Finite Group Databasebeta

← Group #13168637

Character table — Group #13168637

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121236661212121212121212121212122444446612121212121244444466612121212121212121212121212121212124441212121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-111-1-1111111-1-1-1-1111-111-1-111111111-1-1-1-1-1-11-1-1-1-1-1-1111-1-1-1
χ31111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1111111-1-1111-111-1-1-1-111111-1-111-1-1-1-1-1-1-11-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1111-1-1-1-1-11-111-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111111111111111-1-11111-1-111-1-111-1-111-1-1-1-1-111111-11-1-111111111-11-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-11-1-11111-1-1-1-11-1-111-1-1-1-1-1-1-1111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1111-111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11111-1-11111-1-1-1-1111-11-11-1-1-1-1-111-1-111-1-111-1-1-111-1-111-111-1
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111-1-1-1-11111111111111-1-11-1-1-1-111-1-1-1-111-1-1-111-1-11111-1-1-11
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11111-1-1-1-1-1-111-1-1111-1-111-1-11-1-1-1-11111-1-11-11-1-1-1-111-1-111-11
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1111-1-1-1-1-1-1-1-1-1-1111111-11-11-11-1-1-1-111-1-111-1111111-1-1-1-11-11-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1111111-1-1-1-111-1-1-1-11-11-11-11111-1-111-1-1-1111111-1-1-1-11-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-11111-1-111-1-1-1-1-111-1-111-11111-1-1-1-1111-11-1-1-1-111-1-1111-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-11111-1-1111111-1-1-1-1-111-11111-1-11111-1-1-1-1-111-1-11111-1-11-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111-1-111-1-1-1-1-1-1-11-11-111111-1-111-1-11111-1-1-111-1-111-11-11
χ17222222-122-12-1-12222-1-122-1-12-1-1-12-122-1-1-1-12-122-1-1-1-1-1-1-1-122002222-1-1-1-100000022-1-1-1-1002220-1-10000-1-1-1-1200-1-10000000-100
χ18222222-122-12-1-12222-1-122-1-12-1-1-12-122-1-1-1-12-122-1-1-1-1-1-1-1-12200-2-22211-1-1000000-2-2-1-1-1100-2-220-1-100001111-200110000000100
χ19222222-122-12-1-12222-1-122-1-12-1-1-12-122-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20022-2-2-1-111000000-2-2111-10022-20110000-1-1-1-1-200110000000100
χ20222222-122-12-1-12222-1-122-1-12-1-1-12-122-1-1-1-12-122-1-1-1-1-1-1-1-1-2-200-2-2-2-2111100000022111100-2-2-201100001111200-1-10000000-100
χ21222222-122-12-1-12222-1-1-22-1-12-1-1-12-1-2-2-1-1-1-1-21-2-2111111112-2002-222-1-111000000-2-2-1-1-11002-2-20110000-1-111200110000000-100
χ22222222-122-12-1-12222-1-1-22-1-12-1-1-12-1-2-2-1-1-1-1-21-2-2111111112-200-2222111100000022-1-1-1-100-22-2011000011-1-1-200-1-10000000100
χ23222222-122-12-1-12222-1-1-22-1-12-1-1-12-1-2-2-1-1-1-1-21-2-211111111-22002-2-2-2-1-1-1-1000000221111002-220-1-10000-1-111-200-1-10000000100
χ24222222-122-12-1-12222-1-1-22-1-12-1-1-12-1-2-2-1-1-1-1-21-2-211111111-2200-22-2-211-1-1000000-2-2111-100-2220-1-1000011-1-1200110000000-100
χ2522222-12-122-12222-1-12-12-12-1-12-1-1-1222-1-1-1-1-12-1-122-1-1-1-1-1-1222200-1-10022-1-12200002-1-102200-1-1-1-1-1-1-1-10000002000000-1-1-1000
χ2622222-12-122-12222-1-12-12-12-1-12-1-1-1222-1-1-1-1-12-1-122-1-1-1-1-1-122-2-200-1-1002211-2-200002-1-10-2-200-11-1-11111000000-2000000111000
χ2722222-12-122-12222-1-12-12-12-1-12-1-1-1222-1-1-1-1-12-1-122-1-1-1-1-1-1-2-222001100-2-2-1-1-2-20000-211022001-111-1-1-1-1000000-2000000111000
χ2822222-12-122-12222-1-12-12-12-1-12-1-1-1222-1-1-1-1-12-1-122-1-1-1-1-1-1-2-2-2-2001100-2-211220000-2110-2-200111111110000002000000-1-1-1000
χ2922222-12-122-12222-1-12-1-2-12-1-12-1-1-12-2-2-1-1-1-11-211-2-21111112-22-200-1-100-2-2-1-12200002-1-102-2001111-1-111000000-2000000-1-11000
χ3022222-12-122-12222-1-12-1-2-12-1-12-1-1-12-2-2-1-1-1-11-211-2-21111112-2-2200-1-100-2-211-2-200002-1-10-22001-11111-1-1000000200000011-1000
χ3122222-12-122-12222-1-12-1-2-12-1-12-1-1-12-2-2-1-1-1-11-211-2-2111111-222-200110022-1-1-2-20000-21102-200-11-1-1-1-111000000200000011-1000
χ3222222-12-122-12222-1-12-1-2-12-1-12-1-1-12-2-2-1-1-1-11-211-2-2111111-22-220011002211220000-2110-2200-1-1-1-111-1-1000000-2000000-1-11000
χ332222-1222-12222-1-12-1-122-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1002222002200220022000002-1-1-1-10200-1-1-1-1-1-1-1-102000-1-1-1-1000000
χ342222-1222-12222-1-12-1-122-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10022-2-200-2-2002200-2-200000-2-1-1110200-1-1-1-111110-20001111000000
χ352222-1222-12222-1-12-1-122-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100-2-222002200-2-200-2-200000211-1-10-2001111-1-1-1-10-20001111000000
χ362222-1222-12222-1-12-1-122-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100-2-2-2-200-2-200-2-2002200000-211110-2001111111102000-1-1-1-1000000
χ372222-1222-12222-1-12-1-12-2-1-12-1-122-1-111-1-1-1-1-2-21111-2-21111002-22-20022002200-2-200000-2-11-110-200-1-111-1-11102000-1-111000000
χ382222-1222-12222-1-12-1-12-2-1-12-1-122-1-111-1-1-1-1-2-21111-2-21111002-2-2200-2-200220022000002-111-10-200-1-11111-1-10-200011-1-1000000
χ392222-1222-12222-1-12-1-12-2-1-12-1-122-1-111-1-1-1-1-2-21111-2-2111100-222-2002200-2-2002200000-21-1-11020011-1-1-1-1110-200011-1-1000000
χ402222-1222-12222-1-12-1-12-2-1-12-1-122-1-111-1-1-1-1-2-21111-2-2111100-22-2200-2-200-2-200-2-20000021-11-1020011-1-111-1-102000-1-111000000
χ4122-2-2222-2-2-2-2-222-222220-22-2-2-2-222-20022-2-2000000000000000000000000002-22i−2i2i−2i000000000000000000000002i−2i002i−2i2-20000
χ4222-2-2222-2-2-2-2-222-222220-22-2-2-2-222-20022-2-2000000000000000000000000002-2−2i2i−2i2i00000000000000000000000−2i2i00−2i2i2-20000
χ4322-2-2222-2-2-2-2-222-222220-22-2-2-2-222-20022-2-200000000000000000000000000-222i−2i−2i2i00000000000000000000000−2i2i002i−2i-220000
χ4422-2-2222-2-2-2-2-222-222220-22-2-2-2-222-20022-2-200000000000000000000000000-22−2i2i2i−2i000000000000000000000002i−2i00−2i2i-220000
χ4544444-2-2-24-2-2-2-244-2-2-214-2-21-2-211-2-2441111-2-2-2-2-2-2111111440000-2-200-2-200000000-21100000-201100000000000000000000000
χ4644444-2-2-24-2-2-2-244-2-2-214-2-21-2-211-2-2441111-2-2-2-2-2-2111111-4-40000220022000000002-1-10000020-1-100000000000000000000000
χ4744444-2-2-24-2-2-2-244-2-2-21-4-2-21-2-211-2-2-4-41111222222-1-1-1-1-1-14-40000-2-2002200000000-2110000020-1-100000000000000000000000
χ4844444-2-2-24-2-2-2-244-2-2-21-4-2-21-2-211-2-2-4-41111222222-1-1-1-1-1-1-4400002200-2-2000000002-1-100000-201100000000000000000000000
χ494444-24-24-2-24-2-2-2-24-21-24-21-2-21-2-2-21-2-211114-2-2-211-2-2111100004400-2-20000000000000-200-2-2000000001111000000000000000
χ504444-24-24-2-24-2-2-2-24-21-24-21-2-21-2-2-21-2-211114-2-2-211-2-211110000-4-4002200000000000002002200000000-1-1-1-1000000000000000
χ514444-24-24-2-24-2-2-2-24-21-2-4-21-2-21-2-2-21221111-4222-1-122-1-1-1-100004-400-2-20000000000000200-220000000011-1-1000000000000000
χ524444-24-24-2-24-2-2-2-24-21-2-4-21-2-21-2-2-21221111-4222-1-122-1-1-1-10000-4400220000000000000-2002-200000000-1-111000000000000000
χ534444-2-24-2-24-244-2-2-21-2-241-2-21-2-2-21-2-2-21111-2411-2-2-2-21111004400000000-2-20000000000-2-2000-20011110000000000000000000
χ544444-2-24-2-24-244-2-2-21-2-241-2-21-2-2-21-2-2-21111-2411-2-2-2-2111100-4-40000000022000000000022000200-1-1-1-10000000000000000000
χ554444-2-24-2-24-244-2-2-21-2-2-41-2-21-2-2-21-22211112-4-1-12222-1-1-1-1004-400000000-2-20000000000-2200020011-1-10000000000000000000
χ564444-2-24-2-24-244-2-2-21-2-2-41-2-21-2-2-21-22211112-4-1-12222-1-1-1-100-44000000002200000000002-2000-200-1-1110000000000000000000
χ5744-4-444-2-4-42-42-24-444-2-20-4-22-422-24200-2-2220000000000000000000000000000004i−4i00000000000000000000000−2i2i0000000000
χ5844-4-444-2-4-42-42-24-444-2-20-4-22-422-24200-2-222000000000000000000000000000000−4i4i000000000000000000000002i−2i0000000000
χ5944-4-44-242-4-42-444-4-2-24-202422-42-2-2-400-2-222000000000000000000000000004-4000000000000000000000000000000000-220000
χ6044-4-44-242-4-42-444-4-2-24-202422-42-2-2-400-2-22200000000000000000000000000-440000000000000000000000000000000002-20000
χ6144-4-4-244-42-4-4-44-224-2-2402-2-422-44-2200-2-22200000000000000000000000000004i−4i00000000000000000000000000000−2i2i000000
χ6244-4-4-244-42-4-4-44-224-2-2402-2-422-44-2200-2-2220000000000000000000000000000−4i4i000000000000000000000000000002i−2i000000
χ634-44-44444-44-4-4-4-44-444404-44-4-4-4-4-44004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ644-44-444-24-4-2-422-44-44-2-2042-2-4222-4-200-22-22000000000000000000000023−2300000000000000000023−2300000000000000000000000
χ654-44-444-24-4-2-422-44-44-2-2042-2-4222-4-200-22-220000000000000000000000−2323000000000000000000−232300000000000000000000000
χ664-44-44-24-2-442-4-4-442-24-20-2-4-22-4222400-22-22000000000000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ674-44-44-24-2-442-4-4-442-24-20-2-4-22-4222400-22-220000000000000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ684-44-44-2-2-2-4-2222-442-2-210-22122-1-12-2001-11-10000003i−3i3i3i−3i−3i000000−2i32i30023−23000000000i3−i30000000−3300000000000000000000000
χ694-44-44-2-2-2-4-2222-442-2-210-22122-1-12-2001-11-10000003i−3i3i3i−3i−3i0000002i3−2i300−2323000000000−i3i300000003−300000000000000000000000
χ704-44-44-2-2-2-4-2222-442-2-210-22122-1-12-2001-11-1000000−3i3i−3i−3i3i3i000000−2i32i300−2323000000000i3−i300000003−300000000000000000000000
χ714-44-44-2-2-2-4-2222-442-2-210-22122-1-12-2001-11-1000000−3i3i−3i−3i3i3i0000002i3−2i30023−23000000000−i3i30000000−3300000000000000000000000
χ724-44-4-244424-4-4-42-2-4-2-240-22422-4-42-200-22-2200000000000000000000000000000000000000000000000000000000023−2300000000
χ734-44-4-244424-4-4-42-2-4-2-240-22422-4-42-200-22-22000000000000000000000000000000000000000000000000000000000−232300000000
χ744-4-44444-44-444-4-4-4-44440-4-4-4444-4-4-4004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2-4424-22-4-4-44-2-20-4224-2-22-4200-222-20000000000000000000023−230000000000000000000000000023−2300000000000000000
χ764-4-4444-2-4424-22-4-4-44-2-20-4224-2-22-4200-222-200000000000000000000−232300000000000000000000000000−232300000000000000000
χ774-4-444-2424-4-24-4-4-42-24-202-42-24-222-400-222-200000000000000000000000023−2300000000000000000023−23000000000000000000000
χ784-4-444-2424-4-24-4-4-42-24-202-42-24-222-400-222-2000000000000000000000000−2323000000000000000000−2323000000000000000000000
χ794-4-44-244-4-2-444-422-4-2-24022-4-2-24-422−2i32i3-222-200−2i32i3−2i32i300−2i32i3−2i32i30000000000000000000000000000000000000000000000000000000
χ804-4-44-244-4-2-444-422-4-2-24022-4-2-24-4222i3−2i3-222-2002i3−2i32i3−2i3002i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000
χ814-4-44-24-2-4-224-2222-4-21-202-12-21-222-1−2i32i31-1-1100−2i32i3i3−i300i3−i3i3−i30000000023−2300000000000000000000000000−333i−3i000000000000000
χ824-4-44-24-2-4-224-2222-4-21-202-12-21-222-1−2i32i31-1-1100−2i32i3i3−i300i3−i3i3−i300000000−2323000000000000000000000000003−3−3i3i000000000000000
χ834-4-44-24-2-4-224-2222-4-21-202-12-21-222-12i3−2i31-1-11002i3−2i3−i3i300−i3i3−i3i30000000023−2300000000000000000000000000−33−3i3i000000000000000
χ844-4-44-24-2-4-224-2222-4-21-202-12-21-222-12i3−2i31-1-11002i3−2i3−i3i300−i3i3−i3i300000000−2323000000000000000000000000003−33i−3i000000000000000
χ854-4-44-2-242-2-4-24-42221-2-20-1221-2-22-12−2i32i31-1-1100i3−i3−2i32i300i3−i3i3−i300000000000023−23000000000000000000−333i−3i0000000000000000000
χ864-4-44-2-242-2-4-24-42221-2-20-1221-2-22-12−2i32i31-1-1100i3−i3−2i32i300i3−i3i3−i3000000000000−23230000000000000000003−3−3i3i0000000000000000000
χ874-4-44-2-242-2-4-24-42221-2-20-1221-2-22-122i3−2i31-1-1100−i3i32i3−2i300−i3i3−i3i300000000000023−23000000000000000000−33−3i3i0000000000000000000
χ884-4-44-2-242-2-4-24-42221-2-20-1221-2-22-122i3−2i31-1-1100−i3i32i3−2i300−i3i3−i3i3000000000000−23230000000000000000003−33i−3i0000000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000
χ9188-8-88-4-44-8444-48-8-4-4-4204-4-244-22-440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-844-84-4-448-42-404244-24-4-4-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4844-84-88-44-42-4-40-2-44-244-4240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-444444-4-44-42220-22-2-2-2-222-200-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-444444-4-44-42220-22-2-2-2-222-200-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000
χ968-88-8-48-484-4-8444-4-8-42-40-4-2-44-24442002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-48-4484-8-84-442-4-4024-4-2444-2-4002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-44-44444-4422202-22-2-2-2-2-2200-11-110000006i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4-44-44444-4422202-22-2-2-2-2-2200-11-11000000−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000000
χ1008-8-888-4-4484-4-44-8-84-4-42044-2-4-42-244002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-44-4-444442220-2-2-2222-2-2-2−4i34i3-111-1002i3−2i32i3−2i300−i3i3−i3i30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-44-4-444442220-2-2-2222-2-2-24i3−4i3-111-100−2i32i3−2i32i300i3−i3i3−i30000000000000000000000000000000000000000000000000000000

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