Finite Group Databasebeta

← Group #11781221

Character table — Group #11781221

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222224444444444444444466668888888888888888888888812121212121212121212121212122424242424242424242436363636484848144
order1222334444666666121212123466612121212121212121212121288888812121212122424242424242424242424242424242444448824242424242424248812121212242424248888412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11
χ71111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111-1
χ92222222-22-222222222222-2222-2-2-2-2222222-2-2000000-2-2-2-2-2000000000000000022-2-200000000000022-2-2000000000000
χ102222222-22-222222222222-2222-2-2-2-2222222-2-2000000-2-2-2-2-20000000000000000-2-222000000000000-2-222000000000000
χ11222222-22-22222222-2-2-2-22-222222-2-2-2-2-2-2-2-222222200-222-2-200000000000000000000-2-22222-2-2-2-2000000000000000000
χ12222222-22-22222222-2-2-2-22-222222-2-2-2-2-2-2-2-222-2-2-2-200-222-2-20000000000000000000022-2-2-2-22222000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-20000002-2-22200000000000000000000000000000000000000002i2i−2i−2i0000
χ14222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-20000002-2-2220000000000000000000000000000000000000000−2i−2i2i2i0000
χ1522222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-122000022-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000000000000-1-1-1-1000000002-1-10
χ1622222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-122000022-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000111100000000-2110
χ1722222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-1220000-2-2-1-1-1-1-1-2-2-2-21111111111112222000000000000-1-1-1-100000000-2110
χ1822222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-1220000-2-2-1-1-1-1-1-2-2-2-2111111111111-2-2-2-20000000000001111000000002-1-10
χ1922222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-2000000111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i322-2-2000000000000-1-111000000000−i3i30
χ2022222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-2000000111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-2-22200000000000011-1-1000000000i3−i30
χ2122222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-2000000111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i322-2-2000000000000-1-111000000000i3−i30
χ2222222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-2000000111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-2-22200000000000011-1-1000000000−i3i30
χ232222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1000022-1-1-1-1-1-1-1-1220000-1-1-1-100000000
χ242222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-12222-2-22-1-1-1-11111-2-21111-2-21111000022-1-1-1-1-1-1-1-1-2-20000111100000000
χ252222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1-2-2-2-2222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000-2-211111111-2-20000111100000000
χ262222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1-2-2-2-2-2-22-1-1-1-11111-2-21111-2-211110000-2-211111111220000-1-1-1-100000000
χ272222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-1222200-2-1-11133−3−30033−3−30033−3−30000-2-2-1-1-1-1111100000033−3−300000000
χ282222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-1222200-2-1-111−3−33300−3−33300−3−3330000-2-2-1-1-1-11111000000−3−33300000000
χ292222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-1-2-2-2-200-2-1-11133−3−30033−3−30033−3−30000221111-1-1-1-1000000−3−33300000000
χ302222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-1-2-2-2-200-2-1-111−3−33300−3−33300−3−3330000221111-1-1-1-100000033−3−300000000
χ3122-2-222020-22-2-22-2-20000202-2-22-2000000002-222-2-22−202-2002−22−22−22−22−22−22−22−200000022-2-200002−200002−22−200000000
χ3222-2-222020-22-2-22-2-20000202-2-22-2000000002-222-2-2−2202-200−22−22−22−22−22−22−22−2200000022-2-20000−220000−22−2200000000
χ3322-2-222020-22-2-22-2-20000202-2-22-2000000002-2-2-2222−202-2002−22−22−22−22−22−22−22−2000000-2-2220000−220000−22−2200000000
χ3422-2-222020-22-2-22-2-20000202-2-22-2000000002-2-2-222−2202-200−22−22−22−22−22−22−22−22000000-2-22200002−200002−22−200000000
χ3522-2-2-12020-2-1112-2-23−33−3-10-1112-23−303−303−3-1122-2-22−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000-1-11133−3−32−20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ3622-2-2-12020-2-1112-2-23−33−3-10-1112-23−303−303−3-1122-2-2−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000-1-11133−3−3−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ3722-2-2-12020-2-1112-2-23−33−3-10-1112-23−303−303−3-11-2-2222−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000011-1-1−3−333−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ3822-2-2-12020-2-1112-2-23−33−3-10-1112-23−303−303−3-11-2-222−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000011-1-1−3−3332−20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ3922-2-2-12020-2-1112-2-2−33−33-10-1112-2−330−330−33-1122-2-22−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000-1-111−3−3332−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ4022-2-2-12020-2-1112-2-2−33−33-10-1112-2−330−330−33-1122-2-2−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000-1-111−3−333−220000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ4122-2-2-12020-2-1112-2-2−33−33-10-1112-2−330−330−33-11-2-2222−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000011-1-133−3−3−220000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ4222-2-2-12020-2-1112-2-2−33−33-10-1112-2−330−330−33-11-2-222−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000011-1-133−3−32−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ432-22-22220-20-22-2-22-222-2-220-22-20000222-2-2-2002−22−2000000000000000000000002-2002−22−22−22−22−2002-20000002−22−20000
χ442-22-22220-20-22-2-22-222-2-220-22-20000222-2-2-2002−22−200000000000000000000000-22002−22−22−22−22−200-22000000−22−220000
χ452-22-22220-20-22-2-22-222-2-220-22-20000222-2-2-200−22−22000000000000000000000002-200−22−22−22−22−22002-2000000−22−220000
χ462-22-22220-20-22-2-22-222-2-220-22-20000222-2-2-200−22−2200000000000000000000000-2200−22−22−22−22−2200-220000002−22−20000
χ472-22-222-2020-22-2-22-2-2-22220-22-20000-2-2-2222002−22−200000000000000000000000002i−2i−222−22−2−22−2200002i−2i0000−i2i2i2−i20000
χ482-22-222-2020-22-2-22-2-2-22220-22-20000-2-2-2222002−22−20000000000000000000000000−2i2i−222−22−2−22−220000−2i2i0000i2−i2−i2i20000
χ492-22-222-2020-22-2-22-2-2-22220-22-20000-2-2-222200−22−2200000000000000000000000002i−2i2−2−22−222−22−200002i−2i0000i2−i2−i2i20000
χ502-22-222-2020-22-2-22-2-2-22220-22-20000-2-2-222200−22−220000000000000000000000000−2i2i2−2−22−222−22−20000−2i2i0000−i2i2i2−i20000
χ5144444-2-44-44444-2-2-2-4-4-4-4-2-4-2-2-2-2-2-4-4222222440000002-2-222000000000000000000000000000000000000000000000000
χ5244444-2-4-4-4-4444-2-2-2-4-4-4-4-24-2-2-22244222222-4-4000000-222-2-2000000000000000000000000000000000000000000000000
χ534444-244-44-4-2-2-2444-2-2-2-2-2-4-2-2-2-4-4224-2-24-2-222000000-42222000000000000000000000000000000000000000000000000
χ544444-24-4-4-4-4-2-2-24442222-24-2-2-2-4-4-2-2-422-42222000000422-2-2000000000000000000000000000000000000000000000000
χ554444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-2000044-21111-2-2-2-2-2-21111-2-2111100000000000000000000000000000000
χ564444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-20000-4-4-21111222222-1-1-1-122-1-1-1-100000000000000000000000000000000
χ574444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-41112222-211-211220000002-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i300000000000000000000000000000000
χ584444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-41112222-211-211220000002-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i300000000000000000000000000000000
χ594444-2-2-44-44-2-2-2-2-2-222221-4111-2-2222-1-12-1-1-2-2000000211-1-12323−23−2300−3−33300−3−33300000000000000000000000000000000
χ604444-2-2-44-44-2-2-2-2-2-222221-4111-2-2222-1-12-1-1-2-2000000211-1-1−23−2323230033−3−30033−3−300000000000000000000000000000000
χ614444-2-2-4-4-4-4-2-2-2-2-2-222221411122-2-22-1-12-1-122000000-2-1-1110000003i3i−3i−3i00−3i−3i3i3i00000000000000000000000000000000
χ624444-2-2-4-4-4-4-2-2-2-2-2-222221411122-2-22-1-12-1-122000000-2-1-111000000−3i−3i3i3i003i3i−3i−3i00000000000000000000000000000000
χ6344-4-4440-4044-4-44-4-40000404-4-4-4400000000-440000000-4400000000000000000000000000000000000000000000000000
χ6444-4-44-2040-44-4-4-2220000-20-222-22000000004-4000022−220-220022−2222−22−22−22−22−22−22−2200000000000000000000000000000000
χ6544-4-44-2040-44-4-4-2220000-20-222-22000000004-40000−22220-2200−2222−22222−22−22−22−22−22−200000000000000000000000000000000
χ6644-4-44-20-4044-4-4-2220000-20-2222-200000000-4400000002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i600000000000000000000000000000000
χ6744-4-44-20-4044-4-4-2220000-20-2222-200000000-4400000002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i600000000000000000000000000000000
χ6844-4-4-240-404-2224-4-423−2323−23-20-222-44−2323023−23023−232-200000002-2−2323000000000000000000000000000000000000000000000000
χ6944-4-4-240-404-2224-4-4−2323−2323-20-222-4423−230−23230−23232-200000002-223−23000000000000000000000000000000000000000000000000
χ7044-4-4-2-2040-4-222-22223−2323−23101-1-1-2223−230−330−33-22000022−2201-1−332ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000000000000000000000
χ7144-4-4-2-2040-4-222-22223−2323−23101-1-1-2223−230−330−33-220000−222201-1−33−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000000000000000
χ7244-4-4-2-2040-4-222-222−2323−2323101-1-1-22−232303−303−3-22000022−2201-13−32ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000000000000000
χ7344-4-4-2-2040-4-222-222−2323−2323101-1-1-22−232303−303−3-220000−222201-13−3−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000000000000000000000
χ7444-4-4-2-20-404-222-22223−2323−23101-1-12-2−23230−330−332-20000000-113−30000i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ2300000000000000000000000000000000
χ7544-4-4-2-20-404-222-22223−2323−23101-1-12-2−23230−330−332-20000000-113−30000−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ2300000000000000000000000000000000
χ7644-4-4-2-20-404-222-222−2323−2323101-1-12-223−2303−303−32-20000000-11−330000i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ2300000000000000000000000000000000
χ7744-4-4-2-20-404-222-222−2323−2323101-1-12-223−2303−303−32-20000000-11−330000−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ2300000000000000000000000000000000
χ784-44-44-240-40-44-42-2244-4-4-202-220000-2-2-2222000000000000000000000000000004-400000000000000-2200000000000000
χ794-44-44-240-40-44-42-2244-4-4-202-220000-2-2-222200000000000000000000000000000-44000000000000002-200000000000000
χ804-44-44-2-4040-44-42-22-4-444-202-220000222-2-2-200000000000000000000000000000004i−4i00000000000000−2i2i000000000000
χ814-44-44-2-4040-44-42-22-4-444-202-220000222-2-2-20000000000000000000000000000000−4i4i000000000000002i−2i000000000000
χ824-44-4-2440-402-22-44-4-2-222-202-2200004-2-2-4220022−2222−2200000000000000000000000000022−22−22−22−22−22000000000000000000
χ834-44-4-2440-402-22-44-4-2-222-202-2200004-2-2-42200−2222−2222000000000000000000000000000−22222−22−22−22−2000000000000000000
χ844-44-4-24-40402-22-44-422-2-2-202-220000-4224-2-20022−2222−22000000000000000000000000000−2222−22−222−22−2000000000000000000
χ854-44-4-24-40402-22-44-422-2-2-202-220000-4224-2-200−2222−222200000000000000000000000000022−222−22−2−22−22000000000000000000
χ864-4-44440000-4-44-4-44000040-4-4400000000000022−22−22220000000000000000000000000000022−22−22220000000000000000000000
χ874-4-44440000-4-44-4-44000040-4-44000000000000−222222−2200000000000000000000000000000−222222−220000000000000000000000
χ884-4-44-24000022-2-4-4423−23−2323-2022-20000023−230−23230022−22−222200000000000000000000000000000−222−26−6−66000000000000000000
χ894-4-44-24000022-2-4-4423−23−2323-2022-20000023−230−232300−222222−22000000000000000000000000000002−2−22−666−6000000000000000000
χ904-4-44-24000022-2-4-44−232323−23-2022-200000−2323023−230022−22−222200000000000000000000000000000−222−2−666−6000000000000000000
χ914-4-44-24000022-2-4-44−232323−23-2022-200000−2323023−2300−222222−22000000000000000000000000000002−2−226−6−66000000000000000000
χ928-88-8-4-480-804-444-44-4-44420-22-20000-4224-2-20000000000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-80804-444-4444-4-420-22-200004-2-2-4220000000000000000000000000000000000000000000000000000000000000
χ948-8-888-40000-8-8844-40000-4044-400000000000000000000000000000000000000000000000000000000000000000000000
χ958-8-88-4-4000044-444-443−43−434320-2-2200000−2323023−230000000000000000000000000000000000000000000000000000000000000
χ968-8-88-4-4000044-444-4−434343−4320-2-220000023−230−23230000000000000000000000000000000000000000000000000000000000000

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