Finite Group Databasebeta

← Group #13156534

Character table — Group #13156534

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222244444444444444444488888888888888181818181818181818181818242424242424242424242424242424242424242424242424242424363636363636363636363636216
order1222333446666666663336666666661212121212123666121212121212121212124444888888884441212121212121212121212121212121212121212121212121212121224242424242424242
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ511111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-111-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-11-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-11-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-20000000000000000000000000000000000022-2-2000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000000-2-222000000000
χ11222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-122220000000002222220000-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1000000000
χ12222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222000000000-2-2-2-2-2-200001111111111110000-1-1-1-1000000000
χ13222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-20000000002-222-2-20000-1-111-1-1-1-1111100001111000000000
χ14222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2000000000-22-2-222000011-1-11111-1-1-1-100001111000000000
χ15222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-2111122-2-20000000000000000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i30000-1-111000000000
χ16222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-2111122-2-20000000000000000000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i30000-1-111000000000
χ17222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111-2-2220000000000000000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i3000011-1-1000000000
χ18222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111-2-2220000000000000000000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i3000011-1-1000000000
χ1922222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-100000000222220200-1-122-1-100220000-1-1-1-1-1-1-1-100000000-1-1-1-10
χ2022222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1000000002222-20-20011-2-21100-2-200001111111100000000-1-1-1-10
χ2122222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-2-2-220-2001122-1-100-2-200001111-1-1-1-10000000011110
χ2222222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-2-2-2-20200-1-1-2-21100220000-1-1-1-111110000000011110
χ232222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-1000022220000220-1-100-1-1222200-1-1-1-10000-1-1-1-10000-1-1-1-100000
χ242222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-1000022220000-2-20110011-2-2-2-2001111000011110000-1-1-1-100000
χ252222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-200002-201100-1-122-2-20011110000-1-1-1-10000111100000
χ262222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-20000-220-1-10011-2-22200-1-1-1-1000011110000111100000
χ2722-2-22222-2-2-22-2-222-2-2222-2-2-2-222-2-222-22-2-222-2-222-22-22-222-2-200002i2i−2i−2i000000000000000000000000000000000002i2i−2i−2i00000
χ2822-2-22222-2-2-22-2-222-2-2222-2-2-2-222-2-222-22-2-222-2-222-22-22-222-2-20000−2i−2i2i2i00000000000000000000000000000000000−2i−2i2i2i00000
χ2922-2-2222-22-2-22-2-222-2-2222-2-2-2-222-2-22-22-222-22-2-22-22-22-22-2-222000000002i2i−2i−2i000000000000000000000000000000000002i2i−2i−2i0
χ3022-2-2222-22-2-22-2-222-2-2222-2-2-2-222-2-22-22-222-22-2-22-22-22-22-2-22200000000−2i−2i2i2i00000000000000000000000000000000000−2i−2i2i2i0
χ3122-2-22-12-22-212-212-1-2-2-12-111-212-1-21-1-22-2-121-111-1-221-11-111-1-1000000002i2i−2i−2i000003−300−i3i3000000003−33−3−i3−i3i3i300000000−i−iii0
χ3222-2-22-12-22-212-212-1-2-2-12-111-212-1-21-1-22-2-121-111-1-221-11-111-1-1000000002i2i−2i−2i00000−3300i3−i300000000−33−33i3i3−i3−i300000000−i−iii0
χ3322-2-22-12-22-212-212-1-2-2-12-111-212-1-21-1-22-2-121-111-1-221-11-111-1-100000000−2i−2i2i2i000003−300i3−i3000000003−33−3i3i3−i3−i300000000ii−i−i0
χ3422-2-22-12-22-212-212-1-2-2-12-111-212-1-21-1-22-2-121-111-1-221-11-111-1-100000000−2i−2i2i2i00000−3300−i3i300000000−33−33−i3−i3i3i300000000ii−i−i0
χ3522-2-2-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-1-212-111-1-112-2-11-1-11100002i2i−2i−2i00000003−300−i3i30000003−33−30000−i3i3−i3i30000−i−iii00000
χ3622-2-2-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-1-212-111-1-112-2-11-1-11100002i2i−2i−2i0000000−3300i3−i3000000−33−330000i3−i3i3−i30000−i−iii00000
χ3722-2-2-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-1-212-111-1-112-2-11-1-1110000−2i−2i2i2i00000003−300i3−i30000003−33−30000i3−i3i3−i30000ii−i−i00000
χ3822-2-2-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-1-212-111-1-112-2-11-1-1110000−2i−2i2i2i0000000−3300−i3i3000000−33−330000−i3i3−i3i30000ii−i−i00000
χ392-22-2222002-2-2-22-2-22-22222-22-2-2-2-22-200000022-2-20000000000002i−2i2−22−2−i2i2−i2i2000000000000000000000000000002i−2i2−22−2−i2i2−i2i20
χ402-22-2222002-2-2-22-2-22-22222-22-2-2-2-22-200000022-2-20000000000002i−2i−22−22i2−i2i2−i2000000000000000000000000000002i−2i−22−22i2−i2i2−i20
χ412-22-2222002-2-2-22-2-22-22222-22-2-2-2-22-200000022-2-2000000000000−2i2i2−22−2i2−i2i2−i200000000000000000000000000000−2i2i2−22−2i2−i2i2−i20
χ422-22-2222002-2-2-22-2-22-22222-22-2-2-2-22-200000022-2-2000000000000−2i2i−22−22−i2i2−i2i200000000000000000000000000000−2i2i−22−22−i2i2−i2i20
χ432-2-2222200-22-22-2-2-2-22222-22-22-2-22-2-20000002-22-200000000002i−2i00−i2i2i2−i22−2−220000000000000000000000000002i−2i00−i2i2i2−i22−2−220
χ442-2-2222200-22-22-2-2-2-22222-22-22-2-22-2-20000002-22-200000000002i−2i00i2−i2−i2i2−222−20000000000000000000000000002i−2i00i2−i2−i2i2−222−20
χ452-2-2222200-22-22-2-2-2-22222-22-22-2-22-2-20000002-22-20000000000−2i2i00−i2i2i2−i2−222−2000000000000000000000000000−2i2i00−i2i2i2−i2−222−20
χ462-2-2222200-22-22-2-2-2-22222-22-22-2-22-2-20000002-22-20000000000−2i2i00i2−i2−i2i22−2−22000000000000000000000000000−2i2i00i2−i2−i2i22−2−220
χ4744444-24-4-44-244-24-244-24-2-2-24-24-24-2-2-4-4-42-42-2-2-2-2-4-4222222220000000000000000000000000000000000000000000000000000
χ4844444-2-2444-2-24-24-2-2-2-2-21-2-2-21-21-21-2-2-24-24-21111-2-211-2-2111100000000000000400-2-2000000-2-20000111100000000000000000
χ4944444-2-2444-2-24-24-2-2-2-2-21-2-2-21-21-21-2-2-24-24-21111-2-211-2-2111100000000000000-40022000000220000-1-1-1-100000000000000000
χ5044444-2-2-4-44-2-24-24-2-2-2-2-21-2-2-21-21-21-222-42-42111122-1-122-1-1-1-10000000000000000000000000−2i32i30000i3i3−i3−i300000000000000000
χ5144444-2-2-4-44-2-24-24-2-2-2-2-21-2-2-21-21-21-222-42-42111122-1-122-1-1-1-100000000000000000000000002i3−2i30000−i3−i3i3i300000000000000000
χ524444-244-4-4-244-24-2444-2-24-2-2-24-24-24-2-4-42-42-4-2-2-2-222-4-42222220000000000000000000000000000000000000000000000000000
χ534444-24-244-24-2-24-24-2-2-21-2-2-21-21-21-2-2-2-2-24-24111111-2-2-2-21111000000000000040-2-2000000-2-2001111000000000000000000000
χ544444-24-244-24-2-24-24-2-2-21-2-2-21-21-21-2-2-2-2-24-24111111-2-2-2-211110000000000000-40220000002200-1-1-1-1000000000000000000000
χ554444-24-2-4-4-24-2-24-24-2-2-21-2-2-21-21-21-2-2222-42-41111-1-12222-1-1-1-100000000000000000000000−2i32i300i3i3−i3−i3000000000000000000000
χ564444-24-2-4-4-24-2-24-24-2-2-21-2-2-21-21-21-2-2222-42-41111-1-12222-1-1-1-1000000000000000000000002i3−2i300−i3−i3i3i3000000000000000000000
χ574444-2-2444-2-24-2-2-2-2441-2-211-2-2-2-2-2-2144-2-2-2-21111-2-2-2-21111110000000000004000000-2-2-2-200000000000011110000000000000
χ584444-2-2444-2-24-2-2-2-2441-2-211-2-2-2-2-2-2144-2-2-2-21111-2-2-2-2111111000000000000-40000002222000000000000-1-1-1-10000000000000
χ594444-2-24-4-4-2-24-2-2-2-2441-2-211-2-2-2-2-2-21-4-4222211112222-1-1-1-1-1-1000000000000000000000000000000000003-3-330000000000000
χ604444-2-24-4-4-2-24-2-2-2-2441-2-211-2-2-2-2-2-21-4-4222211112222-1-1-1-1-1-100000000000000000000000000000000000-333-30000000000000
χ6144-4-444-24-4-4-4-2-4-444224-2-2-4-422-2-2224-224-4-44-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000000000
χ6244-4-444-2-44-4-4-2-4-444224-2-2-4-422-2-22242-2-444-4-222-22-22-2-4422-2-20000000000000000000000000000000000000000000000000000
χ6344-4-44-244-4-424-424-2-4-4-24-222-424-2-42-24-442-4-2-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000000000
χ6444-4-44-2-24-4-42-2-424-222-2-21222-1-212-1-2-2242-4-21-1-11-221-1-2211-1-100000000000000000000000000000003i−3i−3i3i00000000000000000
χ6544-4-44-2-24-4-42-2-424-222-2-21222-1-212-1-2-2242-4-21-1-11-221-1-2211-1-10000000000000000000000000000000−3i3i3i−3i00000000000000000
χ6644-4-44-2-2-44-42-2-424-222-2-21222-1-212-1-22-2-4-2421-1-112-2-112-2-1-1110000000000000000023−23000000000000−33−3300000000000000000
χ6744-4-44-2-2-44-42-2-424-222-2-21222-1-212-1-22-2-4-2421-1-112-2-112-2-1-11100000000000000000−23230000000000003−33−300000000000000000
χ6844-4-4-244-442-442-4-24-4-4-2-24222-4-242-4-2-4424-2-4-222-22-2-442-222-2-20000000000000000000000000000000000000000000000000000
χ6944-4-4-24-24-42-4-22-4-2422-21-222-121-2-12-2-22-2-4241-1-111-1-22-2211-1-100000000000000023−230000000000−33−33000000000000000000000
χ7044-4-4-24-24-42-4-22-4-2422-21-222-121-2-12-2-22-2-4241-1-111-1-22-2211-1-1000000000000000−232300000000003−33−3000000000000000000000
χ7144-4-4-24-2-442-4-22-4-2422-21-222-121-2-12-22-224-2-41-1-11-112-22-2-1-1110000000000000000000000000003i−3i−3i3i000000000000000000000
χ7244-4-4-24-2-442-4-22-4-2422-21-222-121-2-12-22-224-2-41-1-11-112-22-2-1-111000000000000000000000000000−3i3i3i−3i000000000000000000000
χ7344-4-4-2-244-422422-2-2-4-41-2-2-1-122-2-22214-4-222-21-1-11-22-221-111-1-10000000000000000000−2i32i300000000000000i3−i3i3−i30000000000000
χ7444-4-4-2-244-422422-2-2-4-41-2-2-1-122-2-22214-4-222-21-1-11-22-221-111-1-100000000000000000002i3−2i300000000000000−i3i3−i3i30000000000000
χ7544-4-4-2-24-4422422-2-2-4-41-2-2-1-122-2-2221-442-2-221-1-112-22-2-11-1-111000000000000000000000−2i32i3000000000000i3i3−i3−i30000000000000
χ7644-4-4-2-24-4422422-2-2-4-41-2-2-1-122-2-2221-442-2-221-1-112-22-2-11-1-1110000000000000000000002i3−2i3000000000000−i3−i3i3i30000000000000
χ774-44-444-2004-42-44-4-4-224-2-24-4-22222-2-4000000-2-2220000000000004i−4i0000000000000000000000000000000000000−2i2i000000000
χ784-44-444-2004-42-44-4-4-224-2-24-4-22222-2-4000000-2-222000000000000−4i4i00000000000000000000000000000000000002i−2i000000000
χ794-44-44-240042-4-4-2-424-4-24-2-2242-42-4-22000000-2-222000000000000000000−2i22i2−2i22i200000000000000000000000000000000000i2−i2i2−i20
χ804-44-44-240042-4-4-2-424-4-24-2-2242-42-4-22000000-2-2220000000000000000002i2−2i22i2−2i200000000000000000000000000000000000−i2i2−i2i20
χ814-44-4-24400-2-4-4242-44-4-2-24-22-2-42-4242000000-2-2220000000000000022−2222−2200000000000000000000000000000000000−22−2200000
χ824-44-4-24400-2-4-4242-44-4-2-24-22-2-42-4242000000-2-22200000000000000−2222−2222000000000000000000000000000000000002−22−200000
χ834-4-4444-200-4424-4-4-42-24-2-2-442-222-22-4000000-22-2200000000004i−4i0000000000000000000000000000000000000−2i2i00000000000
χ844-4-4444-200-4424-4-4-42-24-2-2-442-222-22-4000000-22-220000000000−4i4i00000000000000000000000000000000000002i−2i00000000000
χ854-4-444-2400-4-2-442-42-44-24-22-2-4-2-42422000000-22-2200000000000000000022−22−222200000000000000000000000000000000000−222−20
χ864-4-444-2400-4-2-442-42-44-24-22-2-4-2-42422000000-22-22000000000000000000−222222−22000000000000000000000000000000000002−2−220
χ874-4-44-2440024-4-2-42-4-44-2-242-2242-4-2-42000000-22-2200000000000000−2i22i22i2−2i200000000000000000000000000000000000i2−i2−i2i200000
χ884-4-44-2440024-4-2-42-4-44-2-242-2242-4-2-42000000-22-22000000000000002i2−2i2−2i22i200000000000000000000000000000000000−i2i2i2−i200000
χ898888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000000
χ908888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000
χ9188-8-8-4-4-48-844-444-4-444222-2-2-2-222-2-22-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-8844-444-4-444222-2-2-2-222-2-224-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000000
χ938-88-88-4-400844-8-4-84-44-4-42-44-4-24-242400000022-2-200000000000000000000000000000000000000000000000000000000000000
χ948-88-8-48-400-4-84484-8-44-42-4-4424-24-2-4400000022-2-200000000000000000000000000000000000000000000000000000000000000
χ958-88-8-4-4800-44-84-4448-82-4-42-2-44444-4-200000022-2-200000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-400-4444-444-442222-22-2-2-2-22-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-400-4444-444-442222-22-2-2-2-22-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000
χ988-8-888-4-400-8-4484-844-4-4-424-4424-2-4-240000002-22-200000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-400484-4-84-84-4-42-44-4-2-4-242440000002-22-200000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48004-4-8-4444-882-4-4-224-444-44-20000002-22-200000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4004-44-44444-4222-22-22-2-22-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4004-44-44444-4222-22-22-2-22-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000

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