3−1+i30−1−i3−1+i301+i31−i30000-200200001+i31−i30000002-201+i31−i30−1−i3−1+i300000000000000
χ29222-220−1+i3−1−i30−1+i3−1−i30-200-222-2−1+i3−1−i30−1+i3−1−i301−i31+i30000-200200001−i31+i3000000-220−1+i3−1−i301−i31+i300000000000000
χ30222-220−1+i3−1−i30−1+i3−1−i30-200-2-222−1+i3−1−i30−1+i3−1−i301−i31+i30000-200200001−i31+i30000002-201−i31+i30−1+i3−1−i300000000000000
χ3122-12-12222222-1-1-12020-1-1-1-1-1-1222200-120-12222-1-122-1-1-1-100-100-100-1-1-1-1-1000000000
χ3222-12-1222-222-2-1112020-1-1-1-1-1122-2200-1-20-122-2-2-1-1-2-2111100100-1001-1-111000000000
χ3322-12-12−1−i3−1+i32−1−i3−1+i32-1-1-120201+i321−i32-11+i321−i32-1−1−i3−1+i32200-120-1−1−i3−1+i3−1−i3−1+i31+i321−i32−1−i3−1+i31+i321+i321−i321−i3200-100-100-11+i321−i321+i321−i32000000000
χ3422-12-12−1−i3−1+i3-2−1−i3−1+i3-2-11120201+i321−i32-11+i321−i321−1−i3−1+i3-2200-1-20-1−1−i3−1+i31+i31−i31+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i3200100-10011+i321−i32−1−i32−1+i32000000000
χ3522-12-12−1+i3−1−i32−1+i3−1−i32-1-1-120201−i321+i32-11−i321+i32-1−1+i3−1−i32200-120-1−1+i3−1−i3−1+i3−1−i31−i321+i32−1+i3−1−i31−i321−i321+i321+i3200-100-100-11−i321+i321−i321+i32000000000
χ3622-12-12−1+i3−1−i3-2−1+i3−1−i3-2-11120201−i321+i32-11−i321+i321−1+i3−1−i3-2200-1-20-1−1+i3−1−i31−i31+i31−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i3200100-10011−i321+i32−1+i32−1−i32000000000
χ3722-12-1-222222-2-1112020-1-11-1-1-1222-200-1-20-1-2-222-1-1-2-2111100-100100111-1-1000000000
χ3822-12-1-222-2222-1-1-12020-1-11-1-1122-2-200-120-1-2-2-2-2-1-122-1-1-1-100100100-11111000000000
χ3922-12-1-2−1−i3−1+i32−1−i3−1+i3-2-11120201+i321−i3211+i321−i32-1−1−i3−1+i32-200-1-20-11+i31−i3−1−i3−1+i31+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i3200-1001001−1−i32−1+i321+i321−i32000000000
χ4022-12-1-2−1−i3−1+i3-2−1−i3−1+i32-1-1-120201+i321−i3211+i321−i321−1−i3−1+i3-2-200-120-11+i31−i31+i31−i31+i321−i32−1−i3−1+i31+i321+i321−i321−i3200100100-1−1−i32−1+i32−1−i32−1+i32000000000
χ4122-12-1-2−1+i3−1−i32−1+i3−1−i3-2-11120201−i321+i3211−i321+i32-1−1+i3−1−i32-200-1-20-11−i31+i3−1+i3−1−i31−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i3200-1001001−1+i32−1−i321−i321+i32000000000
χ4222-12-1-2−1+i3−1−i3-2−1+i3−1−i32-1-1-120201−i321+i3211−i321+i321−1+i3−1−i3-2-200-120-11−i31+i31−i31+i31−i321+i32−1+i3−1−i31−i321−i321+i321+i3200100100-1−1+i32−1−i32−1+i32−1−i32000000000
χ43333333003003333-13-1300300300-1-133-1-13-1000000000000-1-1-100-100-10000-1-1-1000000
χ44333333003003333-1-3-1-300300300-1-1-3-3-1-1-3-100000000000011-100-100-10000111000000
χ4533333300-300-33-3-3-13-1300300-3001-13-3-11-3-1000000000000-1-1100-10010000-111000000
χ4633333300-300-33-3-3-1-3-1-300300-3001-1-33-113-100000000000011100-100100001-1-1000000
χ4733333-300300-33-3-3-13-1300-300300-11-33-11-3-1000000000000-1-1-100100100001-11000000
χ4833333-300300-33-3-3-1-3-1-300-300300-113-3-113-100000000000011-10010010000-11-1000000
χ4933333-300-3003333-13-1300-300-30011-3-3-1-13-1000000000000-1-1100100-1000011-1000000
χ5033333-300-3003333-1-3-1-300-300-3001133-1-1-3-100000000000011100100-10000-1-11000000
χ5144-2-4-20440440200-4040-2-20-2-20-4-40000200-20000220000000000000000000000000000
χ5244-2-4-20−2−2i3−2+2i30−2−2i3−2+2i30200-40401+i31−i301+i31−i302+2i32−2i30000200-20000−1−i3−1+i30000000000000000000000000000
χ5344-2-4-20−2+2i3−2−2i30−2+2i3−2−2i30200-40401−i31+i301−i31+i302−2i32+2i30000200-20000−1+i3−1−i30000000000000000000000000000
χ54666-660000000-60026-2-6000000000000200-20000000000002-200000000000000000000
χ55666-660000000-6002-6-26000000000000200-2000000000000-2200000000000000000000
χ5666-36-36006006-3-3-3-20-2000-300-300-2-2001-2010000000000000010010010000000000000
χ5766-36-3600-600-6-333-20-2000-3003002-200120100000000000000-100100-10000000000000
χ5866-36-3-600600-6-333-20-2000300-300-2200120100000000000000100-100-10000000000000
χ5966-36-3-600-6006-3-3-3-20-200030030022001-20100000000000000-100-10010000000000000
χ608-880-80-4-404400000000-4-4044000000000000000000000000000000000000000000000
χ618-880-802+2i32−2i30−2−2i3−2+2i3000000002+2i32−2i30−2−2i3−2+2i3000000000000000000000000000000000000000000000
χ628-880-802−2i32+2i30−2+2i3−2−2i3000000002−2i32+2i30−2+2i3−2−2i3000000000000000000000000000000000000000000000
χ638-8-4040-4-40440026−260000220-2-200000000000000000006−66−60000000000000000000000
χ648-8-4040-4-404400−26260000220-2-20000000000000000000−66−660000000000000000000000
χ658-8-40402+2i32−2i30−2−2i3−2+2i30026−260000−1−i3−1+i301+i31−i30000000000000000000−2ζ5−ζ7−ζ13−2ζ232ζ5+ζ7+ζ13+2ζ23ζ5+2ζ7+2ζ13+ζ23−ζ5−2ζ7−2ζ13−ζ230000000000000000000000
χ668-8-40402+2i32−2i30−2−2i3−2+2i300−26260000−1−i3−1+i301+i31−i300000000000000000002ζ5+ζ7+ζ13+2ζ23−2ζ5−ζ7−ζ13−2ζ23−ζ5−2ζ7−2ζ13−ζ23ζ5+2ζ7+2ζ13+ζ230000000000000000000000
χ678-8-40402−2i32+2i30−2+2i3−2−2i30026−260000−1+i3−1−i301−i31+i30000000000000000000ζ5+2ζ7+2ζ13+ζ23−ζ5−2ζ7−2ζ13−ζ23−2ζ5−ζ7−ζ13−2ζ232ζ5+ζ7+ζ13+2ζ230000000000000000000000
χ688-8-40402−2i32+2i30−2+2i3−2−2i300−26260000−1+i3−1−i301−i31+i30000000000000000000−ζ5−2ζ7−2ζ13−ζ23ζ5+2ζ7+2ζ13+ζ232ζ5+ζ7+ζ13+2ζ23−2ζ5−ζ7−ζ13−2ζ230000000000000000000000
χ691212-6-12-6000000060040-40000000000000-20020000000000000000000000000000000000

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