Finite Group Databasebeta

← Group #13168638

Character table — Group #13168638

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121236661212121212121212121212122444446612121212121244444466612121212121212121212121212121212122246612121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-11111111-1111-1111111-1-1-1-11-1-111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1111-111-1-11111-1-111-1-11111-11-1-11111-1-1-1-11111-1-11-1-1-1-1-1-111-11-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-111-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11-111
χ511111111111111111111111111111111111111111111111-11-1111-1-111111111-1-1-1-1-1-1-1-11111-11-1-111111111-11-1-1-111-1-1-1-11-1-1-1
χ611111111111111111111111111111111111111111111111-11-1-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-11-111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-111-1111
χ711111111111111111111111111111111111111111111111-1-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-1-11-1-1-11-1-1-1-1-1-111111-1-111-1-111-1-1-1-111
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
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-111-1-1-1-1-1-111111-11-11-1-11-1-111-1-111-1-1-111-1-1-1-111-1-1111-1
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-1-1-111111111111-1111-1-1-1-1-111-1-1-1-111-1-1-1-1-1111111-1-1-11
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11111111-1-111-1-1-1-1111-1-1-1-11-11-1-1-1-11111-1-11-111111-1-1-1-1-11-11
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111111-1-111-1-111-1-1111-1-11-11-1-1-1-1-1-111-1-11111-111-1-1-1-1111-11-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-111-11-1111111-1-111-1-111-111-1-1-1-1111-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-11-11111-1-1-1-1111-111111-1-1-1-1-111-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11111-1-1111111-1-1-11-1-1-111111-1-11111-1-1-1-1-1-1-1111111-1-11-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-111-1-1-1-111-1-1-11-11-111-111-1-111-1-111-111-1-1-1-111-1-111-11
χ17222222-12-1-12222-122-1-122-1-12-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-122200222220000000022-1-1-1-1-102-120-1-1-1-1-1-10000200-1-100-1-1000000
χ18222222-12-1-12222-122-1-122-1-12-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12-2200-222-2-200000000-2-2-1-1-1-110-2120-1-111110000-200110011000000
χ19222222-12-1-12222-122-1-122-1-12-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-22-2002-2-22200000000-2-21111-102-1-2011-1-1-1-10000-200110011000000
χ20222222-12-1-12222-122-1-122-1-12-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-200-2-2-2-2-20000000022111110-21-201111110000200-1-100-1-1000000
χ21222222-12-1-12222-122-1-1-22-1-12-1-1-1-1211-1-1-1-1-2-2-2-21111111122-200-222-2-20000000022-1-1-11-1021-2011-1-1110000-2001100-1-1000000
χ22222222-12-1-12222-122-1-1-22-1-12-1-1-1-1211-1-1-1-1-2-2-2-2111111112-2-2002222200000000-2-2-1-1-1110-2-1-201111-1-10000200-1-10011000000
χ23222222-12-1-12222-122-1-1-22-1-12-1-1-1-1211-1-1-1-1-2-2-2-211111111-22200-2-2-2-2-200000000-2-2111-1-102120-1-1-1-1110000200-1-10011000000
χ24222222-12-1-12222-122-1-1-22-1-12-1-1-1-1211-1-1-1-1-2-2-2-211111111-2-22002-2-2220000000022111-110-2-120-1-111-1-10000-2001100-1-1000000
χ2522222-12222-1-12-122-1-122-1-12-12-12-1-122-1-1-1-1-12-1-122-1-1-1-1-1-102022200-1-1-1-12222000000002-1-120200-1-1-1-1-1-1-1-102000-1-10000-1000
χ2622222-12222-1-12-122-1-122-1-12-12-12-1-122-1-1-1-1-12-1-122-1-1-1-1-1-1020-2-2200-1-111-2-2-2-20000000021-120-200-1-1-1-111110-20001100001000
χ2722222-12222-1-12-122-1-122-1-12-12-12-1-122-1-1-1-1-12-1-122-1-1-1-1-1-10-2022-20011-1-122-2-200000000-2-11-202001111-1-1-1-10-20001100001000
χ2822222-12222-1-12-122-1-122-1-12-12-12-1-122-1-1-1-1-12-1-122-1-1-1-1-1-10-20-2-2-2001111-2-22200000000-211-20-2001111111102000-1-10000-1000
χ2922222-12222-1-12-122-1-12-2-1-12-12-12-1-1-2-2-1-1-1-11-211-2-21111110202-2-20011-1-1-2-2-2-20000000021-1-20200-1-111-1-11102000110000-1000
χ3022222-12222-1-12-122-1-12-2-1-12-12-12-1-1-2-2-1-1-1-11-211-2-2111111020-22-20011112222000000002-1-1-20-200-1-11111-1-10-2000-1-100001000
χ3122222-12222-1-12-122-1-12-2-1-12-12-12-1-1-2-2-1-1-1-11-211-2-21111110-202-2200-1-1-1-1-2-22200000000-2112020011-1-1-1-1110-2000-1-100001000
χ3222222-12222-1-12-122-1-12-2-1-12-12-12-1-1-2-2-1-1-1-11-211-2-21111110-20-22200-1-11122-2-200000000-2-1120-20011-1-111-1-102000110000-1000
χ332222-122-12222-122-1-12-12-12-1-1-12-12-122-1-1-1-12-1-1-1-1-122-1-1-1-1202220-1-10022-1-10022002-1-120200-1-1-1-10000-1-1-1-1002000000-1-10-100
χ342222-122-12222-122-1-12-12-12-1-1-12-12-122-1-1-1-12-1-1-1-1-122-1-1-1-1202-2-20-1-100-2-21100-2-2002-1-120-200-11-1-10000111100-2000000110100
χ352222-122-12222-122-1-12-12-12-1-1-12-12-122-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2220110022-1-100-2-200-211-202001-1110000-1-1-1-100-2000000110100
χ362222-122-12222-122-1-12-12-12-1-1-12-12-122-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2-2-201100-2-211002200-211-20-200111100001111002000000-1-10-100
χ372222-122-12222-122-1-12-1-2-12-1-1-12-12-1-2-2-1-1-1-1-211111-2-2111120-22-20-1-100221100-2-2002-1-1-20-2001-1110000-1-111002000000110-100
χ382222-122-12222-122-1-12-1-2-12-1-1-12-12-1-2-2-1-1-1-1-211111-2-2111120-2-220-1-100-2-2-1-10022002-1-1-202001111000011-1-100-2000000-1-10100
χ392222-122-12222-122-1-12-1-2-12-1-1-12-12-1-2-2-1-1-1-1-211111-2-21111-2022-2011002211002200-21120-200-1-1-1-10000-1-11100-2000000-1-10100
χ402222-122-12222-122-1-12-1-2-12-1-1-12-12-1-2-2-1-1-1-1-211111-2-21111-202-2201100-2-2-1-100-2-200-21120200-11-1-1000011-1-1002000000110-100
χ412-22-2222-22-2-22-2-2-222220-22-2-2-2-22-220022-2-2000000000000000000000000002i−2i2-22i−2i00000000000000000000000002i−2i2i−2i2-20000
χ422-22-2222-22-2-22-2-2-222220-22-2-2-2-22-220022-2-2000000000000000000000000002i−2i-22−2i2i00000000000000000000000002i−2i−2i2i-220000
χ432-22-2222-22-2-22-2-2-222220-22-2-2-2-22-220022-2-200000000000000000000000000−2i2i2-2−2i2i0000000000000000000000000−2i2i−2i2i2-20000
χ442-22-2222-22-2-22-2-2-222220-22-2-2-2-22-220022-2-200000000000000000000000000−2i2i-222i−2i0000000000000000000000000−2i2i2i−2i-220000
χ4544444-2-24-2-2-2-24-2-24-21-24-21-2-2-21-21-2-2-21111-24-2-2-2-211111104000400-2-200000000000000-20-2-2000011110000000000000000000
χ4644444-2-24-2-2-2-24-2-24-21-24-21-2-2-21-21-2-2-21111-24-2-2-2-21111110-4000-400220000000000000020220000-1-1-1-10000000000000000000
χ4744444-2-24-2-2-2-24-2-24-21-2-4-21-2-2-21-21-22211112-42222-1-1-1-1-1-104000-4002200000000000000-20-22000011-1-10000000000000000000
χ4844444-2-24-2-2-2-24-2-24-21-2-4-21-2-2-21-21-22211112-42222-1-1-1-1-1-10-4000400-2-200000000000000202-20000-1-1110000000000000000000
χ494444-24-2-2-2-244-24-2-2-2-214-2-21-21-21-2-2-2-211114-2-2-211-2-21111404000-2-2000000000000-211-20000-201100000000000000000000000
χ504444-24-2-2-2-244-24-2-2-2-214-2-21-21-21-2-2-2-211114-2-2-211-2-21111-40-4000220000000000002-1-12000020-1-100000000000000000000000
χ514444-24-2-2-2-244-24-2-2-2-21-4-2-21-21-21-2-2221111-4222-1-122-1-1-1-140-4000-2-2000000000000-2112000020-1-100000000000000000000000
χ524444-24-2-2-2-244-24-2-2-2-21-4-2-21-21-21-2-2221111-4222-1-122-1-1-1-1-404000220000000000002-1-1-20000-201100000000000000000000000
χ534444-2-24-244-2-2-2-24-21-2-241-2-21-2-2-2-21441111-2-211-2-2-2-211110004400000-2-2-2-200000000000-2000-20000001111000000000000000
χ544444-2-24-244-2-2-2-24-21-2-241-2-21-2-2-2-21441111-2-211-2-2-2-21111000-4-40000022220000000000020002000000-1-1-1-1000000000000000
χ554444-2-24-244-2-2-2-24-21-2-2-41-2-21-2-2-2-21-4-4111122-1-12222-1-1-1-10004-400000-2-222000000000002000-200000011-1-1000000000000000
χ564444-2-24-244-2-2-2-24-21-2-2-41-2-21-2-2-2-21-4-4111122-1-12222-1-1-1-1000-440000022-2-200000000000-20002000000-1-111000000000000000
χ5744-4-44444-44-4-4-44-4-444404-44-4-44-4-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-242-2-4-4-442-44-2-2042-2-42-222-423−23-22-22000023−2323−232323−23−230000000000000000000000000000000000000000000000000000000
χ5944-4-444-242-2-4-4-442-44-2-2042-2-42-222-4−2323-22-220000−2323−2323−23−2323230000000000000000000000000000000000000000000000000000000
χ6044-4-44-244-4422-4-2-4-4-2-240-2242-4-2-42200-22-220000000000000000000023−2300000000000000000000000023−230000000000000000000
χ6144-4-44-244-4422-4-2-4-4-2-240-2242-4-2-42200-22-2200000000000000000000−2323000000000000000000000000−23230000000000000000000
χ6244-4-44-2-242-222-4-22-4-21-20-2-1-22212-1223−231-11-1000023−23−33−3−3330000000023−2300000000000000000000003-3−330000000000000000000
χ6344-4-44-2-242-222-4-22-4-21-20-2-1-22212-1223−231-11-1000023−23−33−3−33300000000−23230000000000000000000000-333−30000000000000000000
χ6444-4-44-2-242-222-4-22-4-21-20-2-1-22212-12−23231-11-10000−23233−333−3−30000000023−230000000000000000000000-33−330000000000000000000
χ6544-4-44-2-242-222-4-22-4-21-20-2-1-22212-12−23231-11-10000−23233−333−3−300000000−232300000000000000000000003-33−30000000000000000000
χ6644-4-4-244-2-44-4-424-42-24-20-2-4-22242-4200-22-22000000000000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ6744-4-4-244-2-44-4-424-42-24-20-2-4-22242-4200-22-220000000000000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ6844-4-4-24-2-22-2-4-42422-2-210-2212-1-2-12223−231-11-10000−3323−23−3−333000000−2i32i30000000000000i3−i300000003i−3i00000000000000000000000
χ6944-4-4-24-2-22-2-4-42422-2-210-2212-1-2-12223−231-11-10000−3323−23−3−3330000002i3−2i30000000000000−i3i30000000−3i3i00000000000000000000000
χ7044-4-4-24-2-22-2-4-42422-2-210-2212-1-2-122−23231-11-100003−3−232333−3−3000000−2i32i30000000000000i3−i30000000−3i3i00000000000000000000000
χ7144-4-4-24-2-22-2-4-42422-2-210-2212-1-2-122−23231-11-100003−3−232333−3−30000002i3−2i30000000000000−i3i300000003i−3i00000000000000000000000
χ724-44-444-2-4-22-44-4-4244-2-20-4-22-422-22400-2-2220000000000000000000000000000004i−4i000000000000000000000000000−2i2i000000
χ734-44-444-2-4-22-44-4-4244-2-20-4-22-422-22400-2-222000000000000000000000000000000−4i4i0000000000000000000000000002i−2i000000
χ744-44-44-24-44-42-2-42-44-2-2402-2-42-4242-200-2-222000000000000000000000000004i−4i00000000000000000000000000000−2i2i00000000
χ754-44-44-24-44-42-2-42-44-2-2402-2-42-4242-200-2-22200000000000000000000000000−4i4i000000000000000000000000000002i−2i00000000
χ764-44-4-24424-4-442-4-4-2-24-2024222-4-2-4-200-2-22200000000000000000000000000004-40000000000000000000000000000000-220000
χ774-44-4-24424-4-442-4-4-2-24-2024222-4-2-4-200-2-2220000000000000000000000000000-4400000000000000000000000000000002-20000
χ784-4-44444-4-4-44-44-44-44440-4-4-444-4-44-4004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4224-44-4-2-44-2-20-4224-222-2-400-222-20000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ804-4-4444-2-4224-44-4-2-44-2-20-4224-222-2-400-222-200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ814-4-444-24-4-4-4-22424-4-2-24022-4-242-4-2200-222-2000000000000000000000023−2300000000000000000000000023−2300000000000000000
χ824-4-444-24-4-4-4-22424-4-2-24022-4-242-4-2200-222-20000000000000000000000−2323000000000000000000000000−232300000000000000000
χ834-4-44-2442-4-44-4-2-442-24-202-42-2-2-424200-222-200000000000000000000000023−2300000000000000000000000023−23000000000000000
χ844-4-44-2442-4-44-4-2-442-24-202-42-2-2-424200-222-2000000000000000000000000−2323000000000000000000000000−2323000000000000000
χ854-4-44-2-242-4-4-22-22421-2-20-1221-222-2-1001-1-11003-300003-33-3000000000023−2323−230000000000000000000000−33−33000000000000000
χ864-4-44-2-242-4-4-22-22421-2-20-1221-222-2-1001-1-11003-300003-33-30000000000−2323−232300000000000000000000003−33−3000000000000000
χ874-4-44-2-242-4-4-22-22421-2-20-1221-222-2-1001-1-1100-330000-33-33000000000023−23−23230000000000000000000000−333−3000000000000000
χ884-4-44-2-242-4-4-22-22421-2-20-1221-222-2-1001-1-1100-330000-33-330000000000−232323−2300000000000000000000003−3−33000000000000000
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
χ9188-8-8-4-48-4-88444-4-842-4-4024-4-24-444-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-44-4444-44422202-22-2-22-2-2-243−43-11-110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-4444-44422202-22-2-22-2-2-2−4343-11-11000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000
χ948-88-88-4-4-8-444-4-8448-42-4042444-2-4-2-40022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-48-44-44-884-84-4-4-4204-4-24-2424-40022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4848-84-444-8-42-4-40-2-44-244-4420022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-444-4444-42220-22-2-2-2-22-2200-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44-444-4444-42220-22-2-2-2-22-2200-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-844-4484-4-8-42-404-24-4-4-2424002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-44448-8-4-8-44-4-42044-2-424-2-44002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-44-44-442220-2-2-222-2-22-200-111-1006-60000-33-330000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-44-44-442220-2-2-222-2-22-200-111-100-6600003-33-30000000000000000000000000000000000000000000000000000000

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