Finite Group Databasebeta

← Group #13167073

Character table — Group #13167073

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222444444444444444444888888888888888818181818242424242424242424242424242424242424363636365454545454545454727272727272
order12223446663333666666666666121236661212121212121212121212124444441212121212121212121212121212121212121212888888884412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ511111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-1-1-111
χ611111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1111-1-1
χ711111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1111-1-1
χ811111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111111111-1-1-1-1-1-111-1-1-1-1-1-111111-1-1-111
χ922222222222222222222222222222222222222222222-2-2-2-2000000000000000000-2-2-2-200000000000000
χ1022222-2-22222222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000000000000000-2-22200000000000000
χ112222-122-1-1-122-1-122-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1222222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-100000000000000
χ122222-122-1-1-122-1-122-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-2-21111-2-21111-2-21111-1-1-1-100000000000000
χ132222-122-1-1-122-1-122-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3111100000000000000
χ142222-122-1-1-122-1-122-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3111100000000000000
χ152222-1-2-2-1-1-122-1-122-1-12-1-12-1-12211-1-1-1-1-2-21111-2-2111122-2-200−i3i3i3−i300i3i3−i3−i300−i3−i3i3i311-1-100000000000000
χ162222-1-2-2-1-1-122-1-122-1-12-1-12-1-12211-1-1-1-1-2-21111-2-2111122-2-200i3−i3−i3i300−i3−i3i3i300i3i3−i3−i311-1-100000000000000
χ172222-1-2-2-1-1-122-1-122-1-12-1-12-1-12211-1-1-1-1-2-21111-2-21111-2-2222-2-1-111-2-2111122-1-1-1-1-1-11100000000000000
χ182222-1-2-2-1-1-122-1-122-1-12-1-12-1-12211-1-1-1-1-2-21111-2-21111-2-222-2211-1-122-1-1-1-1-2-21111-1-11100000000000000
χ1922-2-2200-22-222222222-2-2-2-2-2-2-2-20022-2-2000000000000002-20000000000000000002-200000022-2-2000000
χ2022-2-2200-22-222222222-2-2-2-2-2-2-2-20022-2-2000000000000002-20000000000000000002-2000000-2-222000000
χ2122-2-2200-22-222222222-2-2-2-2-2-2-2-20022-2-200000000000000-22000000000000000000-220022-2-20000000000
χ2222-2-2200-22-222222222-2-2-2-2-2-2-2-20022-2-200000000000000-22000000000000000000-2200-2-2220000000000
χ232-22-22002-2-22222-2-2-2-2-2-2-2222-22002-2-220000000000002i−2i00000000000000000000002i−2i2−22−2−i2i2−i2i2000000
χ242-22-22002-2-22222-2-2-2-2-2-2-2222-22002-2-220000000000002i−2i00000000000000000000002i−2i−22−22i2−i2i2−i2000000
χ252-22-22002-2-22222-2-2-2-2-2-2-2222-22002-2-22000000000000−2i2i0000000000000000000000−2i2i2−22−2i2−i2i2−i2000000
χ262-22-22002-2-22222-2-2-2-2-2-2-2222-22002-2-22000000000000−2i2i0000000000000000000000−2i2i−22−22−i2i2−i2i2000000
χ272-2-2222i−2i-2-222222-2-2-2-2222-2-2-22-22i−2i2-22-22i−2i2i2i−2i−2i2i−2i2i2i−2i−2i000000000000000000000000002−2−22−i2i2i2−i2000000
χ282-2-2222i−2i-2-222222-2-2-2-2222-2-2-22-22i−2i2-22-22i−2i2i2i−2i−2i2i−2i2i2i−2i−2i00000000000000000000000000−222−2i2−i2−i2i2000000
χ292-2-222−2i2i-2-222222-2-2-2-2222-2-2-22-2−2i2i2-22-2−2i2i−2i−2i2i2i−2i2i−2i−2i2i2i000000000000000000000000002−2−22i2−i2−i2i2000000
χ302-2-222−2i2i-2-222222-2-2-2-2222-2-2-22-2−2i2i2-22-2−2i2i−2i−2i2i2i−2i2i−2i−2i2i2i00000000000000000000000000−222−2−i2i2i2−i2000000
χ3144444444441-2111-211111111-2-244-2-2-2-2111111-2-2-2-2-2-20000222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3244444444441-2111-211111111-2-244-2-2-2-2111111-2-2-2-2-2-20000-2-2-2-2-2-2111111111111000000000000000000
χ334444444444-21-2-2-21-2-2-2-2-2-2-2-211441111-2-2-2-2-2-2111111000000000000000000000000000000000022-1-1-1-1
χ344444444444-21-2-2-21-2-2-2-2-2-2-2-211441111-2-2-2-2-2-21111110000000000000000000000000000000000-2-21111
χ3544444-4-44441-2111-211111111-2-2-4-4-2-2-2-2-1-1-1-1-1-122222200002-222-2-2111111-1-1-1-1-1-1000000000000000000
χ3644444-4-44441-2111-211111111-2-2-4-4-2-2-2-2-1-1-1-1-1-12222220000-22-2-222-1-1-1-1-1-1111111000000000000000000
χ3744444-4-4444-21-2-2-21-2-2-2-2-2-2-2-211-4-41111222222-1-1-1-1-1-100000000000000000000000000000000002-211-1-1
χ3844444-4-4444-21-2-2-21-2-2-2-2-2-2-2-211-4-41111222222-1-1-1-1-1-10000000000000000000000000000000000-22-1-111
χ394444-244-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32-2-21111000022−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000000
χ404444-244-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32-2-211110000-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000000
χ414444-244-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32-2-21111000022−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000000
χ424444-244-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32-2-211110000-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000000
χ434444-2-4-4-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2221111-1-11+3i321−3i321+3i321−3i3222-1-1-1-100002-2−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000000
χ444444-2-4-4-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2221111-1-11+3i321−3i321+3i321−3i3222-1-1-1-10000-221+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000000
χ454444-2-4-4-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2221111-1-11−3i321+3i321−3i321+3i3222-1-1-1-100002-2−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000000
χ464444-2-4-4-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2221111-1-11−3i321+3i321−3i321+3i3222-1-1-1-10000-221−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000000
χ4744-4-4-2002-2244-2-244-2-2-422-422-4-400-2-222000000000000004-4000000000000000000-220000000000000000
χ4844-4-4-2002-2244-2-244-2-2-422-422-4-400-2-22200000000000000-440000000000000000002-20000000000000000
χ494-44-4-200-22244-2-2-4-422-4224-2-2-4400-222-20000000000004i−4i0000000000000000000000−2i2i00000000000000
χ504-44-4-200-22244-2-2-4-422-4224-2-2-4400-222-2000000000000−4i4i00000000000000000000002i−2i00000000000000
χ514-4-4444i−4i-4-441-211-12-1-1111-1-1-1-224i−4i-22-22i−iii−i−i−2i2i−2i−2i2i2i0000000000−i3i3−i3i3−i3i33−33−33−3000000000000000000
χ524-4-4444i−4i-4-441-211-12-1-1111-1-1-1-224i−4i-22-22i−iii−i−i−2i2i−2i−2i2i2i0000000000i3−i3i3−i3i3−i3−33−33−33000000000000000000
χ534-4-4444i−4i-4-44-21-2-22-122-2-2-22221-14i−4i1-11-1−2i2i−2i−2i2i2ii−iii−i−i000000000000000000000000000000000000−i3i33−3
χ544-4-4444i−4i-4-44-21-2-22-122-2-2-22221-14i−4i1-11-1−2i2i−2i−2i2i2ii−iii−i−i000000000000000000000000000000000000i3−i3−33
χ554-4-444−4i4i-4-441-211-12-1-1111-1-1-1-22−4i4i-22-22−ii−i−iii2i−2i2i2i−2i−2i0000000000−i3i3−i3i3−i3i3−33−33−33000000000000000000
χ564-4-444−4i4i-4-441-211-12-1-1111-1-1-1-22−4i4i-22-22−ii−i−iii2i−2i2i2i−2i−2i0000000000i3−i3i3−i3i3−i33−33−33−3000000000000000000
χ574-4-444−4i4i-4-44-21-2-22-122-2-2-22221-1−4i4i1-11-12i−2i2i2i−2i−2i−ii−i−iii000000000000000000000000000000000000−i3i3−33
χ584-4-444−4i4i-4-44-21-2-22-122-2-2-22221-1−4i4i1-11-12i−2i2i2i−2i−2i−ii−i−iii000000000000000000000000000000000000i3−i33−3
χ594-4-44-24i−4i22-21-2−1−3i32−1+3i32-121+3i321−3i321−1−3i32−1+3i32-11+3i321−3i32-22−2i2i1-11-1i−i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ22−2i2iii−i−i0000000000−i3i3−3+i323−i323+i32−3−i323−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22000000000000000000
χ604-4-44-24i−4i22-21-2−1−3i32−1+3i32-121+3i321−3i321−1−3i32−1+3i32-11+3i321−3i32-22−2i2i1-11-1i−i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ22−2i2iii−i−i0000000000i3−i33−i32−3+i32−3−i323+i32−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000000000000
χ614-4-44-24i−4i22-21-2−1+3i32−1−3i32-121−3i321+3i321−1+3i32−1−3i32-11−3i321+3i32-22−2i2i1-11-1i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−2i2iii−i−i0000000000−i3i33+i32−3−i32−3+i323−i323−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000000000000
χ624-4-44-24i−4i22-21-2−1+3i32−1−3i32-121−3i321+3i321−1+3i32−1−3i32-11−3i321+3i32-22−2i2i1-11-1i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−2i2iii−i−i0000000000i3−i3−3−i323+i323−i32−3+i32−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000000000000
χ634-4-44-24i−4i22-244-2-2-4-4224-2-2-4224-4−2i2i-22-224i−4i−2i−2i2i2i4i−4i−2i−2i2i2i0000000000000000000000000000000000000000
χ644-4-44-2−4i4i22-21-2−1−3i32−1+3i32-121+3i321−3i321−1−3i32−1+3i32-11+3i321−3i32-222i−2i1-11-1−iiζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ222i−2i−i−iii0000000000−i3i3−3+i323−i323+i32−3−i32−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000000000000
χ654-4-44-2−4i4i22-21-2−1−3i32−1+3i32-121+3i321−3i321−1−3i32−1+3i32-11+3i321−3i32-222i−2i1-11-1−iiζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ222i−2i−i−iii0000000000i3−i33−i32−3+i32−3−i323+i323−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22000000000000000000
χ664-4-44-2−4i4i22-21-2−1+3i32−1−3i32-121−3i321+3i321−1+3i32−1−3i32-11−3i321+3i32-222i−2i1-11-1−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ222i−2i−i−iii0000000000−i3i33+i32−3−i32−3+i323−i32−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000000000000
χ674-4-44-2−4i4i22-21-2−1+3i32−1−3i32-121−3i321+3i321−1+3i32−1−3i32-11−3i321+3i32-222i−2i1-11-1−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ222i−2i−i−iii0000000000i3−i3−3−i323+i323−i32−3+i323−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000000000000
χ684-4-44-2−4i4i22-244-2-2-4-4224-2-2-4224-42i−2i-22-22−4i4i2i2i−2i−2i−4i4i2i2i−2i−2i0000000000000000000000000000000000000000
χ698888-488-4-4-4-4222-4222-422-42222-4-4-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000
χ708888-4-8-8-4-4-4-4222-4222-422-4222244-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000
χ7188-8-8800-88-82-4222-422-2-2-2-2-2-24400-4-4440000000000000000000000000000000000000000000000000000
χ7288-8-8800-88-8-42-4-4-42-4-4444444-2-20022-2-20000000000000000000000000000000000000000000000000000
χ7388-8-8-4004-442-4−1−3i3−1+3i32-4−1−3i3−1+3i3-21+3i31−3i3-21+3i31−3i3440022-2-20000000000000000000000000000000000000000000000000000
χ7488-8-8-4004-442-4−1+3i3−1−3i32-4−1+3i3−1−3i3-21−3i31+3i3-21−3i31+3i3440022-2-20000000000000000000000000000000000000000000000000000
χ7588-8-8-4004-44-4222-42224-2-24-2-2-2-200-1-1110000000033−3333−330000000000000000000000000000000000000000
χ7688-8-8-4004-44-4222-42224-2-24-2-2-2-200-1-11100000000−3333−33330000000000000000000000000000000000000000
χ778-88-88008-8-82-422-24-2-2-2-2-22224-400-444-40000000000000000000000000000000000000000000000000000
χ788-88-88008-8-8-42-4-44-244444-4-4-4-22002-2-220000000000000000000000000000000000000000000000000000
χ798-88-8-400-4442-4−1−3i3−1+3i3-241+3i31−3i3-21+3i31−3i32−1−3i3−1+3i34-4002-2-220000000000000000000000000000000000000000000000000000
χ808-88-8-400-4442-4−1+3i3−1−3i3-241−3i31+3i3-21−3i31+3i32−1+3i3−1−3i34-4002-2-220000000000000000000000000000000000000000000000000000
χ818-88-8-400-444-42224-2-2-24-2-2-422-2200-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000
χ828-88-8-400-444-42224-2-2-24-2-2-422-2200-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000
χ838-8-88-48i−8i44-4-42224-2-2-2-4224-2-22-2−4i4i-11-11−4i4i2i2i−2i−2i2i−2i−i−iii0000000000000000000000000000000000000000
χ848-8-88-4−8i8i44-4-42224-2-2-2-4224-2-22-24i−4i-11-114i−4i−2i−2i2i2i−2i2iii−i−i0000000000000000000000000000000000000000

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