Finite Group Databasebeta

← Group #13168509

Character table — Group #13168509

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612122236661212121212121212121212122444466661212121222444444666666121212121212121212121212121244661212121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-1111111-1-1-1-1-1-111-1-111111111-1-1-111111-1-1-1-11-1-1-1-1-111-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-11-1111111-1-111-1-1-1-1-1-111-1-111-1-11-1111111-1-11111-11-1-1-1-1-1-111-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-1-11-11111-1-1-1-11111-1-1-1-1-1-111-1-11-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-11111111111111111111-11-1-1-1-111111111-1-1-1-111-1-111-11111-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-11-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-11-1-1-1-1-1-111-1-1-1-1-11-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111111-1-1-1-1-111-1-1111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-111-1-111-1-111111111-1-11-1-1-1-1-1-1-111-1-11-1-1-111-1-111111-1-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-11-111-1-1-111-1-111-11-1-11111-1-111-11-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111111-1-11111-1-111-1-1-111-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1-111-1-1111111-1-1111-1-111111-1-1-1-111-1-111-1-1111111-1-1-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-111-1-11111-1-111-1-1111-11-1-1111-1-111-1-1-11-1-11111-1-1-1-1-111
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111-11111111-1-1111-1-1-111-1-111-1-11-11
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-11111-1-1-1-1-1-11111-1
χ17222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-12220200002222222200002-100-1-10-1-12-1000-1-1-1-1-1-100-1-1-1-1000000000
χ18222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-12-220-2000022-2-2-2-2-2-200002-100-1-10-11-21000-1-11111001111000000000
χ19222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-22-2020000-2-222-2-2-2-20000-21001101-12-100011-1-1-1-1001111000000000
χ20222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-20-20000-2-2-2-222220000-210011011-2100011111100-1-1-1-1000000000
χ21222222-1222-1-12-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-21111111122-20-20000-2-2-2-222-2-200002-100-1-10112-10001111-1-100-1-111000000000
χ22222222-1222-1-12-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-2111111112-2-2020000-2-222-2-22200002-100-1-101-1-2100011-1-1110011-1-1000000000
χ23222222-1222-1-12-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-211111111-2220-2000022-2-2-2-2220000-2100110-112-1000-1-111-1-10011-1-1000000000
χ24222222-1222-1-12-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-211111111-2-22020000222222-2-20000-2100110-1-1-21000-1-1-1-11100-1-111000000000
χ2522222-122-1-12222-122-1-122-1-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-12022022-1-1-1-10000002200-12-1-1-1-1-120002-1-1-1-10000200000-1-10000-100
χ2622222-122-1-12222-122-1-122-1-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-1-20-22022-1-111000000-2-2001-2-1-111-1-20002-1-1110000-200000110000100
χ2722222-122-1-12222-122-1-122-1-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1202-20-2-211-1-1000000-2-200-1211-1-112000-211-1-10000-200000110000100
χ2822222-122-1-12222-122-1-122-1-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2-20-2-2111100000022001-211111-2000-211110000200000-1-10000-100
χ2922222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-222-1-1-1-11-21111-2-2111120-2-2022-1-111000000-2-200-12-1-1-1-11-2000-211110000200000110000-100
χ3022222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-222-1-1-1-11-21111-2-21111-202-2022-1-1-1-100000022001-2-1-11112000-211-1-10000-200000-1-10000100
χ3122222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-2111120-220-2-211110000002200-1211-1-1-1-20002-1-1110000-200000-1-10000100
χ3222222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-21111-20220-2-211-1-1000000-2-2001-21111-120002-1-1-1-10000200000110000-100
χ332222-122-12222-122-1-1-122-1-12-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-102022-1-12200-1-10000002200-1-100202-12-1-1-100-1-1-1-102000000-1-1000-10
χ342222-122-12222-122-1-1-122-1-12-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-10-202-2-1-1220011000000-2-200-1-10020-21-2-1-1-10011110-20000001100010
χ352222-122-12222-122-1-1-122-1-12-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1020-2211-2-200-1-1000000-2-2001100-202-1211100-1-1-1-10-20000001100010
χ362222-122-12222-122-1-1-122-1-12-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-20-2-211-2-2001100000022001100-20-21-211100111102000000-1-1000-10
χ372222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-222-1-1-1-1-2111-2-2111111020-2-2-1-1220011000000-2-200-1-100-20-2-121110011-1-10200000011000-10
χ382222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-222-1-1-1-1-2111-2-21111110-20-22-1-12200-1-10000002200-1-100-2021-211100-1-1110-2000000-1-100010
χ392222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-21111110202-211-2-200110000002200110020-2-12-1-1-10011-1-10-2000000-1-100010
χ402222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-21111110-202211-2-200-1-1000000-2-20011002021-2-1-1-100-1-1110200000011000-10
χ4122-2-2222-22-2-2-222-2-22220-2-2-222-2-2-2200002-2-2200000000000000000000000002-2002i−2i2i−2i00000000000000000000002-2002i−2i2i−2i00000
χ4222-2-2222-22-2-2-222-2-22220-2-2-222-2-2-2200002-2-2200000000000000000000000002-200−2i2i−2i2i00000000000000000000002-200−2i2i−2i2i00000
χ4322-2-2222-22-2-2-222-2-22220-2-2-222-2-2-2200002-2-220000000000000000000000000-22002i−2i−2i2i0000000000000000000000-22002i−2i−2i2i00000
χ4422-2-2222-22-2-2-222-2-22220-2-2-222-2-2-2200002-2-220000000000000000000000000-2200−2i2i2i−2i0000000000000000000000-2200−2i2i2i−2i00000
χ452-22-22222-2-22-2-2-22-2222022-2-2-2-2-22-2002-222-2-2000000000000000002-22-20000002i−2i0000002-2000000000000000000002i−2i00002i−2i000
χ462-22-22222-2-22-2-2-22-2222022-2-2-2-2-22-2002-222-2-2000000000000000002-22-2000000−2i2i0000002-200000000000000000000−2i2i0000−2i2i000
χ472-22-22222-2-22-2-2-22-2222022-2-2-2-2-22-200-2222-2-200000000000000000-22-220000002i−2i000000-22000000000000000000002i−2i0000−2i2i000
χ482-22-22222-2-22-2-2-22-2222022-2-2-2-2-22-200-2222-2-200000000000000000-22-22000000−2i2i000000-2200000000000000000000−2i2i00002i−2i000
χ4944444-2-24-2-2-2-24-2-24-2-214-2-21-21-2-21-2-2-2001111-24-2-211-2-21111404000000-2-20000000000-2-200110-2000000110000000000000000000
χ5044444-2-24-2-2-2-24-2-24-2-214-2-21-21-2-21-2-2-2001111-24-2-211-2-21111-40-40000002200000000002200-1-102000000-1-10000000000000000000
χ5144444-2-24-2-2-2-24-2-24-2-21-4-2-21-21-2-21-2220011112-422-1-122-1-1-1-140-4000000220000000000-2-2001102000000-1-10000000000000000000
χ5244444-2-24-2-2-2-24-2-24-2-21-4-2-21-21-2-21-2220011112-422-1-122-1-1-1-1-404000000-2-200000000002200-1-10-2000000110000000000000000000
χ534444-24-2-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-20011114-2-2-2-2-211111104004000000-2-20000000000000000-2-2-2000001111000000000000000
χ544444-24-2-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-20011114-2-2-2-2-21111110-400-400000022000000000000000022200000-1-1-1-1000000000000000
χ554444-24-2-244-2-2-2-24-21-2-2-41-2-2-2-21-2-2122001111-422222-1-1-1-1-1-10400-40000002200000000000000002-2-200000-1-111000000000000000
χ564444-24-2-244-2-2-2-24-21-2-2-41-2-2-2-21-2-2122001111-422222-1-1-1-1-1-10-4004000000-2-20000000000000000-2220000011-1-1000000000000000
χ574444-2-24-2-2-244-24-2-2-21-24-21-21-2-21-2-244441111-2-211-2-2-2-2111100040-2-2-2-2000000000000001100-20000-211000000000000000000000
χ584444-2-24-2-2-244-24-2-2-21-24-21-21-2-21-2-244-4-41111-2-211-2-2-2-21111000-40222200000000000000-1-100200002-1-1000000000000000000000
χ594444-2-24-2-2-244-24-2-2-21-2-4-21-21-2-21-2-2-4-444111122-1-12222-1-1-1-1000-40-2-2-2-2000000000000001100200002-1-1000000000000000000000
χ604444-2-24-2-2-244-24-2-2-21-2-4-21-21-2-21-2-2-4-4-4-4111122-1-12222-1-1-1-100040222200000000000000-1-100-20000-211000000000000000000000
χ6144-4-444-2-44-4224-2-4-4-24-202-424-22-42-20000-222-200000000000000000000000004-40000000000000000000000000000-2200000000000
χ6244-4-444-2-44-4224-2-4-4-24-202-424-22-42-20000-222-20000000000000000000000000-4400000000000000000000000000002-200000000000
χ6344-4-44-24-4-22-4-4442-44-2-20-422-2-2-42240000-222-2000000000000000000000000000004i−4i0000000000000000000000000000−2i2i0000000
χ6444-4-44-24-4-22-4-4442-44-2-20-422-2-2-42240000-222-200000000000000000000000000000−4i4i00000000000000000000000000002i−2i0000000
χ6544-4-4-24424-4-4-4-24-42-2-24022-4-2422-4-20000-222-200000000000000000000000000000004i−4i0000000000000000000000000000−2i2i00000
χ6644-4-4-24424-4-4-4-24-42-2-24022-4-2422-4-20000-222-20000000000000000000000000000000−4i4i00000000000000000000000000002i−2i00000
χ674-44-444-24-4-4-22-424-4-24-20-242-422-4-220000-2-2220000000000000000000000000004i−4i0000000000000000000000000000−2i2i000000000
χ684-44-444-24-4-4-22-424-4-24-20-242-422-4-220000-2-222000000000000000000000000000−4i4i00000000000000000000000000002i−2i000000000
χ694-44-44-244224-4-4-4-2-44-2-204-2222-42-2-4004-4-2-222000000000000000004-4-2200000000000000-220000000000000000000000000000000
χ704-44-44-244224-4-4-4-2-44-2-204-2222-42-2-400-44-2-22200000000000000000-442-2000000000000002-20000000000000000000000000000000
χ714-44-4-244-2-4-44-42-442-2-240-2-2-42-42242004-4-2-22200000000000000000-224-400000000000000-220000000000000000000000000000000
χ724-44-4-244-2-4-44-42-442-2-240-2-2-42-4224200-44-2-222000000000000000002-2-44000000000000002-20000000000000000000000000000000
χ734-44-4-2-24-2224-42-4-22-21-20-212-122-1-22004-411-1-1003i−3i00003i3i−3i−3i00000-22-22000000000000001-1000000003i−3i000000000000000000000
χ744-44-4-2-24-2224-42-4-22-21-20-212-122-1-22004-411-1-100−3i3i0000−3i−3i3i3i00000-22-22000000000000001-100000000−3i3i000000000000000000000
χ754-44-4-2-24-2224-42-4-22-21-20-212-122-1-2200-4411-1-1003i−3i00003i3i−3i−3i000002-22-200000000000000-1100000000−3i3i000000000000000000000
χ764-44-4-2-24-2224-42-4-22-21-20-212-122-1-2200-4411-1-100−3i3i0000−3i−3i3i3i000002-22-200000000000000-11000000003i−3i000000000000000000000
χ774-4-44444-4-44-44-4-4-444440-4-44-4-444-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000000
χ784-4-4444-2-4-442-2-42-44-24-202-4-2-42-242223−2300-22-22000023−2323−2323−2323−2300000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-442-2-42-44-24-202-4-2-42-2422−232300-22-220000−2323−2323−2323−232300000000000000000000000000000000000000000000000000000000
χ804-4-444-24-42-2-44-4-4244-2-20-42-2224-22-40000-22-2200000000000000000000023−2300000000000000000000000023−230000000000000000000
χ814-4-444-24-42-2-44-4-4244-2-20-42-2224-22-40000-22-22000000000000000000000−2323000000000000000000000000−23230000000000000000000
χ824-4-444-2-2-42-22-2-4224-2-2102212-1-2-2-1223−23001-11-10000−3323−23−33−3300000000023−23000000000000003-300000000−330000000000000000000
χ834-4-444-2-2-42-22-2-4224-2-2102212-1-2-2-1223−23001-11-10000−3323−23−33−33000000000−232300000000000000-33000000003−30000000000000000000
χ844-4-444-2-2-42-22-2-4224-2-2102212-1-2-2-12−2323001-11-100003−3−23233−33−300000000023−2300000000000000-3300000000−330000000000000000000
χ854-4-444-2-2-42-22-2-4224-2-2102212-1-2-2-12−2323001-11-100003−3−23233−33−3000000000−2323000000000000003-3000000003−30000000000000000000
χ864-4-44-2442-44-442-4-4-2-2-2402242-4-2-2-420000-22-2200000000000000000000000−2i32i3000000000000000000000000−2i32i300000000000000000
χ874-4-44-2442-44-442-4-4-2-2-2402242-4-2-2-420000-22-22000000000000000000000002i3−2i30000000000000000000000002i3−2i300000000000000000
χ884-4-44-24-22-442-222-4-21-2-20-12-2221-22-123−23001-11-1000023−23−33−33−3300000000000−2i32i3000000000000000000000000i3−i33i−3i000000000000000
χ894-4-44-24-22-442-222-4-21-2-20-12-2221-22-123−23001-11-1000023−23−33−33−33000000000002i3−2i3000000000000000000000000−i3i3−3i3i000000000000000
χ904-4-44-24-22-442-222-4-21-2-20-12-2221-22-1−2323001-11-10000−23233−33−33−300000000000−2i32i3000000000000000000000000i3−i3−3i3i000000000000000
χ914-4-44-24-22-442-222-4-21-2-20-12-2221-22-1−2323001-11-10000−23233−33−33−3000000000002i3−2i3000000000000000000000000−i3i33i−3i000000000000000
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
χ9488-8-88-4-4-8-44448-44-8-4-42044-2-4244-2-400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-48-448-844-4-4-842-4-40-244-4-4-244200002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-484-44-8-8-4844-42-404-242-44-24-400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-44-4444-4-4442220-2-2-222-2-2-220000-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-44-4444-4-4442220-2-2-222-2-2-220000-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000
χ998-88-88-4-4844-44-84-4-8-4-420-4-4-24-24424000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-48-4-4-8-8-4444842-4-402-4444-24-4-2000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-4-444-4444-44222022-2-2-2-2-22-20000-1-111006i−6i0000−3i−3i3i3i00000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4-444-4444-44222022-2-2-2-2-22-20000-1-11100−6i6i00003i3i−3i−3i00000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-4844-4-884-84-4-42-404-2-4-24-424400002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-444-44-4444-42220-2-22-2-222-2-243−4300-11-110000−2323−23233−33−300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-444-44-4444-42220-2-22-2-222-2-2−434300-11-11000023−2323−23−33−3300000000000000000000000000000000000000000000000000000000

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