Finite Group Databasebeta

← Group #13168520

Character table — Group #13168520

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order12223336666666663334666666666121244366612121212121212121212121224444661212121212124466612121212121212121212121212121212124444412121212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-111111-1-111-1-11111-111-1-111111-1-111-1-1-1-111-1-1-1-1-1-1-111-1-1-11-1
χ31111111111111111111111111111111111111111111111111-1111-1-1-1111111-1-1-1-1-1111-111-111-1-111111111-1-1-1-1-1-1-111-1-1-1-11-1-1
χ41111111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-11111-1-1-11-11-1-1-1-111-1-1-1-111-1-1-1-1-1-111111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-11111-1-111-1-111111-11-11111-1-11111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-1-1111-1-1-1-1-1-1-1-1111-1-1-11-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1111-11
χ71111111111111111111111111111111-1-11111111111111111-11-11-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-11111-111
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1111-1-1-1-111-111-1-111-1-1-1-11-11-1111-1-1-1-111-1-11-11
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11111111111111-11-1-1-1-1-111-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-11111-1-1-1-1-1-11111111111-1-1-1-11-1-11-1-1-111-1-1-1-11111-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-11-1-111111-1-1-1-111-11-11111-1-111-1-1-1-1-111
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111-11-111-1-1-1-1-11111-1-1-11-11111-1-111-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-111-1-1-1-1-1-1111
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-111-1-1-11-111111-1-1111111-1-1-111-1-1-1-1111111-1-1-1-11
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-11111-1-11-1-111-1-111111-11-1111-1-1-1-111111-1-1
χ17222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1220222200220022-1-1-10-10-1-12200-1-1-1-100-1-100002-1-1-1-1000000000
χ18222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-12-20-222200-2-200-2-2-1-1-1010-11-2200-1-11100110000-21111000000000
χ19222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1-2202-2-2-2002200-2-21110-101-12-20011-1-100-1-10000-21111000000000
χ20222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1-2-20-2-2-2-200-2-2002211101011-2-2001111001100002-1-1-1-1000000000
χ21222222-1222-12-1-1222-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-2111111220-2-22200-2-200-2-2-1-1-10101-12-20011-1-1001100002-1-111000000000
χ22222222-1222-12-1-1222-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-21111112-202-22200220022-1-1-10-1011-2-200111100-1-10000-211-1-1000000000
χ23222222-1222-12-1-1222-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-2111111-220-22-2-200-2-20022111010-1-12200-1-1-1-100110000-211-1-1000000000
χ24222222-1222-12-1-1222-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-2111111-2-2022-2-2002200-2-21110-10-11-2200-1-11100-1-100002-1-111000000000
χ2522222-12-12-122222-1-12-12-12-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-120202-1-12200-1-1002-1-1-102200-1-1-1-1-100-1-10000220000000-1-1000-10
χ2622222-12-12-122222-1-12-12-12-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-1-2020-2112200-1-100-211-102-2001-1-11100-1-10000-2-200000001100010
χ2722222-12-12-122222-1-12-12-12-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-120-202-1-1-2-20011002-1-110-2200-111-1-100110000-2-200000001100010
χ2822222-12-12-122222-1-12-12-12-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-20-20-211-2-2001100-21110-2-2001111100110000220000000-1-1000-10
χ2922222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-222-1-1-1-11-21111-2-2111120-20-2-1-12200-1-1002-1-110-2-2001-1-111001100002-20000000-1-100010
χ3022222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-222-1-1-1-11-21111-2-21111-20-202112200-1-100-21110-2200-1-1-1-1-100110000-22000000011000-10
χ3122222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-211112020-2-1-1-2-20011002-1-1-102-2001111100-1-10000-22000000011000-10
χ3222222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-21111-2020211-2-2001100-211-102200-111-1-100-1-100002-20000000-1-100010
χ332222-1222-122-122-12-1-122-1-122-1-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-10222000-1-1-1-1220000022-102-10-1-100-1-1-1-1-1-1220000000-1-10000-100
χ342222-1222-122-122-12-1-122-1-122-1-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-10-22-2000-1-11122000002-2-10-210-1-10011-1-111-2-20000000110000100
χ352222-1222-122-122-12-1-122-1-122-1-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-102-2200011-1-1-2-200000-22102-101100-1-111-1-1-2-20000000110000100
χ362222-1222-122-122-12-1-122-1-122-1-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2-20001111-2-200000-2-210-2101100111111220000000-1-10000-100
χ372222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-222-1-1-1-1-21-2-21111111102-2-2000-1-1112200000-2-2102-10-1-100-1-111112-20000000110000-100
χ382222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-222-1-1-1-1-21-2-2111111110-2-22000-1-1-1-12200000-2210-210-1-1001111-1-1-220000000-1-10000100
χ392222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-2-2-2-1-1-1-1-21-2-211111111022-20001111-2-2000002-2-102-101100-1-1-1-111-220000000-1-10000100
χ402222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-2-2-2-1-1-1-1-21-2-2111111110-22200011-1-1-2-20000022-10-210110011-1-1-1-12-20000000110000-100
χ412-2-22222-22-2-2-22-2-222220-22-2-22-22-2-2002-222-2-200000000000000000002-2002-22i−2i00000000002-20000000000000002i−2i00002i−2i000
χ422-2-22222-22-2-2-22-2-222220-22-2-22-22-2-2002-222-2-200000000000000000002-2002-2−2i2i00000000002-2000000000000000−2i2i0000−2i2i000
χ432-2-22222-22-2-2-22-2-222220-22-2-22-22-2-200-2222-2-20000000000000000000-2200-222i−2i0000000000-220000000000000002i−2i0000−2i2i000
χ442-2-22222-22-2-2-22-2-222220-22-2-22-22-2-200-2222-2-20000000000000000000-2200-22−2i2i0000000000-22000000000000000−2i2i00002i−2i000
χ4544444-2-2-24-2-24-2-24-2-2-214-2-211-2-21-2-2-2-2001111-2411-2-2-2-2111140004-2-200000000-211000-200-20011000000000000000000000000
χ4644444-2-2-24-2-24-2-24-2-2-214-2-211-2-21-2-2-2-2001111-2411-2-2-2-21111-4000-422000000002-1-1000200200-1-1000000000000000000000000
χ4744444-2-2-24-2-24-2-24-2-2-21-4-2-211-2-21-2-2220011112-4-1-12222-1-1-1-14000-4-2-200000000-211000200200-1-1000000000000000000000000
χ4844444-2-2-24-2-24-2-24-2-2-21-4-2-211-2-21-2-2220011112-4-1-12222-1-1-1-1-4000422000000002-1-1000-200-20011000000000000000000000000
χ494444-24-24-24-2-2-2-2-24-21-24-21-2-2-21-2-21-2-20011114-2-2-2-2-2111111040400000-2-200000000-200-2-200000110011000000000000000000
χ504444-24-24-24-2-2-2-2-24-21-24-21-2-2-21-2-21-2-20011114-2-2-2-2-21111110-40-40000022000000002002200000-1-100-1-1000000000000000000
χ514444-24-24-24-2-2-2-2-24-21-2-4-21-2-2-21-2-2122001111-422222-1-1-1-1-1-1040-4000002200000000200-2-2000001100-1-1000000000000000000
χ524444-24-24-24-2-2-2-2-24-21-2-4-21-2-2-21-2-2122001111-422222-1-1-1-1-1-10-40400000-2-200000000-2002200000-1-10011000000000000000000
χ534444-2-24-2-2-24-244-2-21-2-241-2-2-21-2-21-244441111-2-2-2-211-2-211110040000-2-200-2-200000-20-200001100001100000000000000000000
χ544444-2-24-2-2-24-244-2-21-2-241-2-2-21-2-21-244-4-41111-2-2-2-211-2-2111100-40000220022000002020000-1-10000-1-100000000000000000000
χ554444-2-24-2-2-24-244-2-21-2-2-41-2-2-21-2-21-2-4-44411112222-1-122-1-1-1-100-40000-2-200-2-2000002020000110000-1-100000000000000000000
χ564444-2-24-2-2-24-244-2-21-2-2-41-2-2-21-2-21-2-4-4-4-411112222-1-122-1-1-1-1004000022002200000-20-20000-1-100001100000000000000000000
χ5744-4-44444-4-4-4-4-444-444404-44-4-44-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-4-42-42-24-44-2-2042-22-4-22-4223−2300-22-220023−230023−232323−23−2300000000000000000000000000000000000000000000000000000
χ5944-4-444-24-4-42-42-24-44-2-2042-22-4-22-42−232300-22-2200−232300−2323−23−23232300000000000000000000000000000000000000000000000000000
χ6044-4-44-24-2-42-4-4-4442-24-20-2-4-222422-40000-22-2200000000000000000−2i32i3000000000−2i32i300000000000000000000000000000000000
χ6144-4-44-24-2-42-4-4-4442-24-20-2-4-222422-40000-22-22000000000000000002i3−2i30000000002i3−2i300000000000000000000000000000000000
χ6244-4-44-2-2-2-422-42-242-2-210-221-12-2-12223−23001-11-100−330023−23−3−33300000−2i32i3000000000i3−i30000000003i−3i000000000000000000000000
χ6344-4-44-2-2-2-422-42-242-2-210-221-12-2-12223−23001-11-100−330023−23−3−333000002i3−2i3000000000−i3i3000000000−3i3i000000000000000000000000
χ6444-4-44-2-2-2-422-42-242-2-210-221-12-2-122−2323001-11-1003−300−232333−3−300000−2i32i3000000000i3−i3000000000−3i3i000000000000000000000000
χ6544-4-44-2-2-2-422-42-242-2-210-221-12-2-122−2323001-11-1003−300−232333−3−3000002i3−2i3000000000−i3i30000000003i−3i000000000000000000000000
χ6644-4-4-24442-4-42-44-2-4-2-240-224-42-2-4220000-22-2200000000000000000000023−23000000000000000000000023−23000000000000000000
χ6744-4-4-24442-4-42-44-2-4-2-240-224-42-2-4220000-22-22000000000000000000000−23230000000000000000000000−2323000000000000000000
χ6844-4-4-24-242-4222-2-2-4-21-20-2-1-222122-123−23001-11-10023−2300−33−3−33300000000023−230000000000000000003-300−33000000000000000000
χ6944-4-4-24-242-4222-2-2-4-21-20-2-1-222122-123−23001-11-10023−2300−33−3−333000000000−2323000000000000000000-33003−3000000000000000000
χ7044-4-4-24-242-4222-2-2-4-21-20-2-1-222122-1−2323001-11-100−2323003−333−3−300000000023−23000000000000000000-3300−33000000000000000000
χ7144-4-4-24-242-4222-2-2-4-21-20-2-1-222122-1−2323001-11-100−2323003−333−3−3000000000−23230000000000000000003-3003−3000000000000000000
χ724-44-4444-4-4444-4-4-4-44440-4-4-44-4-4-44400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ734-44-444-2-4-44-2422-4-44-2-20-422-2-4224-20000-222-2000000000000000000000000000000000000000000000000000023−2300000000000
χ744-44-444-2-4-44-2422-4-44-2-20-422-2-4224-20000-222-20000000000000000000000000000000000000000000000000000−232300000000000
χ754-44-44-242-4-244-4-4-42-24-202-42-22-42-240000-222-2000000000000000000000000000000000000000000000000000000000023−2300000
χ764-44-44-242-4-244-4-4-42-24-202-42-22-42-240000-222-20000000000000000000000000000000000000000000000000000000000−232300000
χ774-44-4-244-4244-2-4-42-4-2-24022-4422-4-2-20000-222-20000000000000000000000000000000000000000000000000000000023−230000000
χ784-44-4-244-4244-2-4-42-4-2-24022-4422-4-2-20000-222-200000000000000000000000000000000000000000000000000000000−23230000000
χ794-4-4444-2-44-42-4-22-444-2-20-4-22242-2-420000-2-22200000000000000000000000004i−4i000000000000000000000000000−2i2i000000000
χ804-4-4444-2-44-42-4-22-444-2-20-4-22242-2-420000-2-2220000000000000000000000000−4i4i0000000000000000000000000002i−2i000000000
χ814-4-444-24242-4-44-4-4-2-24-202422-2-4-22-4004-4-2-22200000000000000000004-400-22000000000000-2200000000000000000000000000
χ824-4-444-24242-4-44-4-4-2-24-202422-2-4-22-400-44-2-2220000000000000000000-44002-20000000000002-200000000000000000000000000
χ834-4-44-244-4-2-4-424-424-2-2402-2-4-4-22422004-4-2-2220000000000000000000-22004-4000000000000-2200000000000000000000000000
χ844-4-44-244-4-2-4-424-424-2-2402-2-4-4-2242200-44-2-22200000000000000000002-200-440000000000002-200000000000000000000000000
χ854-4-44-2-242-22-424-42-21-2-20-1-22212-2-12004-411-1-100003i−3i003i−3i3i−3i0000000-2200-220000000000001-100003i−3i00000000000000000000
χ864-4-44-2-242-22-424-42-21-2-20-1-22212-2-12004-411-1-10000−3i3i00−3i3i−3i3i0000000-2200-220000000000001-10000−3i3i00000000000000000000
χ874-4-44-2-242-22-424-42-21-2-20-1-22212-2-1200-4411-1-100003i−3i003i−3i3i−3i00000002-2002-2000000000000-110000−3i3i00000000000000000000
χ884-4-44-2-242-22-424-42-21-2-20-1-22212-2-1200-4411-1-10000−3i3i00−3i3i−3i3i00000002-2002-2000000000000-1100003i−3i00000000000000000000
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
χ9188-8-8-4-48-444-84-88-442-4-4024-44-2-44-2400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-444444-4-4422202-22-2-22-2-2-243−4300-11-1100−232300−232333−3−300000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-444444-4-4422202-22-2-22-2-2-2−434300-11-110023−230023−23−3−33300000000000000000000000000000000000000000000000000000
χ948-88-88-4-44-8-4-4844-84-4-42044-2244-2-4-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-48-4-848-4-4444-8-42-404-24-44-24-4200002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4844-48-4-8-8442-4-40-244-4-2442-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-444-4-4-444442220-2-2-22-2-2-2220000-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-444-4-4-444442220-2-2-22-2-2-2220000-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000000000000
χ998-8-888-4-44844-8-44-8-4-4-4204-4-2-2-44244000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-4-8-4-844-4448-42-404244-4-2-44-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-4444-444-42220-22-2-22-22-2-20000-1-11100006i−6i00−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-4444-444-42220-22-2-22-22-2-20000-1-1110000−6i6i003i−3i3i−3i00000000000000000000000000000000000000000000000000000

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