Finite Group Databasebeta

← Group #13167046

Character table — Group #13167046

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
χ511111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ611111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-11-1-111
χ711111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-1-11-1-111
χ811111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111111-111-1-1
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
χ112222-122-1-1-122-1-122-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-100000000000000
χ122222-122-1-1-122-1-122-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-21111-2-21111-2-21111-1-1-1-100000000000000
χ132222-122-1-1-122-1-122-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3111100000000000000
χ142222-122-1-1-122-1-122-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3111100000000000000
χ152222-1-2-2-1-1-122-1-122-1-122-1-12-1-1211-1-1-1-1-2-2-2-21111111122-2-200−i3i3i3−i300−i3−i3i3i300i3i3−i3−i311-1-100000000000000
χ162222-1-2-2-1-1-122-1-122-1-122-1-12-1-1211-1-1-1-1-2-2-2-21111111122-2-200i3−i3−i3i300i3i3−i3−i300−i3−i3i3i311-1-100000000000000
χ172222-1-2-2-1-1-122-1-122-1-122-1-12-1-1211-1-1-1-1-2-2-2-211111111-2-2222-2-1-11122-1-1-1-1-2-21111-1-11100000000000000
χ182222-1-2-2-1-1-122-1-122-1-122-1-12-1-1211-1-1-1-1-2-2-2-211111111-2-222-2211-1-1-2-2111122-1-1-1-1-1-11100000000000000
χ1922-2-222-22-2-22222-2-2-2-22222-2-2-2-22-22-2-2222-2-222-2-222-2-20000000000000000000000000022−2−222−2−2000000
χ2022-2-222-22-2-22222-2-2-2-22222-2-2-2-22-22-2-2222-2-222-2-222-2-200000000000000000000000000−2−222−2−222000000
χ2122-2-22-222-2-22222-2-2-2-22222-2-2-2-2-222-2-22-2-222-2-222-2-2220000000000000000000000000022−2−2−2−222000000
χ2222-2-22-222-2-22222-2-2-2-22222-2-2-2-2-222-2-22-2-222-2-222-2-22200000000000000000000000000−2−22222−2−2000000
χ232-22-2200-2-2222222-2-2-2-2-2-2-2222-20022-2-20000000000002-200000000000000000000002-2−i2i2−i2i2−i2i2−i2i2000000
χ242-22-2200-2-2222222-2-2-2-2-2-2-2222-20022-2-20000000000002-200000000000000000000002-2i2−i2i2−i2i2−i2i2−i2000000
χ252-22-2200-2-2222222-2-2-2-2-2-2-2222-20022-2-2000000000000-220000000000000000000000-22−i2i2−i2i2i2−i2i2−i2000000
χ262-22-2200-2-2222222-2-2-2-2-2-2-2222-20022-2-2000000000000-220000000000000000000000-22i2−i2i2−i2−i2i2−i2i2000000
χ272-2-22200-22-22222-2222-2-2-2-2-2-2-22002-22-2000000000000002-20000000000000000002-20000002i−2i−2i2i000000
χ282-2-22200-22-22222-2222-2-2-2-2-2-2-22002-22-2000000000000002-20000000000000000002-2000000−2i2i2i−2i000000
χ292-2-22200-22-22222-2222-2-2-2-2-2-2-22002-22-200000000000000-22000000000000000000-22002i−2i−2i2i0000000000
χ302-2-22200-22-22222-2222-2-2-2-2-2-2-22002-22-200000000000000-22000000000000000000-2200−2i2i2i−2i0000000000
χ3144444444441-211-21111-211111-244-2-2-2-21-21-21111-2-2-2-20000222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3244444444441-211-21111-211111-244-2-2-2-21-21-21111-2-2-2-20000-2-2-2-2-2-2111111111111000000000000000000
χ334444444444-21-2-21-2-2-2-21-2-2-2-2-21441111-21-21-2-2-2-21111000000000000000000000000000000000022-1-1-1-1
χ344444444444-21-2-21-2-2-2-21-2-2-2-2-21441111-21-21-2-2-2-211110000000000000000000000000000000000-2-21111
χ3544444-4-44441-211-21111-211111-2-4-4-2-2-2-2-12-12-1-1-1-1222200002-222-2-2-1-1-1-1-1-1111111000000000000000000
χ3644444-4-44441-211-21111-211111-2-4-4-2-2-2-2-12-12-1-1-1-122220000-22-2-222111111-1-1-1-1-1-1000000000000000000
χ3744444-4-4444-21-2-21-2-2-2-21-2-2-2-2-21-4-411112-12-12222-1-1-1-100000000000000000000000000000000002-2-1-111
χ3844444-4-4444-21-2-21-2-2-2-21-2-2-2-2-21-4-411112-12-12222-1-1-1-10000000000000000000000000000000000-2211-1-1
χ394444-244-2-2-21-2−1−3i32−1+3i32-21−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2-2-211111-21-2−1−3i32−1+3i32−1−3i32−1+3i321111000022−1−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+3i32-21−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2-2-211111-21-2−1−3i32−1+3i32−1−3i32−1+3i3211110000-2-21+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+3i32−1−3i32-21−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2-2-211111-21-2−1+3i32−1−3i32−1+3i32−1−3i321111000022−1+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+3i32−1−3i32-21−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2-2-211111-21-2−1+3i32−1−3i32−1+3i32−1−3i3211110000-2-21−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+3i32-21−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2221111-12-121+3i321−3i321+3i321−3i32-1-1-1-100002-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000000
χ444444-2-4-4-2-2-21-2−1−3i32−1+3i32-21−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2221111-12-121+3i321−3i321+3i321−3i32-1-1-1-10000-221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000000
χ454444-2-4-4-2-2-21-2−1+3i32−1−3i32-21−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2221111-12-121−3i321+3i321−3i321+3i32-1-1-1-100002-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000000
χ464444-2-4-4-2-2-21-2−1+3i32−1−3i32-21−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2221111-12-121−3i321+3i321−3i321+3i32-1-1-1-10000-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000000
χ4744-4-444-44-4-41-2112-1-1-11-211-1-1-124-4-222-21-2-1211-1-1-2-22200000000003−33−33−33−33−33−3000000000000000000
χ4844-4-444-44-4-41-2112-1-1-11-211-1-1-124-4-222-21-2-1211-1-1-2-2220000000000−33−33−33−33−33−33000000000000000000
χ4944-4-444-44-4-4-21-2-2-1222-21-2-2222-14-41-1-11-212-1-2-22211-1-10000000000000000000000000000000000003−33−3
χ5044-4-444-44-4-4-21-2-2-1222-21-2-2222-14-41-1-11-212-1-2-22211-1-1000000000000000000000000000000000000−33−33
χ5144-4-44-444-4-41-2112-1-1-11-211-1-1-12-44-222-2-121-2-1-11122-2-200000000003−33−33−3−33−33−33000000000000000000
χ5244-4-44-444-4-41-2112-1-1-11-211-1-1-12-44-222-2-121-2-1-11122-2-20000000000−33−33−333−33−33−3000000000000000000
χ5344-4-44-444-4-4-21-2-2-1222-21-2-2222-1-441-1-112-1-2122-2-2-1-1110000000000000000000000000000000000003−3−33
χ5444-4-44-444-4-4-21-2-2-1222-21-2-2222-1-441-1-112-1-2122-2-2-1-111000000000000000000000000000000000000−333−3
χ5544-4-4-24-4-2221-2−1−3i32−1+3i322-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i322-221-1-111-2-12−1−3i32−1+3i321+3i321−3i3211-1-100000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22000000000000000000
χ5644-4-4-24-4-2221-2−1−3i32−1+3i322-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i322-221-1-111-2-12−1−3i32−1+3i321+3i321−3i3211-1-10000000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000000000000
χ5744-4-4-24-4-2221-2−1+3i32−1−3i322-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i322-221-1-111-2-12−1+3i32−1−3i321−3i321+3i3211-1-100000000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000000000000
χ5844-4-4-24-4-2221-2−1+3i32−1−3i322-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i322-221-1-111-2-12−1+3i32−1−3i321−3i321+3i3211-1-10000000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000000000000
χ5944-4-4-24-4-22244-2-2-4-42244-2-2-422-4-22-222-244-4-4-2-222-2-2220000000000000000000000000000000000000000
χ6044-4-4-2-44-2221-2−1−3i32−1+3i322-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i3222-21-1-11-121-21+3i321−3i32−1−3i32−1+3i32-1-11100000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000000000000
χ6144-4-4-2-44-2221-2−1−3i32−1+3i322-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i3222-21-1-11-121-21+3i321−3i32−1−3i32−1+3i32-1-1110000000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22000000000000000000
χ6244-4-4-2-44-2221-2−1+3i32−1−3i322-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i3222-21-1-11-121-21−3i321+3i32−1+3i32−1−3i32-1-11100000000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000000000000
χ6344-4-4-2-44-2221-2−1+3i32−1−3i322-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i3222-21-1-11-121-21−3i321+3i32−1+3i32−1−3i32-1-1110000000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000000000000
χ6444-4-4-2-44-22244-2-2-4-42244-2-2-422-42-2-222-2-4-44422-2-222-2-20000000000000000000000000000000000000000
χ654-44-4-20022-244-2-24-422-4-4224-2-2-400-2-2220000000000004-40000000000000000000000-2200000000000000
χ664-44-4-20022-244-2-24-422-4-4224-2-2-400-2-222000000000000-4400000000000000000000002-200000000000000
χ674-4-44-2002-2244-2-2-44-2-2-4-422-422400-22-22000000000000004-4000000000000000000-220000000000000000
χ684-4-44-2002-2244-2-2-44-2-2-4-422-422400-22-2200000000000000-440000000000000000002-20000000000000000
χ698888-488-4-4-4-42222-422-4222-4222-4-4-1-1-1-1-42-422222-1-1-1-10000000000000000000000000000000000000000
χ708888-4-8-8-4-4-4-42222-422-4222-422244-1-1-1-14-24-2-2-2-2-211110000000000000000000000000000000000000000
χ7188-8-8-48-8-444-4222-24-2-2-42224-2-2-2-44-111-1-424-222-2-2-1-1110000000000000000000000000000000000000000
χ7288-8-8-4-88-444-4222-24-2-2-42224-2-2-24-4-111-14-2-42-2-22211-1-10000000000000000000000000000000000000000
χ738-88-8800-8-882-422-4-2-2-2-24-2-2222400-4-4440000000000000000000000000000000000000000000000000000
χ748-88-8800-8-88-42-4-424444-244-4-4-4-20022-2-20000000000000000000000000000000000000000000000000000
χ758-88-8-40044-42-4−1−3i3−1+3i3-4-21+3i31−3i3-241+3i31−3i32−1−3i3−1+3i340022-2-20000000000000000000000000000000000000000000000000000
χ768-88-8-40044-42-4−1+3i3−1−3i3-4-21−3i31+3i3-241−3i31+3i32−1+3i3−1−3i340022-2-20000000000000000000000000000000000000000000000000000
χ778-88-8-40044-4-422224-2-24-2-2-2-422-200-1-1110000000033−3333−330000000000000000000000000000000000000000
χ788-88-8-40044-4-422224-2-24-2-2-2-422-200-1-11100000000−3333−33330000000000000000000000000000000000000000
χ798-8-88800-88-82-4224222-24-2-2-2-2-2-400-44-440000000000000000000000000000000000000000000000000000
χ808-8-88800-88-8-42-4-4-2-4-4-44-2444442002-22-20000000000000000000000000000000000000000000000000000
χ818-8-88-4004-442-4−1−3i3−1+3i342−1−3i3−1+3i3-241+3i31−3i3-21+3i31−3i3-4002-22-20000000000000000000000000000000000000000000000000000
χ828-8-88-4004-442-4−1+3i3−1−3i342−1+3i3−1−3i3-241−3i31+3i3-21−3i31+3i3-4002-22-20000000000000000000000000000000000000000000000000000
χ838-8-88-4004-44-4222-2-4224-2-2-24-2-2200-11-110000000033−33−33330000000000000000000000000000000000000000
χ848-8-88-4004-44-4222-2-4224-2-2-24-2-2200-11-1100000000−333333−330000000000000000000000000000000000000000

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