Finite Group Databasebeta

← Group #13169249

Character table — Group #13169249

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612124436661212121212121212121212122444412121212121212122244444466661212121212121212121212121212121244661212121212122212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-1111111-1-1-1-111-1-1-1-11111-1-111-1111-1-1-1-111111-1-1-111-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-11-11111-1-1111111-1-1-1-1-1-1-1-1-1-1111-111-1-111111111-1111-1-1-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-1-11-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-11111111111111111111-11-1-111-1-111-1-1-1-11111111111-111-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-11-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-11-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11-1-1-11111-1-1-1-11-1-1-111-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1111111-1-111-1-11111-1-1-1-11-1-1-111-1-111-1-11-111-1-1-1-111111-1-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-11111-1-1-11-1-111-1-11111-11-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111111111-1-111-1-1-1-1-1-1-111-11111-1-111-1-1-1-1111111-1-1-1-1-1-11
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1-11111-1-1111111111-1-11-1-1-1-111-1-111-1-1111111-1-111-1-1-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-111-1-11111-1-11111-1-11-111-1-111-1-1-1-111-11-1-111-1-111-1-1-111
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1111-1-111-1-1111-111-1-1-1-111-1-11-11
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1
χ17222222-1-12-122222-1-1-122-1-12-12-12-1-12222-1-1-1-1-1222-1-1-1-1-1-1-1-1020222200-1-1-1-12200000000002-1202-100-1-1-1-1-1-1-1-102-1-1000000000-10
χ18222222-1-12-122222-1-1-122-1-12-12-12-1-12222-1-1-1-1-1222-1-1-1-1-1-1-1-10-202-22200-1-111-2-20000000000-2120-2-1001111-1-1-1-10-21100000000010
χ19222222-1-12-122222-1-1-122-1-12-12-12-1-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1020-22-2-20011-1-1-2-200000000002-1-202100-1-1-1-111110-21100000000010
χ20222222-1-12-122222-1-1-122-1-12-12-12-1-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10-20-2-2-2-2001111220000000000-21-20-21001111111102-1-1000000000-10
χ21222222-1-12-122222-1-1-12-2-1-12-12-12-1-1-2-222-1-1-1-11-2-2-211111111020-2-22200-1-111-2-200000000002-1-20-210011-1-1-1-1110211000000000-10
χ22222222-1-12-122222-1-1-12-2-1-12-12-12-1-1-2-222-1-1-1-11-2-2-2111111110-20-222200-1-1-1-1220000000000-21-202100-1-111-1-1110-2-1-100000000010
χ23222222-1-12-122222-1-1-12-2-1-12-12-12-1-1-2-2-2-2-1-1-1-11-2-2-2111111110202-2-2-20011112200000000002-120-2-10011-1-111-1-10-2-1-100000000010
χ24222222-1-12-122222-1-1-12-2-1-12-12-12-1-1-2-2-2-2-1-1-1-11-2-2-2111111110-2022-2-20011-1-1-2-20000000000-21202-100-1-11111-1-10211000000000-10
χ2522222-12222-1-122-122-1-122-1-1-1-12-12-12222-1-1-1-12-1-1-1-1-122-1-1-1-120220-1-1-1-12200002200002-1-1-100-1202-1-10000-1-1-1-12000-1-1000000-100
χ2622222-12222-1-122-122-1-122-1-1-1-12-12-12222-1-1-1-12-1-1-1-1-122-1-1-1-1-20-220-1-111220000-2-20000-211100-1-202110000-1-1-1-1-200011000000100
χ2722222-12222-1-122-122-1-122-1-1-1-12-12-122-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1202-2011-1-1-2-20000-2-200002-1-1-100120-2-1-100001111-200011000000100
χ2822222-12222-1-122-122-1-122-1-1-1-12-12-122-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2-201111-2-20000220000-2111001-20-211000011112000-1-1000000-100
χ2922222-12222-1-122-122-1-1-22-1-1-1-12-12-1-2-222-1-1-1-1-211111-2-2111120-2-20-1-111220000-2-200002-1-1-1001-20-2110000-1-111200011000000-100
χ3022222-12222-1-122-122-1-1-22-1-1-1-12-12-1-2-222-1-1-1-1-211111-2-21111-202-20-1-1-1-1220000220000-211100120-2-1-10000-1-111-2000-1-1000000100
χ3122222-12222-1-122-122-1-1-22-1-1-1-12-12-1-2-2-2-2-1-1-1-1-211111-2-2111120-2201111-2-200002200002-1-1-100-1-20211000011-1-1-2000-1-1000000100
χ3222222-12222-1-122-122-1-1-22-1-1-1-12-12-1-2-2-2-2-1-1-1-1-211111-2-21111-2022011-1-1-2-20000-2-20000-211100-1202-1-1000011-1-1200011000000-100
χ332222-1222-1222-1-122-12-12-12-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-1222020022002200002222-12-1-1-120-1-10-1-1-1-1-1-10000000000-1-1-1-100000
χ342222-1222-1222-1-122-12-12-12-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-12-220-2002200-2-20000-2-2-2-2-12-1-11-20-110-1-111110000000000111100000
χ352222-1222-1222-1-122-12-12-12-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-1-22-20200-2-200220000-2-2-2-21-211-1201-1011-1-1-1-10000000000111100000
χ362222-1222-1222-1-122-12-12-12-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-1-2-2-20-200-2-200-2-2000022221-2111-201101111110000000000-1-1-1-100000
χ372222-1222-1222-1-122-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-211-2-211111122-20-200-2-200-2-20000-2-222-12-1-1-1201101111-1-10000000000-1-11100000
χ382222-1222-1222-1-122-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-211-2-21111112-2-20200-2-20022000022-2-2-12-1-11-201-1011-1-111000000000011-1-100000
χ392222-1222-1222-1-122-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-211-2-2111111-2220-2002200-2-2000022-2-21-211-120-110-1-111-1-1000000000011-1-100000
χ402222-1222-1222-1-122-12-1-2-12-12-1-1-1-121100-1-1-1-1-2-211-2-2111111-2-2202002200220000-2-2221-2111-20-1-10-1-1-1-1110000000000-1-11100000
χ4122-2-2222-222-22-2-2-2-22220-2-2-222-2-22-2002i−2i2-2-22000000000000000002i−2i002i−2i0000002i−2i0000000000000000002i−2i00000000002i−2i2-2000
χ4222-2-2222-222-22-2-2-2-22220-2-2-222-2-22-2002i−2i2-2-22000000000000000002i−2i002i−2i000000−2i2i0000000000000000002i−2i0000000000−2i2i-22000
χ4322-2-2222-222-22-2-2-2-22220-2-2-222-2-22-200−2i2i2-2-2200000000000000000−2i2i00−2i2i0000002i−2i000000000000000000−2i2i00000000002i−2i-22000
χ4422-2-2222-222-22-2-2-2-22220-2-2-222-2-22-200−2i2i2-2-2200000000000000000−2i2i00−2i2i000000−2i2i000000000000000000−2i2i0000000000−2i2i2-2000
χ452-22-22222-2-2-2-22-22-2222022-2-2-2-22-2-2000022-2-200000000000000000000000002-22i−2i002i−2i00000000000000000000002-22i−2i2i−2i0000000
χ462-22-22222-2-2-2-22-22-2222022-2-2-2-22-2-2000022-2-200000000000000000000000002-2−2i2i00−2i2i00000000000000000000002-2−2i2i−2i2i0000000
χ472-22-22222-2-2-2-22-22-2222022-2-2-2-22-2-2000022-2-20000000000000000000000000-222i−2i00−2i2i0000000000000000000000-222i−2i−2i2i0000000
χ482-22-22222-2-2-2-22-22-2222022-2-2-2-22-2-2000022-2-20000000000000000000000000-22−2i2i002i−2i0000000000000000000000-22−2i2i2i−2i0000000
χ4944444-2-2-24-2-2-244-2-2-21-24-21-21-2-2-2-2144441111-2-2-2-211-2-2111100040-2-200-2-20000000000000000-200-20000001111000000000000000
χ5044444-2-2-24-2-2-244-2-2-21-24-21-21-2-2-2-2144-4-41111-2-2-2-211-2-21111000-4022002200000000000000002002000000-1-1-1-1000000000000000
χ5144444-2-2-24-2-2-244-2-2-21-2-4-21-21-2-2-2-21-4-44411112222-1-122-1-1-1-1000-40-2-200-2-20000000000000000200200000011-1-1000000000000000
χ5244444-2-2-24-2-2-244-2-2-21-2-4-21-21-2-2-2-21-4-4-4-411112222-1-122-1-1-1-1000402200220000000000000000-200-2000000-1-111000000000000000
χ534444-24-2-2-2-244-2-24-21-2-241-2-2-2-21-21-2-2-2001111-24-2-2-2-211111104004000000-2-2000000000000-2-200-200011110000000000000000000
χ544444-24-2-2-2-244-2-24-21-2-241-2-2-2-21-21-2-2-2001111-24-2-2-2-21111110-400-40000002200000000000022002000-1-1-1-10000000000000000000
χ554444-24-2-2-2-244-2-24-21-2-2-41-2-2-2-21-21-2220011112-42222-1-1-1-1-1-10400-400000022000000000000-2-2002000-1-1110000000000000000000
χ564444-24-2-2-2-244-2-24-21-2-2-41-2-2-2-21-21-2220011112-42222-1-1-1-1-1-10-4004000000-2-20000000000002200-200011-1-10000000000000000000
χ574444-2-244-24-2-2-2-2-24-2-214-2-21-21-21-2-2-2-20011114-211-2-2-2-211114040000-2-2000000000000-2-211000-2001100000000000000000000000
χ584444-2-244-24-2-2-2-2-24-2-214-2-21-21-21-2-2-2-20011114-211-2-2-2-21111-40-400002200000000000022-1-1000200-1-100000000000000000000000
χ594444-2-244-24-2-2-2-2-24-2-21-4-2-21-21-21-2-222001111-42-1-12222-1-1-1-140-4000022000000000000-2-211000200-1-100000000000000000000000
χ604444-2-244-24-2-2-2-2-24-2-21-4-2-21-21-21-2-222001111-42-1-12222-1-1-1-1-4040000-2-200000000000022-1-1000-2001100000000000000000000000
χ6144-4-444-224-2-44-4-4-42-2-24022-4-242-4-22004i−4i-222-2000000000000000004i−4i00−2i2i00000000000000000000000000−2i2i00000000000000000
χ6244-4-444-224-2-44-4-4-42-2-24022-4-242-4-2200−4i4i-222-200000000000000000−4i4i002i−2i000000000000000000000000002i−2i00000000000000000
χ6344-4-44-24-4442-2-4-42-44-2-20-422-2-2-4242004i−4i-222-200000000000000000−2i2i004i−4i00000000000000000000000000−2i2i00000000000000000
χ6444-4-44-24-4442-2-4-42-44-2-20-422-2-2-424200−4i4i-222-2000000000000000002i−2i00−4i4i000000000000000000000000002i−2i00000000000000000
χ6544-4-44-2-224-22-2-4-422-21-202-121-222-2-1004i−4i1-1-1100003-30033-3-300000−2i2i00−2i2i00000000000000000000000000i−i3i−3i000000000000000
χ6644-4-44-2-224-22-2-4-422-21-202-121-222-2-1004i−4i1-1-110000-3300-3-33300000−2i2i00−2i2i00000000000000000000000000i−i−3i3i000000000000000
χ6744-4-44-2-224-22-2-4-422-21-202-121-222-2-100−4i4i1-1-1100003-30033-3-3000002i−2i002i−2i00000000000000000000000000−ii−3i3i000000000000000
χ6844-4-44-2-224-22-2-4-422-21-202-121-222-2-100−4i4i1-1-110000-3300-3-333000002i−2i002i−2i00000000000000000000000000−ii3i−3i000000000000000
χ6944-4-4-244-4-24-4422-4-4-24-202-424-222-2-40000-222-2000000000000000000000000000004i−4i000000000000000000000000000000−2i2i00000
χ7044-4-4-244-4-24-4422-4-4-24-202-424-222-2-40000-222-200000000000000000000000000000−4i4i0000000000000000000000000000002i−2i00000
χ714-44-444-2-2-42-4-44-442-2-240-2-2-42-424220000-2-22200000000000000000000000004-40000000000000000000000000000-2200000000000
χ724-44-444-2-2-42-4-44-442-2-240-2-2-42-424220000-2-2220000000000000000000000000-4400000000000000000000000000002-200000000000
χ734-44-44-244-4-4224-4-2-44-2-204-2222-4-2-420000-2-2220000000000000000000000000004i−4i0000000000000000000000000000−2i2i000000000
χ744-44-44-244-4-4224-4-2-44-2-204-2222-4-2-420000-2-222000000000000000000000000000−4i4i00000000000000000000000000002i−2i000000000
χ754-44-4-24442-4-4-4-224-4-24-20-242-422-22-40000-2-22200000000000000000000000000000004i−4i00000000000000000000000000−2i2i0000000
χ764-44-4-24442-4-4-4-224-4-24-20-242-422-22-40000-2-2220000000000000000000000000000000−4i4i000000000000000000000000002i−2i0000000
χ774-4-44444-4-4-44-4-44-444440-4-44-4-44-4-4400004-44-400000000000000000000000000000000000000000000000000000000000000000000
χ784-4-4444-22-424-4-44-4-2-2-2402242-4-2-42-20000-22-2200000000000000000000000−2i32i300000000000000000000−2i32i3000000000000000000000
χ794-4-4444-22-424-4-44-4-2-2-2402242-4-2-42-20000-22-22000000000000000000000002i3−2i3000000000000000000002i3−2i3000000000000000000000
χ804-4-444-24-4-4-4-22-44244-2-20-42-22242-4-20000-22-22000000000000000000023−23000000000000000000000023−2300000000000000000000000
χ814-4-444-24-4-4-4-22-44244-2-20-42-22242-4-20000-22-220000000000000000000−23230000000000000000000000−232300000000000000000000000
χ824-4-44-244-42-44-42-2-44-24-202-4-2-42-222423−2300-22-220023−230023−2323−2323−2300000000000000000000000000000000000000000000000000000000
χ834-4-44-244-42-44-42-2-44-24-202-4-2-42-2224−232300-22-2200−232300−2323−2323−232300000000000000000000000000000000000000000000000000000000
χ844-4-44-24-22224-42-2-4-21-2-20-12-22212-1-223−23001-11-10023−2300−33−33−3300000000000−2i32i300000000000000000000i3−i33i−3i0000000000000000000
χ854-4-44-24-22224-42-2-4-21-2-20-12-22212-1-223−23001-11-10023−2300−33−33−33000000000002i3−2i300000000000000000000−i3i3−3i3i0000000000000000000
χ864-4-44-24-22224-42-2-4-21-2-20-12-22212-1-2−2323001-11-100−2323003−33−33−300000000000−2i32i300000000000000000000i3−i3−3i3i0000000000000000000
χ874-4-44-24-22224-42-2-4-21-2-20-12-22212-1-2−2323001-11-100−2323003−33−33−3000000000002i3−2i300000000000000000000−i3i33i−3i0000000000000000000
χ884-4-44-2-24-42-4-222-224-2-2102212-1-2-12-223−23001-11-100−330023−23−33−33000000023−23000000000000003-3000000−3300000000000000000000000
χ894-4-44-2-24-42-4-222-224-2-2102212-1-2-12-223−23001-11-100−330023−23−33−330000000−232300000000000000-330000003−300000000000000000000000
χ904-4-44-2-24-42-4-222-224-2-2102212-1-2-12-2−2323001-11-1003−300−23233−33−3000000023−2300000000000000-33000000−3300000000000000000000000
χ914-4-44-2-24-42-4-222-224-2-2102212-1-2-12-2−2323001-11-1003−300−23233−33−30000000−2323000000000000003-30000003−300000000000000000000000
χ928888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ938888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9488-8-8-48-44-4-4-8844-842-4-40-244-4-4-242400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-48-8-484-4444-8-4-42044-2-424-2-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-44-4-44-444442220-2-2-222-2-22-20000-111-100006-600-3-33300000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-44-4-44-444442220-2-2-222-2-22-20000-111-10000-660033-3-300000000000000000000000000000000000000000000000000000000
χ988-88-88-4-4-4-84448-8-44-42-40-424-244-44-2000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ998-88-8-48-4-444-8-8-44842-4-402-4444-2-4-24000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4884-844-44-4-8-4-420-4-4-24-24244000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-4-44444-44-44222022-2-2-2-22-2-20000-1-1110000000033−33−333300000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4-44444-44-44222022-2-2-2-22-2-20000-1-11100000000−333333−3300000000000000000000000000000000000000000000000000000000
χ1038-8-888-4-44-84-44-884-4-42-404-2-4-24-444200002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-4444-444-44-42220-2-22-2-22-2-2243−4300-11-1100−232300−23233−33−300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4444-444-44-42220-2-22-2-22-2-22−434300-11-110023−230023−23−33−3300000000000000000000000000000000000000000000000000000000

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