Finite Group Databasebeta

← Group #13168544

Character table — Group #13168544

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order1222333666666666333466666666612124436661212121212121212121212122444412121212121212124466661212121212121212121212121212121222244666612121212446122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111-111-1-11111-1-111-1-111-1-1-1-1-111-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-1-11111111-1-111-1-1-1-1-1-1-11111111-1-1111111-1-1-111-1-1-1-1-1-111-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11-1-111-1-111-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-111-1-1-1-1111111111111-1-111-1-11111-1-111-1-11-1-111-1-111-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-11111111111111111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-111-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11111-1-111-1-11111-1-1-1-11-111-1-1-1-1-1-1111-111-111-1-1-1-111-1-11-11
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-1111111-11-1-1-1111-1-111-1-1-1-11-1-1-11-1-1-1-111-1-11111-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111111111-1-1-1-11-1-1-11-11111-1-1-1-111-11-11-1-1-111111111-1-1-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-111-1-1-11111111-1-1-1-1-111-111111-1-1-1-1-1-1-111
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-111-1-11111-1-1111-1-1-1-1-1-1-11111-111-111111-1-1-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-1-1-1-1111111-1111-11-1-1-1-11111-1-1-11-11-1-1-1111111-1-1-1-11
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-11-1111-1-1-111-1-111111-1-1-11-1-1-1-111-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-1-1-1-1-1-1-11111-11-1-1111111-1-11-111-111-1-1-1-111111-1-1
χ17222222-1-1222-1-12222-1-122-1-1-12-1-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-12220022-1-1-1-100002-1-1-120-1200-1-1-1-100-1-1002200000-1-1000000-100
χ18222222-1-1222-1-12222-1-122-1-1-12-1-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-1-2-220022-1-1110000-2111-20-1200-1-11100-1-100-2-20000011000000100
χ19222222-1-1222-1-12222-1-122-1-1-12-1-12-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-122-200-2-211-1-100002-1-1-1201-20011-1-1001100-2-20000011000000100
χ20222222-1-1222-1-12222-1-122-1-1-12-1-12-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-2-2-200-2-211110000-2111-201-20011110011002200000-1-1000000-100
χ21222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-222-1-1-1-11-211-2-21111112-2-20022-1-11100002-1-1-1-201-200-1-1110011002-20000011000000-100
χ22222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-222-1-1-1-11-211-2-2111111-22-20022-1-1-1-10000-2111201-200-1-1-1-1001100-2200000-1-1000000100
χ23222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-2-2-2-1-1-1-11-211-2-21111112-2200-2-2111100002-1-1-1-20-1200111100-1-100-2200000-1-1000000100
χ24222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-2-2-2-1-1-1-11-211-2-2111111-22200-2-211-1-10000-211120-120011-1-100-1-1002-20000011000000-100
χ2522222-1222-1-1222-12-12-12-12-1-1-12-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-1220220000222222-12-1-1-1-100-1200-1-1-1-100-1-100200-1-100-1-10000000
χ2622222-1222-1-1222-12-12-12-12-1-1-12-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-1220-2-2000022-2-2-2-2-12-1-1-11001-200-1-111001100-2001100110000000
χ2722222-1222-1-1222-12-12-12-12-1-1-12-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-1-2-20220000-2-222-2-21-2111-100-120011-1-100-1-100-2001100110000000
χ2822222-1222-1-1222-12-12-12-12-1-1-12-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-1-2-20-2-20000-2-2-2-2221-21111001-2001111001100200-1-100-1-10000000
χ2922222-1222-1-1222-12-12-1-2-12-1-1-12-1-121100-1-1-1-1-2-21111-2-211112-202-20000-2-222-2-2-12-1-11100-1-200111100-1-100200-1-100110000000
χ3022222-1222-1-1222-12-12-1-2-12-1-1-12-1-121100-1-1-1-1-2-21111-2-211112-20-220000-2-2-2-222-12-1-11-100120011-1-1001100-2001100-1-10000000
χ3122222-1222-1-1222-12-12-1-2-12-1-1-12-1-121100-1-1-1-1-2-21111-2-21111-2202-200002222221-211-1100-1-200-1-11100-1-100-2001100-1-10000000
χ3222222-1222-1-1222-12-12-1-2-12-1-1-12-1-121100-1-1-1-1-2-21111-2-21111-220-22000022-2-2-2-21-211-1-1001200-1-1-1-1001100200-1-100110000000
χ332222-1222-12222-12-1-1-122-1-122-1-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-100222-1-12200-1-1000000022-12-1-1-100-1-1-1-1-1-100022000000-1-1000-10
χ342222-1222-12222-12-1-1-122-1-122-1-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-1002-2-2-1-12200110000000-22-1-21-1-10011-1-111000-2-20000001100010
χ352222-1222-12222-12-1-1-122-1-122-1-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-100-22211-2-200-1-100000002-212-11100-1-111-1-1000-2-20000001100010
χ362222-1222-12222-12-1-1-122-1-122-1-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-100-2-2-211-2-200110000000-2-21-21110011111100022000000-1-1000-10
χ372222-1222-12222-12-1-1-12-2-1-122-1-12-1-1-2-222-1-1-1-1-21-2-21111111100-22-2-1-12200-1-10000000-2-2121-1-1001111-1-10002-2000000-1-100010
χ382222-1222-12222-12-1-1-12-2-1-122-1-12-1-1-2-222-1-1-1-1-21-2-21111111100-2-22-1-122001100000002-21-2-1-1-100-1-11111000-2200000011000-10
χ392222-1222-12222-12-1-1-12-2-1-122-1-12-1-1-2-2-2-2-1-1-1-1-21-2-2111111110022-211-2-200-1-10000000-22-121110011-1-1-1-1000-2200000011000-10
χ402222-1222-12222-12-1-1-12-2-1-122-1-12-1-1-2-2-2-2-1-1-1-1-21-2-211111111002-2211-2-20011000000022-1-2-11100-1-1-1-1110002-2000000-1-100010
χ4122-2-2222-222-2-22-2-2-222202-2-2-2-222-2-2002-222-2-2000000000000000002-22-200002i−2i00000000002-2000000000000000002i−2i002i−2i000
χ4222-2-2222-222-2-22-2-2-222202-2-2-2-222-2-2002-222-2-2000000000000000002-22-20000−2i2i00000000002-200000000000000000−2i2i00−2i2i000
χ4322-2-2222-222-2-22-2-2-222202-2-2-2-222-2-200-2222-2-200000000000000000-22-2200002i−2i0000000000-22000000000000000002i−2i00−2i2i000
χ4422-2-2222-222-2-22-2-2-222202-2-2-2-222-2-200-2222-2-200000000000000000-22-220000−2i2i0000000000-2200000000000000000−2i2i002i−2i000
χ4544444-2-2-24-2-2-2-24-24-2-214-2-211-2-21-2-2-2-2001111-2411-2-2-2-21111440000000-2-20000-2-211-2000000011000000000000000000000000
χ4644444-2-2-24-2-2-2-24-24-2-214-2-211-2-21-2-2-2-2001111-2411-2-2-2-21111-4-4000000022000022-1-120000000-1-1000000000000000000000000
χ4744444-2-2-24-2-2-2-24-24-2-21-4-2-211-2-21-2-2220011112-4-1-12222-1-1-1-14-40000000220000-2-21120000000-1-1000000000000000000000000
χ4844444-2-2-24-2-2-2-24-24-2-21-4-2-211-2-21-2-2220011112-4-1-12222-1-1-1-1-440000000-2-2000022-1-1-2000000011000000000000000000000000
χ494444-24-2-2-244-2-2-24-2-21-24-21-2-2-21-2-2144441111-2-2-2-2-2-211111100400-2-2-2-2000000000000-2-2001100001100000000000000000000
χ504444-24-2-2-244-2-2-24-2-21-24-21-2-2-21-2-2144-4-41111-2-2-2-2-2-211111100-40022220000000000002200-1-10000-1-100000000000000000000
χ514444-24-2-2-244-2-2-24-2-21-2-4-21-2-2-21-2-21-4-4441111222222-1-1-1-1-1-100-400-2-2-2-20000000000002200110000-1-100000000000000000000
χ524444-24-2-2-244-2-2-24-2-21-2-4-21-2-2-21-2-21-4-4-4-41111222222-1-1-1-1-1-1004002222000000000000-2-200-1-100001100000000000000000000
χ534444-2-244-2-2-244-2-2-21-2-241-2-2-21-2-21-2-2-20011114-2-2-211-2-2111100044000000-2-20000000-200-2-20000110011000000000000000000
χ544444-2-244-2-2-244-2-2-21-2-241-2-2-21-2-21-2-2-20011114-2-2-211-2-21111000-4-4000000220000000200220000-1-100-1-1000000000000000000
χ554444-2-244-2-2-244-2-2-21-2-2-41-2-2-21-2-21-222001111-4222-1-122-1-1-1-10004-4000000-2-20000000200-220000-1-10011000000000000000000
χ564444-2-244-2-2-244-2-2-21-2-2-41-2-2-21-2-21-222001111-4222-1-122-1-1-1-1000-44000000220000000-2002-200001100-1-1000000000000000000
χ5744-4-444-2244-42-2-4-4-44-2-204222-4-2-2-42004-4-2-222000000000000000004-4-220000000000000000-2200000000000000000000000000
χ5844-4-444-2244-42-2-4-4-44-2-204222-4-2-2-4200-44-2-22200000000000000000-442-200000000000000002-200000000000000000000000000
χ5944-4-44-24-44-22-44-42-4-24-20-2-42224-22-40000-2-22200000000000000000000000004i−4i00000000000000000000000000000−2i2i0000000
χ6044-4-44-24-44-22-44-42-4-24-20-2-42224-22-40000-2-2220000000000000000000000000−4i4i000000000000000000000000000002i−2i0000000
χ6144-4-4-244-4-24-4-442-42-2-240-22-4-42-2422004-4-2-22200000000000000000-224-40000000000000000-2200000000000000000000000000
χ6244-4-4-244-4-24-4-442-42-2-240-22-4-42-242200-44-2-222000000000000000002-2-4400000000000000002-200000000000000000000000000
χ6344-4-4-24-22-24-42-22-42-21-20-2-12221-22-1004-411-1-10000003i−3i3i3i−3i−3i00000-22-2200000000000000001-100003i−3i00000000000000000000
χ6444-4-4-24-22-24-42-22-42-21-20-2-12221-22-1004-411-1-1000000−3i3i−3i−3i3i3i00000-22-2200000000000000001-10000−3i3i00000000000000000000
χ6544-4-4-24-22-24-42-22-42-21-20-2-12221-22-100-4411-1-10000003i−3i3i3i−3i−3i000002-22-20000000000000000-110000−3i3i00000000000000000000
χ6644-4-4-24-22-24-42-22-42-21-20-2-12221-22-100-4411-1-1000000−3i3i−3i−3i3i3i000002-22-20000000000000000-1100003i−3i00000000000000000000
χ674-44-4444-4-4-4-44-444-44440-4-4-44-4-4-44400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-22-4-4-4-2244-44-2-20-422-2-4224-20000-222-2000000000000000000000000000000000000000000000000000000−2i32i3000000000
χ694-44-444-22-4-4-4-2244-44-2-20-422-2-4224-20000-222-20000000000000000000000000000000000000000000000000000002i3−2i3000000000
χ704-44-44-24-4-4224-44-2-4-24-202-42-22-42-240000-222-20000000000000000000000000000000000000000000000000000−2i32i300000000000
χ714-44-44-24-4-4224-44-2-4-24-202-42-22-42-240000-222-200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ724-44-4-244-42-4-44-4-242-2-24022-4422-4-2-20000-222-2000000000000000000000000000000000000000000000000000000000023−2300000
χ734-44-4-244-42-4-44-4-242-2-24022-4422-4-2-20000-222-20000000000000000000000000000000000000000000000000000000000−232300000
χ744-4-444444-4-44-4-4-4-444440-444-44-4-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2-2-4-4422-4-444-2-20-4-2-22422-420000-22-2200000000000000000000023−23000000000000000023−23000000000000000000000000
χ764-4-4444-2-2-4-4422-4-444-2-20-4-2-22422-420000-22-22000000000000000000000−23230000000000000000−2323000000000000000000000000
χ774-4-444-244-42-2-4-4-424-24-2024-22-2-422-423−2300-22-220023−2323−230023−2323−2300000000000000000000000000000000000000000000000000000
χ784-4-444-244-42-2-4-4-424-24-2024-22-2-422-4−232300-22-2200−2323−232300−2323−232300000000000000000000000000000000000000000000000000000
χ794-4-444-2-2-2-42-222-424-2-2102-21-1-22-12223−23001-11-100−3323−2300−33−3300000000023−230000003-300000000−33000000000000000000000000
χ804-4-444-2-2-2-42-222-424-2-2102-21-1-22-12223−23001-11-100−3323−2300−33−33000000000−2323000000-33000000003−3000000000000000000000000
χ814-4-444-2-2-2-42-222-424-2-2102-21-1-22-122−2323001-11-1003−3−2323003−33−300000000023−23000000-3300000000−33000000000000000000000000
χ824-4-444-2-2-2-42-222-424-2-2102-21-1-22-122−2323001-11-1003−3−2323003−33−3000000000−23230000003-3000000003−3000000000000000000000000
χ834-4-44-24442-44-4-42-4-2-2-2402-24-4-22-4220000-22-220000000000000000000000023−230000000000000000000023−23000000000000000000
χ844-4-44-24442-44-4-42-4-2-2-2402-24-4-22-4220000-22-2200000000000000000000000−232300000000000000000000−2323000000000000000000
χ854-4-44-2-24422-2-4-422-21-2-20-1-2-22122-1223−23001-11-10023−23−3300−33−330000000000023−2300000000000000003-300−33000000000000000000
χ864-4-44-2-24422-2-4-422-21-2-20-1-2-22122-1223−23001-11-10023−23−3300−33−3300000000000−23230000000000000000-33003−3000000000000000000
χ874-4-44-2-24422-2-4-422-21-2-20-1-2-22122-12−2323001-11-100−23233−3003−33−30000000000023−230000000000000000-3300−33000000000000000000
χ884-4-44-2-24422-2-4-422-21-2-20-1-2-22122-12−2323001-11-100−23233−3003−33−300000000000−232300000000000000003-3003−3000000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9188-8-88-4-448-444-4-84-8-4-420-44-2-24-4244000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-8-4-44-884442-4-402444-2-4-4-24000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-4-444-444422202-2-2-2-222-2-20000-1-1110000006i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-4-444-444422202-2-2-2-222-2-20000-1-111000000−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000000000
χ958-88-88-4-44-844-448-4-8-4-42044-2244-2-4-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-444-8-8-44-484-42-404-24-44-24-4200002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-48-84448-8-4-442-4-40-244-4-2442-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44444-44-4-442220-2-2-22-2-2-2220000-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-44444-44-4-442220-2-2-22-2-2-2220000-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000000000000
χ1008-8-88-48-4-44-88444-8-4-42-4042-44-4-244-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-444-44444-42220-222-22-2-2-2-243−4300-11-1100−2323−2323003−33−300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-444-44444-42220-222-22-2-2-2-2−434300-11-110023−2323−2300−33−3300000000000000000000000000000000000000000000000000000

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