Finite Group Databasebeta

← Group #11923338

Character table — Group #11923338

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size112224444444444666688888888121212121212121216161616161616161616161618182424242424242432323232363636484848484848
order12346223366812242422443366661212244468812666612122424242424242466121212122466662486612122424
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111-11-111111111-111-111-11111111111111-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1
χ31111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i3211−1−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+i3211−1−i32−1+i3211−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ41111111−1−i32−1+i32−1−i32−1+i3211111-11-1−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32-111-111-11−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i32111+i321−i321−1−i32−1−i32−1+i32−1+i32-1-1-11+i321−i321+i321−i321+i321−i32
χ51111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i3211−1+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−i3211−1+i32−1−i3211−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ61111111−1+i32−1−i32−1+i32−1−i3211111-11-1−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32-111-111-11−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i32111−i321+i321−1+i32−1+i32−1−i32−1−i32-1-1-11−i321+i321−i321+i321−i321+i32
χ7111111-11111-11-1-11111111-1111111-1-11-1-111-11-111-1-1-1-1-1-111111-111-11-11-1-11-111-1-1-1-1
χ8111111-11111-11-1-11-11-1111-11111-11-111-1111-11-111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-11-11-11-1-11111
χ9111111-1−1−i32−1+i32−1−i32−1+i32-11-1-11111−1−i32−1+i321-1−1−i32−1+i32−1−i32−1+i3211-1-11-1-11−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i3211−1−i32−1+i321-1−1−i32−1+i32-1−1−i321+i32−1+i321−i32-11-1−1−i32−1+i321+i321−i321+i321−i32
χ10111111-1−1−i32−1+i32−1−i32−1+i32-11-1-11-11-1−1−i32−1+i321-1−1−i32−1+i32−1−i32−1+i32-11-111-111−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-1-11+i321−i321-11+i321−i32-1−1−i321+i32−1+i321−i321-111+i321−i32−1−i32−1+i32−1−i32−1+i32
χ11111111-1−1+i32−1−i32−1+i32−1−i32-11-1-11111−1+i32−1−i321-1−1+i32−1−i32−1+i32−1−i3211-1-11-1-11−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i3211−1+i32−1−i321-1−1+i32−1−i32-1−1+i321−i32−1−i321+i32-11-1−1+i32−1−i321−i321+i321−i321+i32
χ12111111-1−1+i32−1−i32−1+i32−1−i32-11-1-11-11-1−1+i32−1−i321-1−1+i32−1−i32−1+i32−1−i32-11-111-111−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-1-11−i321+i321-11−i321+i32-1−1+i321−i32−1−i321+i321-111−i321+i32−1+i32−1−i32−1+i32−1−i32
χ1311111-111111-11-1-1111111-111111-1-1111-1-11-11-1111-1-1-1-1-1-11111-1111-1-11-111-1-1-1-111-1-1
χ1411111-111111-11-1-11-11-111-1111111-11-11-111-11-1111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-11-11111-1-111
χ1511111-11−1−i32−1+i32−1−i32−1+i32-11-1-11111−1−i32−1+i32-11−1−i32−1+i32−1−i32−1+i32-1-1111-1-111+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i3211−1−i32−1+i32-11−1−i32−1+i32-11+i32−1−i321−i32−1+i321-1-11+i321−i32−1−i32−1+i321+i321−i32
χ1611111-11−1−i32−1+i32−1−i32−1+i32-11-1-11-11-1−1−i32−1+i32-11−1−i32−1+i32−1−i32−1+i321-11-11-1111+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-1-11+i321−i32-111+i321−i32-11+i32−1−i321−i32−1+i32-111−1−i32−1+i321+i321−i32−1−i32−1+i32
χ1711111-11−1+i32−1−i32−1+i32−1−i32-11-1-11111−1+i32−1−i32-11−1+i32−1−i32−1+i32−1−i32-1-1111-1-111−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i3211−1+i32−1−i32-11−1+i32−1−i32-11−i32−1+i321+i32−1−i321-1-11−i321+i32−1+i32−1−i321−i321+i32
χ1811111-11−1+i32−1−i32−1+i32−1−i32-11-1-11-11-1−1+i32−1−i32-11−1+i32−1−i32−1+i32−1−i321-11-11-1111−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-1-11−i321+i32-111−i321+i32-11−i32−1+i321+i32−1−i32-111−1+i32−1−i321−i321+i32−1+i32−1−i32
χ1911111-1-111111111111111-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1111-1-1-1-1-1-11-1-1-1-111
χ2011111-1-1111111111-11-111-1-111111-1-1111-11-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-11111-1-1
χ2111111-1-1−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32-1-1−1−i32−1+i32−1−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−i32−1+i32-1-1−1−i32−1+i3211+i321+i321−i321−i32-1-111+i321−i321+i321−i32−1−i32−1+i32
χ2211111-1-1−1−i32−1+i32−1−i32−1+i3211111-11-1−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1+i321-1-1111-111+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i32-1-11+i321−i3211+i321+i321−i321−i3211-1−1−i32−1+i32−1−i32−1+i321+i321−i32
χ2311111-1-1−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32-1-1−1+i32−1−i32−1+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+i32−1−i32-1-1−1+i32−1−i3211−i321−i321+i321+i32-1-111−i321+i321−i321+i32−1+i32−1−i32
χ2411111-1-1−1+i32−1−i32−1+i32−1−i3211111-11-1−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1−i321-1-1111-111−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i32-1-11−i321+i3211−i321−i321+i321+i3211-1−1+i32−1−i32−1+i32−1−i321−i321+i32
χ25222-220022220-200-222-2220022-2-20000-20020000-2-2000000-222200-2-200000000000000
χ26222-220022220-200-2-222220022-2-20000-20020000-2-20000002-2-2-2002200000000000000
χ27222-2200−1−i3−1+i3−1−i3−1+i30-200-222-2−1−i3−1+i300−1−i3−1+i31+i31−i30000-200200001+i31−i3000000-22−1−i3−1+i3001+i31−i300000000000000
χ28222-2200−1−i3−1+i3−1−i3−1+i30-200-2-222−1−i3−1+i300−1−i3−1+i31+i31−i30000-200200001+i31−i30000002-21+i31−i300−1−i3−1+i300000000000000
χ29222-2200−1+i3−1−i3−1+i3−1−i30-200-222-2−1+i3−1−i300−1+i3−1−i31−i31+i30000-200200001−i31+i3000000-22−1+i3−1−i3001−i31+i300000000000000
χ30222-2200−1+i3−1−i3−1+i3−1−i30-200-2-222−1+i3−1−i300−1+i3−1−i31−i31+i30000-200200001−i31+i30000002-21−i31+i300−1+i3−1−i300000000000000
χ3122-12-12222222-1-1-12020-1-1-1-1-1-1220220-120-12222-1-122-1-1-1-10000-1-100-1-1-1-1-1000000000
χ3222-12-122−1−i3−1+i3−1−i3−1+i32-1-1-120201+i321−i32-1-11+i321−i32−1−i3−1+i30220-120-1−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i31+i321+i321−i321−i320000-1-100-11+i321+i321−i321−i32000000000
χ3322-12-122−1+i3−1−i3−1+i3−1−i32-1-1-120201−i321+i32-1-11−i321+i32−1+i3−1−i30220-120-1−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i31−i321−i321+i321+i320000-1-100-11−i321−i321+i321+i32000000000
χ3422-12-12-22222-2-1112020-1-1-11-1-12202-20-1-20-12-22-2-1-1-2-211110000-11001-11-11000000000
χ3522-12-12-2−1−i3−1+i3−1−i3−1+i3-2-11120201+i321−i32-111+i321−i32−1−i3−1+i302-20-1-20-1−1−i31+i3−1+i31−i31+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i320000-110011+i32−1−i321−i32−1+i32000000000
χ3622-12-12-2−1+i3−1−i3−1+i3−1−i3-2-11120201−i321+i32-111−i321+i32−1+i3−1−i302-20-1-20-1−1+i31−i3−1−i31+i31−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i320000-110011−i32−1+i321+i32−1−i32000000000
χ3722-12-1-222222-2-1112020-1-11-1-1-1220-220-1-20-1-22-22-1-1-2-2111100001-10011-11-1000000000
χ3822-12-1-22−1−i3−1+i3−1−i3−1+i3-2-11120201+i321−i321-11+i321−i32−1−i3−1+i30-220-1-20-11+i3−1−i31−i3−1+i31+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i3200001-1001−1−i321+i32−1+i321−i32000000000
χ3922-12-1-22−1+i3−1−i3−1+i3−1−i3-2-11120201−i321+i321-11−i321+i32−1+i3−1−i30-220-1-20-11−i3−1+i31+i3−1−i31−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i3200001-1001−1+i321−i32−1−i321+i32000000000
χ4022-12-1-2-222222-1-1-12020-1-111-1-1220-2-20-120-1-2-2-2-2-1-122-1-1-1-100001100-11111000000000
χ4122-12-1-2-2−1−i3−1+i3−1−i3−1+i32-1-1-120201+i321−i32111+i321−i32−1−i3−1+i30-2-20-120-11+i31+i31−i31−i31+i321−i32−1−i3−1+i31+i321+i321−i321−i3200001100-1−1−i32−1−i32−1+i32−1+i32000000000
χ4222-12-1-2-2−1+i3−1−i3−1+i3−1−i32-1-1-120201−i321+i32111−i321+i32−1+i3−1−i30-2-20-120-11−i31−i31+i31+i31−i321+i32−1+i3−1−i31−i321−i321+i321+i3200001100-1−1+i32−1+i32−1−i32−1−i32000000000
χ43333333300003333-13-13003300003-1-13-1-13-1000000000000-1-100-1-100-10000-1-1-1000000
χ44333333300003333-1-3-1-300330000-3-1-1-3-1-1-3-10000000000001100-1-100-10000111000000
χ45333333-30000-33-3-3-13-13003-300003-11-3-11-3-1000000000000-1-100-1100100001-11000000
χ46333333-30000-33-3-3-1-3-1-3003-30000-3-113-113-10000000000001100-110010000-11-1000000
χ4733333-330000-33-3-3-13-1300-330000-31-13-11-3-1000000000000-1-1001-10010000-111000000
χ4833333-330000-33-3-3-1-3-1-300-33000031-1-3-113-100000000000011001-100100001-1-1000000
χ4933333-3-300003333-13-1300-3-30000-311-3-1-13-1000000000000-1-1001100-1000011-1000000
χ5033333-3-300003333-1-3-1-300-3-300003113-1-1-3-100000000000011001100-10000-1-11000000
χ5144-2-4-20044440200-4040-2-200-2-2-4-40000200-20000220000000000000000000000000000
χ5244-2-4-200−2−2i3−2+2i3−2−2i3−2+2i30200-40401+i31−i3001+i31−i32+2i32−2i30000200-20000−1−i3−1+i30000000000000000000000000000
χ5344-2-4-200−2+2i3−2−2i3−2+2i3−2−2i30200-40401−i31+i3001−i31+i32−2i32+2i30000200-20000−1+i3−1−i30000000000000000000000000000
χ54666-660000000-60026-2-6000000000000200-20000000000002-200000000000000000000
χ55666-660000000-6002-6-26000000000000200-2000000000000-2200000000000000000000
χ5666-36-36600006-3-3-3-20-2000-3-300000-2-201-2010000000000000000110010000000000000
χ5766-36-36-60000-6-333-20-2000-3300000-220120100000000000000001-100-10000000000000
χ5866-36-3-660000-6-333-20-20003-3000002-2012010000000000000000-1100-10000000000000
χ5966-36-3-6-600006-3-3-3-20-200033000002201-2010000000000000000-1-10010000000000000
χ608-880-800-4-44400000000-4-4004400000000000000000000000000000000000000000000
χ618-880-8002+2i32−2i3−2−2i3−2+2i3000000002+2i32−2i300−2−2i3−2+2i300000000000000000000000000000000000000000000
χ628-880-8002−2i32+2i3−2+2i3−2−2i3000000002−2i32+2i300−2+2i3−2−2i300000000000000000000000000000000000000000000
χ638-8-40400-4-444002i6−2i600002200-2-2000000000000000000i6−i6i6−i60000000000000000000000
χ648-8-40400-4-44400−2i62i600002200-2-2000000000000000000−i6i6−i6i60000000000000000000000
χ658-8-404002+2i32−2i3−2−2i3−2+2i3002i6−2i60000−1−i3−1+i3001+i31−i3000000000000000000−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ23ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ230000000000000000000000
χ668-8-404002+2i32−2i3−2−2i3−2+2i300−2i62i60000−1−i3−1+i3001+i31−i30000000000000000002ζ5−ζ7+ζ13−2ζ23−2ζ5+ζ7−ζ13+2ζ23−ζ5+2ζ7−2ζ13+ζ23ζ5−2ζ7+2ζ13−ζ230000000000000000000000
χ678-8-404002−2i32+2i3−2+2i3−2−2i3002i6−2i60000−1+i3−1−i3001−i31+i3000000000000000000ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ23−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ230000000000000000000000
χ688-8-404002−2i32+2i3−2+2i3−2−2i300−2i62i60000−1+i3−1−i3001−i31+i3000000000000000000−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.