Finite Group Databasebeta

← Group #13169311

Character table — Group #13169311

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order12223336666666663334666666666121244366612121212121212121212121224444121212121212121222666612121212121212121212121212121212244446666121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111-1-1111111-1-111111-11-1-1111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-1111-11111-1-111-1-1-1-1-1-1-111111-1-111111111-1-11-11-1-1-1-111-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-1-11-1-1-111-1-11111-1-1-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-11-1-1-111-1-11111-1-11
χ51111111111111111111111111111111-1-11111111111111111111-1111-1-111-1-111111111-111-1111111-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-11111-1-1-1-111-1-1-111-1-1-1-1-1-1111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-11111-11-1-1-1-1-1-111-1-111-1-1-1111-1-1-1-1-11111-1-11-11
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111111111-1-1-111-1-1-1-1-11111-1-1-11-1-11-1-111-1-1-1-11111-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11111-1-111-1-11-11-1-1111111-1-111-1-1-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1-1-11-1-111-111-1-11111-1-11-1-11111-1-1-1-111-1-1-111
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-1-1-1-1-1-1-11111-111-1-11-1-111-1-1-1-1111-1-11111-1-1-1-11111-11-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1111-11-1-1111111-1-1-1-1-1-11
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-111-1-1-1-1111-1-111111-1-1-1-111-11-1-11-1-111-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11-1111111-1-111-1-111-1111-1-1-1-1-11111111-1-1
χ17222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-12220222002200222-1-1-1-1-102-10-1-1-1-1-1-100000002000-1-100-1-100000
χ18222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-12-2-202-2-2002200-2-22-1-1-1-110-210-1-111110000000-200011001100000
χ19222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-2220-22200-2-200-2-2-21111-102-1011-1-1-1-10000000-200011001100000
χ20222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-20-2-2-200-2-20022-2111110-21011111100000002000-1-100-1-100000
χ21222222-122-1-1222-122-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-21111111122-20-22200-2-200-2-22-1-1-11-10-21011-1-111000000020001100-1-100000
χ22222222-122-1-1222-122-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-2111111112-220-2-2-200-2-200222-1-1-11102-101111-1-10000000-2000-1-1001100000
χ23222222-122-1-1222-122-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-211111111-22-2022200220022-2111-1-10-210-1-1-1-1110000000-2000-1-1001100000
χ24222222-122-1-1222-122-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-211111111-2-2202-2-2002200-2-2-2111-1102-10-1-111-1-1000000020001100-1-100000
χ2522222-12-1222-1-1222-12-12-12-1-1-12-12-12222-1-1-1-1-12-1-1-1-122-1-1-1-12002200-1-1-1-12200-12-1-120-1002-1-10000-1-1-1-122000-1-100000000-100
χ2622222-12-1222-1-1222-12-12-12-1-1-12-12-12222-1-1-1-1-12-1-1-1-122-1-1-1-1-2002-200-1-11122001-211-20-1002110000-1-1-1-1-2-20001100000000100
χ2722222-12-1222-1-1222-12-12-12-1-1-12-12-122-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1200-220011-1-1-2-200-12-1-120100-2-1-100001111-2-20001100000000100
χ2822222-12-1222-1-1222-12-12-12-1-1-12-12-122-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-200-2-2001111-2-2001-211-20100-2110000111122000-1-100000000-100
χ2922222-12-1222-1-1222-12-1-2-12-1-1-12-12-1-2-222-1-1-1-11-21111-2-21111200-2-200-1-1112200-12-1-1-20100-2110000-1-111-220001100000000-100
χ3022222-12-1222-1-1222-12-1-2-12-1-1-12-12-1-2-222-1-1-1-11-21111-2-21111-200-2200-1-1-1-122001-21120100-2-1-10000-1-1112-2000-1-100000000100
χ3122222-12-1222-1-1222-12-1-2-12-1-1-12-12-1-2-2-2-2-1-1-1-11-21111-2-211112002-2001111-2-200-12-1-1-20-100211000011-1-12-2000-1-100000000100
χ3222222-12-1222-1-1222-12-1-2-12-1-1-12-12-1-2-2-2-2-1-1-1-11-21111-2-21111-200220011-1-1-2-2001-21120-1002-1-1000011-1-1-220001100000000-100
χ332222-1222-12222-12-1-1-122-1-12-12-12-1-12222-1-1-1-12-1-1-122-1-1-1-1-1-102220-1-12200-1-1000000022-12-100-1-1-1-1-1-1-1-1002020000-1-100000-10
χ342222-1222-12222-12-1-1-122-1-12-12-12-1-12222-1-1-1-12-1-1-122-1-1-1-1-1-10-2-220112200-1-10000000-221-2-1001111-1-1-1-100-20-20000110000010
χ352222-1222-12222-12-1-1-122-1-12-12-12-1-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1022-20-1-1-2-2001100000002-2-12100-1-1-1-1111100-20-20000110000010
χ362222-1222-12222-12-1-1-122-1-12-12-12-1-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-2-2-2011-2-200110000000-2-21-210011111111002020000-1-100000-10
χ372222-1222-12222-12-1-1-12-2-1-12-12-12-1-1-2-222-1-1-1-1-2111-2-211111102-2-20-1-12200-1-100000002-21-2100-1-111-1-1110020-20000-1-10000010
χ382222-1222-12222-12-1-1-12-2-1-12-12-12-1-1-2-222-1-1-1-1-2111-2-21111110-22-20112200-1-10000000-2-2-1210011-1-1-1-11100-20200001100000-10
χ392222-1222-12222-12-1-1-12-2-1-12-12-12-1-1-2-2-2-2-1-1-1-1-2111-2-211111102-220-1-1-2-200110000000221-2-100-1-11111-1-100-20200001100000-10
χ402222-1222-12222-12-1-1-12-2-1-12-12-12-1-1-2-2-2-2-1-1-1-1-2111-2-21111110-222011-2-200110000000-22-12-10011-1-111-1-10020-20000-1-10000010
χ412-22-22222-2-2-2-2-222-22220-2-2-222-2-22-2002i−2i2-2-2200000000000000000002i−2i002i−2i2-200000000000000002i−2i0000000002-200002i−2i000
χ422-22-22222-2-2-2-2-222-22220-2-2-222-2-22-2002i−2i2-2-2200000000000000000002i−2i002i−2i-2200000000000000002i−2i000000000-220000−2i2i000
χ432-22-22222-2-2-2-2-222-22220-2-2-222-2-22-200−2i2i2-2-220000000000000000000−2i2i00−2i2i2-20000000000000000−2i2i0000000002-20000−2i2i000
χ442-22-22222-2-2-2-2-222-22220-2-2-222-2-22-200−2i2i2-2-220000000000000000000−2i2i00−2i2i-220000000000000000−2i2i000000000-2200002i−2i000
χ4544444-2-2-24-2-2-2-24-24-2-214-2-21-21-21-2-2-2-2001111-24-2-211-2-21111400040000-2-20000-2-211-2000001100000000000000000000000000
χ4644444-2-2-24-2-2-2-24-24-2-214-2-21-21-21-2-2-2-2001111-24-2-211-2-21111-4000-4000022000022-1-1200000-1-100000000000000000000000000
χ4744444-2-2-24-2-2-2-24-24-2-21-4-2-21-21-21-2-2220011112-422-1-122-1-1-1-14000-40000220000-2-211200000-1-100000000000000000000000000
χ4844444-2-2-24-2-2-2-24-24-2-21-4-2-21-21-21-2-2220011112-422-1-122-1-1-1-1-400040000-2-2000022-1-1-2000001100000000000000000000000000
χ494444-24-24-2-2-244-2-2-2-21-24-21-2-2-21-21-2-2-20011114-2-2-2-2-211111104400-2-20000000000000-20-2-200011110000000000000000000000
χ504444-24-24-2-2-244-2-2-2-21-24-21-2-2-21-21-2-2-20011114-2-2-2-2-21111110-4-4002200000000000002022000-1-1-1-10000000000000000000000
χ514444-24-24-2-2-244-2-2-2-21-2-4-21-2-2-21-21-222001111-422222-1-1-1-1-1-104-400-2-20000000000000-202200011-1-10000000000000000000000
χ524444-24-24-2-2-244-2-2-2-21-2-4-21-2-2-21-21-222001111-422222-1-1-1-1-1-10-440022000000000000020-2-2000-1-1110000000000000000000000
χ534444-2-24-2-244-2-2-24-21-2-241-2-21-2-2-2-2144441111-2-211-2-2-2-211110004000-2-200-2-200000000-200-20000001111000000000000000000
χ544444-2-24-2-244-2-2-24-21-2-241-2-21-2-2-2-2144-4-41111-2-211-2-2-2-21111000-4000220022000000002002000000-1-1-1-1000000000000000000
χ554444-2-24-2-244-2-2-24-21-2-2-41-2-21-2-2-2-21-4-444111122-1-12222-1-1-1-1000-4000-2-200-2-200000000200200000011-1-1000000000000000000
χ564444-2-24-2-244-2-2-24-21-2-2-41-2-21-2-2-2-21-4-4-4-4111122-1-12222-1-1-1-1000400022002200000000-200-2000000-1-111000000000000000000
χ5744-4-4444-444-44-4-4-4-444404-44-4-44-4-4-4000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-44-224-4-42-44-2-2042-2-42-222-423−2300-2-222000023−2323−232323−23−2300000000000000000000000000000000000000000000000000000
χ5944-4-444-2-44-224-4-42-44-2-2042-2-42-222-4−232300-2-2220000−2323−2323−23−23232300000000000000000000000000000000000000000000000000000
χ6044-4-44-24244-4-22-4-4-4-24-20-2-4-22242-420000-2-22200000000000000000000023−230000000000000023−2300000000000000000000000000
χ6144-4-44-24244-4-22-4-4-4-24-20-2-4-22242-420000-2-222000000000000000000000−232300000000000000−232300000000000000000000000000
χ6244-4-44-2-224-22-22-42-4-2-210-2212-1-2-12223−230011-1-10000−3323−23−3−33300000000023−230000003-3000000−3300000000000000000000000000
χ6344-4-44-2-224-22-22-42-4-2-210-2212-1-2-12223−230011-1-10000−3323−23−3−333000000000−2323000000-330000003−300000000000000000000000000
χ6444-4-44-2-224-22-22-42-4-2-210-2212-1-2-122−23230011-1-100003−3−232333−3−300000000023−23000000-33000000−3300000000000000000000000000
χ6544-4-44-2-224-22-22-42-4-2-210-2212-1-2-122−23230011-1-100003−3−232333−3−3000000000−23230000003-30000003−300000000000000000000000000
χ6644-4-4-244-4-24-44-42-42-2-240-2242-4-2-4220000-2-22200000000000000000−2i32i300000000000000000000−2i32i3000000000000000000000000
χ6744-4-4-244-4-24-44-42-42-2-240-2242-4-2-4220000-2-222000000000000000002i3−2i3000000000000000000002i3−2i3000000000000000000000000
χ6844-4-4-24-2-4-2-224-4222-21-20-2-1-22212-1223−230011-1-1000023−23−33−3−33300000−2i32i300000000000000000000i3−i33i−3i0000000000000000000000
χ6944-4-4-24-2-4-2-224-4222-21-20-2-1-22212-1223−230011-1-1000023−23−33−3−333000002i3−2i300000000000000000000−i3i3−3i3i0000000000000000000000
χ7044-4-4-24-2-4-2-224-4222-21-20-2-1-22212-12−23230011-1-10000−23233−333−3−300000−2i32i300000000000000000000i3−i3−3i3i0000000000000000000000
χ7144-4-4-24-2-4-2-224-4222-21-20-2-1-22212-12−23230011-1-10000−23233−333−3−3000002i3−2i300000000000000000000−i3i33i−3i0000000000000000000000
χ724-44-444-24-422-4-44-2-44-2-20-4224-222-2-40000-222-200000000000000000000000004-4000000000000000000000000000-22000000000
χ734-44-444-24-422-4-44-2-44-2-20-4224-222-2-40000-222-20000000000000000000000000-440000000000000000000000000002-2000000000
χ744-44-44-24-2-4-4-42244-4-24-202-42-2-2-4242004i−4i-222-20000000000000000000−2i2i004i−4i000000000000000000−2i2i00000000000000000000
χ754-44-44-24-2-4-4-42244-4-24-202-42-2-2-424200−4i4i-222-200000000000000000002i−2i00−4i4i0000000000000000002i−2i00000000000000000000
χ764-44-4-24442-4-4-4-4-242-2-24022-4-242-4-22004i−4i-222-200000000000000000004i−4i00−2i2i000000000000000000−2i2i00000000000000000000
χ774-44-4-24442-4-4-4-4-242-2-24022-4-242-4-2200−4i4i-222-20000000000000000000−4i4i002i−2i0000000000000000002i−2i00000000000000000000
χ784-44-4-2-24-22-4-422-2421-2-20-1221-222-2-1004i−4i1-1-11003-300003-33-30000000−2i2i00−2i2i000000000000000000i−i3i−3i000000000000000000
χ794-44-4-2-24-22-4-422-2421-2-20-1221-222-2-1004i−4i1-1-1100-330000-33-330000000−2i2i00−2i2i000000000000000000i−i−3i3i000000000000000000
χ804-44-4-2-24-22-4-422-2421-2-20-1221-222-2-100−4i4i1-1-11003-300003-33-300000002i−2i002i−2i000000000000000000−ii−3i3i000000000000000000
χ814-44-4-2-24-22-4-422-2421-2-20-1221-222-2-100−4i4i1-1-1100-330000-33-3300000002i−2i002i−2i000000000000000000−ii3i−3i000000000000000000
χ824-4-44444-4-4-44-44-4-444440-44-4-4-4-44-4400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-2-4-42-2-44-4244-2-20-4-22-422-2240000-22-22000000000000000000000000000000000000000000000000000000000023−2300000
χ844-4-4444-2-4-42-2-44-4244-2-20-4-22-422-2240000-22-220000000000000000000000000000000000000000000000000000000000−232300000
χ854-4-444-242-4-442-2-4-44-24-2024222-4-2-4-20000-22-220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ864-4-444-242-4-442-2-4-44-24-2024222-4-2-4-20000-22-2200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ874-4-44-244-42-44-442-4-2-2-2402-2-42-4242-20000-22-220000000000000000000000000000000000000000000000000000000023−230000000
χ884-4-44-244-42-44-442-4-2-2-2402-2-42-4242-20000-22-2200000000000000000000000000000000000000000000000000000000−23230000000
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
χ9188-8-8-4-484-48-8-444-842-4-4024-4-24-444-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-44-4-44-4444422202-22-2-22-2-2-243−4300-1-1110000−2323−232333−3−300000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-4-44-4444422202-22-2-22-2-2-2−434300-1-111000023−2323−23−3−33300000000000000000000000000000000000000000000000000000
χ948-88-88-4-4-4-844448-4-8-4-42044-2-424-2-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-48-48444-8-8-4-44-42-404-24-4-4-242400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4-444444-4-442220-2-2-222-2-22-20000-111-1006-60000-33-3300000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-444444-4-442220-2-2-222-2-22-20000-111-100-6600003-33-300000000000000000000000000000000000000000000000000000
χ988-8-888-4-44-84-44-4-848-4-4204-4-24-2424-400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-844-4-8844-4-42-4042444-2-4-2-400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-884-44-8-42-4-40-2-44-244-44200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-44-444-42220-22-2-2-2-22-220000-11-110000000033−33−333300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-44-444-42220-22-2-2-2-22-220000-11-1100000000−333333−3300000000000000000000000000000000000000000000000000000

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