Finite Group Databasebeta

← Group #78985

Character table — Group #78985

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size112222222444444444488888121212122424112222222444444444488888121212122424
order12234461212244461212121212681224242224482226446121224446121212121268122424222448
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1
χ311111111111-1-111-1-1-1-11-11-1-11111-1-111111111111-1-111-1-1-1-11-11-1-11111-1-1
χ411111111111-1-111-1-1-1-11-11-1-1-1-1-1-11111111111111-1-111-1-1-1-11-11-1-1-1-1-1-111
χ5111111111-1-111111111-1-1-1-1-111-1-11-1111111111-1-111111111-1-1-1-1-111-1-11-1
χ6111111111-1-111111111-1-1-1-1-1-1-111-11111111111-1-111111111-1-1-1-1-1-1-111-11
χ7111111111-1-1-1-111-1-1-1-1-11-11111-1-1-11111111111-1-1-1-111-1-1-1-1-11-11111-1-1-11
χ8111111111-1-1-1-111-1-1-1-1-11-111-1-1111-1111111111-1-1-1-111-1-1-1-1-11-111-1-1111-1
χ92222-2-22-2-200002-20000000002-200002222-2-22-2-200002-20000000002-20000
χ102222-2-22-2-200002-2000000000-2200002222-2-22-2-200002-2000000000-220000
χ11222-122-1-1-12222-1-1-1-1-1-1-12-1-1-1000000222-122-1-1-12222-1-1-1-1-1-1-12-1-1-1000000
χ12222-122-1-1-122-2-2-1-11111-1-2-111000000222-122-1-1-122-2-2-1-11111-1-2-111000000
χ13222-122-1-1-1-2-222-1-1-1-1-1-11-2111000000222-122-1-1-1-2-222-1-1-1-1-1-11-2111000000
χ14222-122-1-1-1-2-2-2-2-1-11111121-1-1000000222-122-1-1-1-2-2-2-2-1-11111121-1-1000000
χ1522-222-22220000-2-2000000000002-20022-222-22220000-2-2000000000002-200
χ1622-222-22220000-2-200000000000-220022-222-22220000-2-200000000000-2200
χ1722-22-222-2-22-200-22000020-20000000022-22-222-2-22-200-22000020-200000000
χ1822-22-222-2-2-2200-220000-2020000000022-22-222-2-2-2200-220000-20200000000
χ1922-2-1-22-1112-2001-133−3−3-1013−300000022-2-1-22-1112-2001-133−3−3-1013−3000000
χ2022-2-1-22-1112-2001-1−3−333-101−3300000022-2-1-22-1112-2001-1−3−333-101−33000000
χ2122-2-1-22-111-22001-133−3−310-1−3300000022-2-1-22-111-22001-133−3−310-1−33000000
χ2222-2-1-22-111-22001-1−3−33310-13−300000022-2-1-22-111-22001-1−3−33310-13−3000000
χ23444-2-4-4-2220000-22000000000000000444-2-4-4-2220000-22000000000000000
χ2444-4-24-4-2-2-200002200000000000000044-4-24-4-2-2-2000022000000000000000
χ254-40400-400002i−2i002i−2i2i−2i000000000004-40400-400002i−2i002i−2i2i−2i00000000000
χ264-40400-40000−2i2i00−2i2i−2i2i000000000004-40400-40000−2i2i00−2i2i−2i2i00000000000
χ274-40-200223−23002i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000004-40-200223−23002i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000
χ284-40-200223−2300−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000004-40-200223−2300−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000
χ294-40-2002−2323002i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000004-40-2002−2323002i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000
χ304-40-2002−232300−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000004-40-2002−232300−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ32111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3311111111111-1-111-1-1-1-11-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-111-1-1-1-111
χ3411111111111-1-111-1-1-1-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-1111111-1-1
χ35111111111-1-111111111-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-111-11
χ36111111111-1-111111111-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-11-1
χ37111111111-1-1-1-111-1-1-1-1-11-11111-1-1-11-1-1-1-1-1-1-1-1-11111-1-111111-11-1-1-1-1111-1
χ38111111111-1-1-1-111-1-1-1-1-11-111-1-1111-1-1-1-1-1-1-1-1-1-11111-1-111111-11-1-111-1-1-11
χ392222-2-22-2-200002-20000000002-20000-2-2-2-222-2220000-22000000000-220000
χ402222-2-22-2-200002-2000000000-220000-2-2-2-222-2220000-220000000002-20000
χ41222-122-1-1-12222-1-1-1-1-1-1-12-1-1-1000000-2-2-21-2-2111-2-2-2-21111111-2111000000
χ42222-122-1-1-122-2-2-1-11111-1-2-111000000-2-2-21-2-2111-2-22211-1-1-1-1121-1-1000000
χ43222-122-1-1-1-2-222-1-1-1-1-1-11-2111000000-2-2-21-2-211122-2-2111111-12-1-1-1000000
χ44222-122-1-1-1-2-2-2-2-1-11111121-1-1000000-2-2-21-2-2111222211-1-1-1-1-1-2-111000000
χ4522-222-22220000-2-2000000000002-200-2-22-2-22-2-2-200002200000000000-2200
χ4622-222-22220000-2-200000000000-2200-2-22-2-22-2-2-2000022000000000002-200
χ4722-22-222-2-22-200-22000020-200000000-2-22-22-2-222-22002-20000-20200000000
χ4822-22-222-2-2-2200-220000-20200000000-2-22-22-2-2222-2002-2000020-200000000
χ4922-2-1-22-1112-2001-133−3−3-1013−3000000-2-2212-21-1-1-2200-11−3−33310-1−33000000
χ5022-2-1-22-1112-2001-1−3−333-101−33000000-2-2212-21-1-1-2200-1133−3−310-13−3000000
χ5122-2-1-22-111-22001-133−3−310-1−33000000-2-2212-21-1-12-200-11−3−333-1013−3000000
χ5222-2-1-22-111-22001-1−3−33310-13−3000000-2-2212-21-1-12-200-1133−3−3-101−33000000
χ53444-2-4-4-2220000-22000000000000000-4-4-42442-2-200002-2000000000000000
χ5444-4-24-4-2-2-2000022000000000000000-4-442-442220000-2-2000000000000000
χ554-40400-400002i−2i002i−2i2i−2i00000000000-440-40040000−2i2i00−2i2i−2i2i00000000000
χ564-40400-40000−2i2i00−2i2i−2i2i00000000000-440-400400002i−2i002i−2i2i−2i00000000000
χ574-40-200223−23002i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000-440200-2−232300−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000
χ584-40-200223−2300−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000-440200-2−2323002i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000
χ594-40-2002−2323002i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000-440200-223−2300−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000
χ604-40-2002−232300−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000-440200-223−23002i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.