Finite Group Databasebeta

← Group #13168477

Character table — Group #13168477

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order12223336666666663334666666666121244366612121212121212121212121224444661212121212124466612121212121212121212121212121212124444412121212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-111-1-11111-1-1111-111-111-111-1-1-1-111111-11-1-1-1-1-1-1-1-111-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-11-1-1111111-1-1-1-1-11-1-11111-1-111111111-11-11-111-1-1-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11-1-11111-1-111-1-11
χ51111111111111111111111111111111-1-111111111111111111-11111111-1-1-1-1111111111-1-11111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-111-1-1-1-1-1-1-1-1111-111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-11-11-1-111-1-1-1-1-1-1-1-1-11-1-11-1-11-1-11111-1-1-1-11-11-1-1-1-1-1-1-1-111111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-11111-1-1-1-1-11-1-1-1-11111-1-111-1-11-1-111-1-111-1-1-111
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111111111-1-1-11-1-1-1-1-111-1-111-1-11-1-11-111-1-1111111-1-1-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1111-1-1-1111-1-11111-1-1-111-1-1-1-1-1-111-1-11111-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1111-1-1-11111-1-111-1-1-1-11111111-1-1-1-1-1-11-11
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111-1-1-1111-1-1-1-111-1-111-1-11111111-1-1-1-1111-1-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-111111-1-1-1111-1-1-111-1-1-1-111-111-1-1-1-1-1-111-1-1-1-1111
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-1-1111-111111-1-111-1-1111-1-11-111-1-11111-1-1-1-11
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-11111-1-11-1-111-1-11111-11-1
χ17222222-122-122-1-1222-1-1222-1-1-1-1-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-1202222222000022-1-1-1-12-1-1002-1-1-1-1-1-100000000200-1-1-1-10000000
χ18222222-122-122-1-1222-1-1222-1-1-1-1-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-120-22-222-2-20000-2-2-1-1-112-1100-2-1-1111100000000-20011110000000
χ19222222-122-122-1-1222-1-1222-1-1-1-1-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-1-202-22-2-2220000-2-2111-1-21-100211-1-1-1-100000000-20011110000000
χ20222222-122-122-1-1222-1-1222-1-1-1-1-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-1-20-2-2-2-2-2-2-20000221111-21100-211111100000000200-1-1-1-10000000
χ21222222-122-122-1-1222-1-1-222-1-1-1-1-1-121100-1-1-1-1-2-21111-2-21111202-2-222-2-20000-2-2-1-1-1-1-2110021111-1-100000000200-1-1110000000
χ22222222-122-122-1-1222-1-1-222-1-1-1-1-1-121100-1-1-1-1-2-21111-2-2111120-2-222222000022-1-1-11-21-100-211-1-11100000000-20011-1-10000000
χ23222222-122-122-1-1222-1-1-222-1-1-1-1-1-121100-1-1-1-1-2-21111-2-21111-2022-2-2-2-2-2000022111-12-11002-1-111-1-100000000-20011-1-10000000
χ24222222-122-122-1-1222-1-1-222-1-1-1-1-1-121100-1-1-1-1-2-21111-2-21111-20-222-2-2220000-2-211112-1-100-2-1-1-1-11100000000200-1-1110000000
χ2522222-12-1222-122-12-12-12-1-12-1-12-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-122020-1-100-1-122002-1-10-120-120-1-10000-1-1-1-120200000000-1-100-100
χ2622222-12-1222-122-12-12-12-1-12-1-12-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-1-220-201100-1-12200-21101-20-120110000-1-1-1-1-20-2000000001100100
χ2722222-12-1222-122-12-12-12-1-12-1-12-12-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-12-2020-1-10011-2-2002-1-10-1201-20-1-100001111-20-2000000001100100
χ2822222-12-1222-122-12-12-12-1-12-1-12-12-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-2-20-20110011-2-200-21101-201-20110000111120200000000-1-100-100
χ2922222-12-1222-122-12-12-1-2-1-12-1-12-12-1-2-222-1-1-1-11-211-2-21111112-20-20-1-100-1-122002-1-101-201-20110000-1-11120-200000000-1-100100
χ3022222-12-1222-122-12-12-1-2-1-12-1-12-12-1-2-222-1-1-1-11-211-2-2111111-2-20201100-1-12200-2110-1201-20-1-10000-1-111-202000000001100-100
χ3122222-12-1222-122-12-12-1-2-1-12-1-12-12-1-2-2-2-2-1-1-1-11-211-2-2111111220-20-1-10011-2-2002-1-101-20-12011000011-1-1-202000000001100-100
χ3222222-12-1222-122-12-12-1-2-1-12-1-12-12-1-2-2-2-2-1-1-1-11-211-2-2111111-22020110011-2-200-2110-120-120-1-1000011-1-120-200000000-1-100100
χ332222-1222-12-12222-1-1-122-1-1-122-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-10220200-1-122-1-10000020022-1-100-1-1-1-1-1-1-1-102020-1-1000000000-10
χ342222-1222-12-12222-1-1-122-1-1-122-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-102-20-2001122-1-100000-200-22-11001111-1-1-1-10-20-201100000000010
χ352222-1222-12-12222-1-1-122-1-1-122-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-220200-1-1-2-211000002002-21-100-1-1-1-111110-20-201100000000010
χ362222-1222-12-12222-1-1-122-1-1-122-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-20-20011-2-21100000-200-2-211001111111102020-1-1000000000-10
χ372222-1222-12-12222-1-1-12-2-1-1-122-12-1-1-2-222-1-1-1-1-21-2-2111111110-220-2001122-1-100000200-2-21-10011-1-1-1-111020-2011000000000-10
χ382222-1222-12-12222-1-1-12-2-1-1-122-12-1-1-2-222-1-1-1-1-21-2-2111111110-2-20200-1-122-1-100000-2002-21100-1-111-1-1110-2020-1-100000000010
χ392222-1222-12-12222-1-1-12-2-1-1-122-12-1-1-2-2-2-2-1-1-1-1-21-2-2111111110220-20011-2-21100000200-22-1-10011-1-111-1-10-2020-1-100000000010
χ402222-1222-12-12222-1-1-12-2-1-1-122-12-1-1-2-2-2-2-1-1-1-1-21-2-21111111102-20200-1-1-2-21100000-20022-1100-1-11111-1-1020-2011000000000-10
χ4122-2-2222-2-22-2-2-2-2222220-2-2-2-22-2-222002-22-2-220000000000000000000002-22-22i−2i00000000000000002-2000000000002i−2i002i−2i000
χ4222-2-2222-2-22-2-2-2-2222220-2-2-2-22-2-222002-22-2-220000000000000000000002-22-2−2i2i00000000000000002-200000000000−2i2i00−2i2i000
χ4322-2-2222-2-22-2-2-2-2222220-2-2-2-22-2-22200-222-2-22000000000000000000000-22-222i−2i0000000000000000-22000000000002i−2i00−2i2i000
χ4422-2-2222-2-22-2-2-2-2222220-2-2-2-22-2-22200-222-2-22000000000000000000000-22-22−2i2i0000000000000000-2200000000000−2i2i002i−2i000
χ4544444-2-2-24-24-2-2-2-24-2-214-2-2-211-21-2-2-2-2001111-2411-2-2-2-2111140040-2-200000000-2110-2-200001100000000000000000000000000
χ4644444-2-2-24-24-2-2-2-24-2-214-2-2-211-21-2-2-2-2001111-2411-2-2-2-21111-400-4022000000002-1-10220000-1-100000000000000000000000000
χ4744444-2-2-24-24-2-2-2-24-2-21-4-2-2-211-21-2-2220011112-4-1-12222-1-1-1-1400-40-2-200000000-2110220000-1-100000000000000000000000000
χ4844444-2-2-24-24-2-2-2-24-2-21-4-2-2-211-21-2-2220011112-4-1-12222-1-1-1-1-4004022000000002-1-10-2-200001100000000000000000000000000
χ494444-24-24-2-2-24-2-24-2-21-24-2-21-2-21-21-2-2-20011114-2-2-211-2-211110040400-2-2000000000-200-200-20011110000000000000000000000
χ504444-24-24-2-2-24-2-24-2-21-24-2-21-2-21-21-2-2-20011114-2-2-211-2-2111100-40-40022000000000200200200-1-1-1-10000000000000000000000
χ514444-24-24-2-2-24-2-24-2-21-2-4-2-21-2-21-21-222001111-4222-1-122-1-1-1-10040-40022000000000-200200-200-1-1110000000000000000000000
χ524444-24-24-2-2-24-2-24-2-21-2-4-2-21-2-21-21-222001111-4222-1-122-1-1-1-100-40400-2-2000000000200-20020011-1-10000000000000000000000
χ534444-2-24-2-24-2-244-2-21-2-2411-2-2-2-2-2-2144441111-2-2-2-2-2-2111111040000000-2-2-2-2000000000-2-200000001111000000000000000000
χ544444-2-24-2-24-2-244-2-21-2-2411-2-2-2-2-2-2144-4-41111-2-2-2-2-2-21111110-400000002222000000000220000000-1-1-1-1000000000000000000
χ554444-2-24-2-24-2-244-2-21-2-2-411-2-2-2-2-2-21-4-4441111222222-1-1-1-1-1-10-40000000-2-2-2-200000000022000000011-1-1000000000000000000
χ564444-2-24-2-24-2-244-2-21-2-2-411-2-2-2-2-2-21-4-4-4-41111222222-1-1-1-1-1-10400000002222000000000-2-20000000-1-111000000000000000000
χ5744-4-444-2-4-4-2-4-422444-2-20-4-422-222-240000-222-200000000000000000000000004i−4i00000000000000000000000000000−2i2i0000000
χ5844-4-444-2-4-4-2-4-422444-2-20-4-422-222-240000-222-20000000000000000000000000−4i4i000000000000000000000000000002i−2i0000000
χ5944-4-44-242-44-42-4-4-24-24-2022-42-2-424-2004-4-222-2000000000000000000000-224-4000000000000000000-2200000000000000000000
χ6044-4-44-242-44-42-4-4-24-24-2022-42-2-424-200-44-222-20000000000000000000002-2-440000000000000000002-200000000000000000000
χ6144-4-4-244-4242-4-4-44-2-2-240222-442-4-2-2004-4-222-20000000000000000000004-4-22000000000000000000-2200000000000000000000
χ6244-4-4-244-4242-4-4-44-2-2-240222-442-4-2-200-44-222-2000000000000000000000-442-20000000000000000002-200000000000000000000
χ6344-4-4-2-2422422-4-4-2-21-2-20-1-122-222-21004-41-1-110000003-333-3-3000000000-22-220000000000000000001-13-3000000000000000000
χ6444-4-4-2-2422422-4-4-2-21-2-20-1-122-222-21004-41-1-11000000-33-3-333000000000-22-220000000000000000001-1-33000000000000000000
χ6544-4-4-2-2422422-4-4-2-21-2-20-1-122-222-2100-441-1-110000003-333-3-30000000002-22-2000000000000000000-11-33000000000000000000
χ6644-4-4-2-2422422-4-4-2-21-2-20-1-122-222-2100-441-1-11000000-33-3-3330000000002-22-2000000000000000000-113-3000000000000000000
χ674-44-4444-4-4-4444-4-4-444404-44-4-4-44-4-4000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-4-4244-22-4-44-2-204-4-2222-22-40000-2-22200000000000000000000000000000000000000000000000000000023−23000000000
χ694-44-444-2-4-4244-22-4-44-2-204-4-2222-22-40000-2-222000000000000000000000000000000000000000000000000000000−2323000000000
χ704-44-44-242-4-44-24-42-4-24-20-22422-4-2-420000-2-222000000000000000000000000000000000000000000000000000000000023−2300000
χ714-44-44-242-4-44-24-42-4-24-20-22422-4-2-420000-2-2220000000000000000000000000000000000000000000000000000000000−232300000
χ724-44-4-244-42-4-244-4-42-2-240-22-2-4-424220000-2-2220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ734-44-4-244-42-4-244-4-42-2-240-22-2-4-424220000-2-22200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ744-4-4444444-4-4-4-44-4-44440-44-44-44-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2442-4-42-2-4-44-2-20-442-22-222-423−2300-22-220023−2323−230023−2323−2300000000000000000000000000000000000000000000000000000
χ764-4-4444-2442-4-42-2-4-44-2-20-442-22-222-4−232300-22-2200−2323−232300−2323−232300000000000000000000000000000000000000000000000000000
χ774-4-444-24-24-4-42-442-4-24-202-2-4-2242-420000-22-2200000000000000000−2i32i3000000000−2i32i300000000000000000000000000000000000
χ784-4-444-24-24-4-42-442-4-24-202-2-4-2242-420000-22-22000000000000000002i3−2i30000000002i3−2i300000000000000000000000000000000000
χ794-4-444-2-2-242-422-22-4-2-2102-221-1-2-12223−23001-11-100−3323−2300−33−3300000−2i32i3000000000i3−i300000003i−3i00000000000000000000000000
χ804-4-444-2-2-242-422-22-4-2-2102-221-1-2-12223−23001-11-100−3323−2300−33−33000002i3−2i3000000000−i3i30000000−3i3i00000000000000000000000000
χ814-4-444-2-2-242-422-22-4-2-2102-221-1-2-122−2323001-11-1003−3−2323003−33−300000−2i32i3000000000i3−i30000000−3i3i00000000000000000000000000
χ824-4-444-2-2-242-422-22-4-2-2102-221-1-2-122−2323001-11-1003−3−2323003−33−3000002i3−2i3000000000−i3i300000003i−3i00000000000000000000000000
χ834-4-44-2444-2-42-4-44-42-2-2402-224-4-2-4220000-22-220000000000000000000−2i32i3000000000000000000−2i32i3000000000000000000000000
χ844-4-44-2444-2-42-4-44-42-2-2402-224-4-2-4220000-22-2200000000000000000002i3−2i30000000000000000002i3−2i3000000000000000000000000
χ854-4-44-24-24-222-42-2-42-21-202-2-1-2212-1223−23001-11-10023−23−3300−33−330000000−2i32i3000000000000000000i3−i33i−3i0000000000000000000000
χ864-4-44-24-24-222-42-2-42-21-202-2-1-2212-1223−23001-11-10023−23−3300−33−3300000002i3−2i3000000000000000000−i3i3−3i3i0000000000000000000000
χ874-4-44-24-24-222-42-2-42-21-202-2-1-2212-12−2323001-11-100−23233−3003−33−30000000−2i32i3000000000000000000i3−i3−3i3i0000000000000000000000
χ884-4-44-24-24-222-42-2-42-21-202-2-1-2212-12−2323001-11-100−23233−3003−33−300000002i3−2i3000000000000000000−i3i33i−3i0000000000000000000000
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
χ9188-8-88-4-44-8-4-8444-48-4-420444-224-2-4-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-84-44-8448-4-42-4044-24-4-242-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-444-44444-4-42220-2-2-2-22-2-2220000-111-10000006-6-3-33300000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-444-44444-4-42220-2-2-2-22-2-2220000-111-1000000-6633-3-300000000000000000000000000000000000000000000000000000
χ958-88-88-4-44-848-4-444-8-4-420-44-4-2-24244000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-4-844-48-44-84-42-40-44244-2-4-24000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4844-8-4-48-8442-4-402-2-4444-44-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4444-4-4-444422202-22-2-2-22-2-20000-1-1110000000033−33−333300000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4444-4-4-444422202-22-2-2-22-2-20000-1-11100000000−333333−3300000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-4-4-844-88442-4-40-224-44-444-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-4-44444-4442220-22-22-22-2-2-243−4300-11-1100−2323−2323003−33−300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-4-44444-4442220-22-22-22-2-2-2−434300-11-110023−2323−2300−33−3300000000000000000000000000000000000000000000000000000

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