Finite Group Databasebeta

← Group #13167067

Character table — Group #13167067

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
χ112222-122-1-1-122-1-12222-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1222222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-100000000000000
χ122222-122-1-1-122-1-12222-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-2-21111-2-21111-2-21111-1-1-1-100000000000000
χ132222-122-1-1-122-1-12222-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3111100000000000000
χ142222-122-1-1-122-1-12222-1-1-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3111100000000000000
χ152222-1-2-2-1-1-122-1-12222-1-1-1-12-1-1211-1-1-1-1-2-21111-2-2111122-2-200−i3i3i3−i300−i3−i3i3i300i3i3−i3−i311-1-100000000000000
χ162222-1-2-2-1-1-122-1-12222-1-1-1-12-1-1211-1-1-1-1-2-21111-2-2111122-2-200i3−i3−i3i300i3i3−i3−i300−i3−i3i3i311-1-100000000000000
χ172222-1-2-2-1-1-122-1-12222-1-1-1-12-1-1211-1-1-1-1-2-21111-2-21111-2-2222-2-1-11122-1-1-1-1-2-21111-1-11100000000000000
χ182222-1-2-2-1-1-122-1-12222-1-1-1-12-1-1211-1-1-1-1-2-21111-2-21111-2-222-2211-1-1-2-2111122-1-1-1-1-1-11100000000000000
χ1922-2-22002-2-2222222-2-222-2-2-2-2-2-20022-2-2000000000000002-20000000000000000002-200000022-2-2000000
χ2022-2-22002-2-2222222-2-222-2-2-2-2-2-20022-2-2000000000000002-20000000000000000002-2000000-2-222000000
χ2122-2-22002-2-2222222-2-222-2-2-2-2-2-20022-2-200000000000000-22000000000000000000-220022-2-20000000000
χ2222-2-22002-2-2222222-2-222-2-2-2-2-2-20022-2-200000000000000-22000000000000000000-2200-2-2220000000000
χ232-22-2200-22-22222-2-222-2-222-2-2-2-2002-22-20000000000002-200000000000000000000002-22−22−22−22−2000000
χ242-22-2200-22-22222-2-222-2-222-2-2-2-2002-22-20000000000002-200000000000000000000002-2−22−22−22−22000000
χ252-22-2200-22-22222-2-222-2-222-2-2-2-2002-22-2000000000000-220000000000000000000000-222−22−2−22−22000000
χ262-22-2200-22-22222-2-222-2-222-2-2-2-2002-22-2000000000000-220000000000000000000000-22−22−222−22−2000000
χ272-2-2222-2-2-222222-2-2-2-2-2-2-2-222222-22-2-222-222-2-22-222-2-2000000000000000000000000002−2−222−2−22000000
χ282-2-2222-2-2-222222-2-2-2-2-2-2-2-222222-22-2-222-222-2-22-222-2-200000000000000000000000000−222−2−222−2000000
χ292-2-222-22-2-222222-2-2-2-2-2-2-2-22222-222-2-22-22-2-222-22-2-222000000000000000000000000002−2−22−222−2000000
χ302-2-222-22-2-222222-2-2-2-2-2-2-2-22222-222-2-22-22-2-222-22-2-22200000000000000000000000000−222−22−2−22000000
χ3144444444441-2111-21-21111111-244-2-2-2-2111111-2-2-2-2-2-20000222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3244444444441-2111-21-21111111-244-2-2-2-2111111-2-2-2-2-2-20000-2-2-2-2-2-2111111111111000000000000000000
χ334444444444-21-2-2-21-21-2-2-2-2-2-2-21441111-2-2-2-2-2-2111111000000000000000000000000000000000022-1-1-1-1
χ344444444444-21-2-2-21-21-2-2-2-2-2-2-21441111-2-2-2-2-2-21111110000000000000000000000000000000000-2-21111
χ3544444-4-44441-2111-21-21111111-2-4-4-2-2-2-2-1-1-1-1-1-122222200002-222-2-2-1-1-1-1-1-1111111000000000000000000
χ3644444-4-44441-2111-21-21111111-2-4-4-2-2-2-2-1-1-1-1-1-12222220000-22-2-222111111-1-1-1-1-1-1000000000000000000
χ3744444-4-4444-21-2-2-21-21-2-2-2-2-2-2-21-4-41111222222-1-1-1-1-1-100000000000000000000000000000000002-2-1-111
χ3844444-4-4444-21-2-2-21-21-2-2-2-2-2-2-21-4-41111222222-1-1-1-1-1-10000000000000000000000000000000000-2211-1-1
χ394444-244-2-2-21-2−1−3i32−1+3i321-21-2−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2111111−1−3i32−1+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+3i321-21-2−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2111111−1−3i32−1+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+3i32−1−3i321-21-2−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2111111−1+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+3i32−1−3i321-21-2−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2111111−1+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+3i321-21-2−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2221111-1-11+3i321−3i321+3i321−3i3222-1-1-1-100002-2−1−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+3i321-21-2−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2221111-1-11+3i321−3i321+3i321−3i3222-1-1-1-10000-221+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+3i32−1−3i321-21-2−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2221111-1-11−3i321+3i321−3i321+3i3222-1-1-1-100002-2−1+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+3i32−1−3i321-21-2−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2221111-1-11−3i321+3i321−3i321+3i3222-1-1-1-10000-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000000
χ4744-4-4-200-22244-2-244-4-4-2-222-422-400-2-222000000000000004-4000000000000000000-220000000000000000
χ4844-4-4-200-22244-2-244-4-4-2-222-422-400-2-22200000000000000-440000000000000000002-20000000000000000
χ494-44-4-2002-2244-2-2-4-44422-2-2-422-400-22-220000000000004-40000000000000000000000-2200000000000000
χ504-44-4-2002-2244-2-2-4-44422-2-2-422-400-22-22000000000000-4400000000000000000000002-200000000000000
χ514-4-4444-4-4-441-211-12-12-1-1-1-1111-24-4-222-21-111-1-1-22-2-2220000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000
χ524-4-4444-4-4-441-211-12-12-1-1-1-1111-24-4-222-21-111-1-1-22-2-2220000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000
χ534-4-4444-4-4-44-21-2-22-12-12222-2-2-214-41-1-11-22-2-2221-111-1-1000000000000000000000000000000000000−i3i3−i3i3
χ544-4-4444-4-4-44-21-2-22-12-12222-2-2-214-41-1-11-22-2-2221-111-1-1000000000000000000000000000000000000i3−i3i3−i3
χ554-4-444-44-4-441-211-12-12-1-1-1-1111-2-44-222-2-11-1-1112-222-2-20000000000−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3000000000000000000
χ564-4-444-44-4-441-211-12-12-1-1-1-1111-2-44-222-2-11-1-1112-222-2-20000000000i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3000000000000000000
χ574-4-444-44-4-44-21-2-22-12-12222-2-2-21-441-1-112-222-2-2-11-1-111000000000000000000000000000000000000−i3i3i3−i3
χ584-4-444-44-4-44-21-2-22-12-12222-2-2-21-441-1-112-222-2-2-11-1-111000000000000000000000000000000000000i3−i3−i3i3
χ594-4-44-24-422-21-2−1−3i32−1+3i32-12-121+3i321−3i321+3i321−3i321−1−3i32−1+3i32-2-221-1-111-1−1−3i32−1+3i321+3i321−3i32-2211-1-10000000000−i3i3−3+i323−i323+i32−3−i32−i3i3−3+i323−i323+i32−3−i32000000000000000000
χ604-4-44-24-422-21-2−1−3i32−1+3i32-12-121+3i321−3i321+3i321−3i321−1−3i32−1+3i32-2-221-1-111-1−1−3i32−1+3i321+3i321−3i32-2211-1-10000000000i3−i33−i32−3+i32−3−i323+i32i3−i33−i32−3+i32−3−i323+i32000000000000000000
χ614-4-44-24-422-21-2−1+3i32−1−3i32-12-121−3i321+3i321−3i321+3i321−1+3i32−1−3i32-2-221-1-111-1−1+3i32−1−3i321−3i321+3i32-2211-1-10000000000−i3i33+i32−3−i32−3+i323−i32−i3i33+i32−3−i32−3+i323−i32000000000000000000
χ624-4-44-24-422-21-2−1+3i32−1−3i32-12-121−3i321+3i321−3i321+3i321−1+3i32−1−3i32-2-221-1-111-1−1+3i32−1−3i321−3i321+3i32-2211-1-10000000000i3−i3−3−i323+i323−i32−3+i32i3−i3−3−i323+i323−i32−3+i32000000000000000000
χ634-4-44-24-422-244-2-2-4-4-4-422224-2-24-22-222-24-4-2-2224-4-2-2220000000000000000000000000000000000000000
χ644-4-44-2-4422-21-2−1−3i32−1+3i32-12-121+3i321−3i321+3i321−3i321−1−3i32−1+3i32-22-21-1-11-111+3i321−3i32−1−3i32−1+3i322-2-1-1110000000000−i3i3−3+i323−i323+i32−3−i32i3−i33−i32−3+i32−3−i323+i32000000000000000000
χ654-4-44-2-4422-21-2−1−3i32−1+3i32-12-121+3i321−3i321+3i321−3i321−1−3i32−1+3i32-22-21-1-11-111+3i321−3i32−1−3i32−1+3i322-2-1-1110000000000i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i32000000000000000000
χ664-4-44-2-4422-21-2−1+3i32−1−3i32-12-121−3i321+3i321−3i321+3i321−1+3i32−1−3i32-22-21-1-11-111−3i321+3i32−1+3i32−1−3i322-2-1-1110000000000−i3i33+i32−3−i32−3+i323−i32i3−i3−3−i323+i323−i32−3+i32000000000000000000
χ674-4-44-2-4422-21-2−1+3i32−1−3i32-12-121−3i321+3i321−3i321+3i321−1+3i32−1−3i32-22-21-1-11-111−3i321+3i32−1+3i32−1−3i322-2-1-1110000000000i3−i3−3−i323+i323−i32−3+i32−i3i33+i32−3−i32−3+i323−i32000000000000000000
χ684-4-44-2-4422-244-2-2-4-4-4-422224-2-242-2-222-2-4422-2-2-4422-2-20000000000000000000000000000000000000000
χ698888-488-4-4-4-4222-42-422222-4222-4-4-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000
χ708888-4-8-8-4-4-4-4222-42-422222-422244-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000
χ7188-8-88008-8-82-4222-4-2422-2-2-2-2-2400-4-4440000000000000000000000000000000000000000000000000000
χ7288-8-88008-8-8-42-4-4-424-2-4-444444-20022-2-20000000000000000000000000000000000000000000000000000
χ7388-8-8-400-4442-4−1−3i3−1+3i32-4-24−1−3i3−1+3i31+3i31−3i3-21+3i31−3i340022-2-20000000000000000000000000000000000000000000000000000
χ7488-8-8-400-4442-4−1+3i3−1−3i32-4-24−1+3i3−1−3i31−3i31+3i3-21−3i31+3i340022-2-20000000000000000000000000000000000000000000000000000
χ7588-8-8-400-444-4222-424-222-2-24-2-2-200-1-1110000000033−3333−330000000000000000000000000000000000000000
χ7688-8-8-400-444-4222-424-222-2-24-2-2-200-1-11100000000−3333−33330000000000000000000000000000000000000000
χ778-88-8800-88-82-422-242-4-2-222-2-2-2400-44-440000000000000000000000000000000000000000000000000000
χ788-88-8800-88-8-42-4-44-2-4244-4-4444-2002-22-20000000000000000000000000000000000000000000000000000
χ798-88-8-4004-442-4−1−3i3−1+3i3-242-41+3i31−3i3−1−3i3−1+3i3-21+3i31−3i34002-22-20000000000000000000000000000000000000000000000000000
χ808-88-8-4004-442-4−1+3i3−1−3i3-242-41−3i31+3i3−1+3i3−1−3i3-21−3i31+3i34002-22-20000000000000000000000000000000000000000000000000000
χ818-88-8-4004-44-42224-2-42-2-2224-2-2-200-11-110000000033−33−33330000000000000000000000000000000000000000
χ828-88-8-4004-44-42224-2-42-2-2224-2-2-200-11-1100000000−333333−330000000000000000000000000000000000000000
χ838-8-88-48-844-4-42224-24-2-2-2-2-2-4222-44-111-1-4422-2-22-2-1-1110000000000000000000000000000000000000000
χ848-8-88-4-8844-4-42224-24-2-2-2-2-2-42224-4-111-14-4-2-222-2211-1-10000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).