Finite Group Databasebeta

← Group #13168548

Character table — Group #13168548

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order1222333666666666333466666666644366612121212121212121212121212244446612121212121212121212446661212121212121212121212121212122224466121212124466122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1111111111-1-1-1-1-1-1111111-1-1111111-1-1-1-111-1-1-111-1-1-1-1-1-1-11-1-1
χ3111111111111111111111111111111111111111111111111-1-1111-1-11111-1-11111-1-1-1-1-1-1111111-1-1111111-1-1-111-1-111-1-1-1-1-1-11-1
χ4111111111111111111111111111111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-11-1-1-1-1-1-111111-1-11
χ511111111111111111111111111111-1-1111111111111111111111-111-1-1-1-1111111111111-1-111-1-111-1-11111-1-11-1-1-1-1-1-111-1-11-1-1-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ711111111111111111111111111111-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-111-1-1-1-111-11-11
χ811111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-1-111-1-111111-1-1-11-111-1-1-1-111-1-11-1-11-1-1-1-1-11111-111-1
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1111111-1-1-1-111-1-1111-1-1-1-1111-1-1-1-1-1-1111-11-11-1-111-1-1-1-111-11
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-11-1-11-11111-1-111-1-1-1111-111-1-1-1-1-1-11-111
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1111111-1-11111-1-1-11-1-1-111111-1-1-1-111-11-1-1111111111-1-1-1-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-1-1-1-1-111-1-111111-1111-1-1-1-1-11111-1-1-11-1-11111111-1-1-1-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-1111-111-11-1-1-1-111-1-111-1111-111-1-1-1-1111-11-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1111111-1-11-11-11-1-111-1-11111-1-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-111-1-11111-1-1-1111-11-1-11111-1-1111-1-11-1-1-1-1-111-1-1-1111
χ17222222-1-1222-1-12222-1-122-1-12-1-1-1-1222-1-1-1-12-1222-1-1-1-1-1-1-1-1220022222-1-1-1-1000000-1-1-12-1200-1-1-1-1-1-1000022000-1-10000000-100
χ18222222-1-1222-1-12222-1-122-1-12-1-1-1-1222-1-1-1-12-1222-1-1-1-1-1-1-1-1-2-2002-2-222-1-111000000111-2-1200-1-111-1-10000-2-2000110000000100
χ19222222-1-1222-1-12222-1-122-1-12-1-1-1-12-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-12200-222-2-211-1-1000000-1-1-121-20011-1-1110000-2-2000110000000100
χ20222222-1-1222-1-12222-1-122-1-12-1-1-1-12-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-1-2-200-2-2-2-2-21111000000111-21-200111111000022000-1-10000000-100
χ21222222-1-1222-1-12222-1-1-22-1-12-1-1-1-1222-1-1-1-1-21-2-2-2111111112-200-22222-1-111000000-1-1-1-21-200-1-1111100002-2000110000000-100
χ22222222-1-1222-1-12222-1-1-22-1-12-1-1-1-1222-1-1-1-1-21-2-2-211111111-2200-2-2-222-1-1-1-100000011121-200-1-1-1-1110000-22000-1-10000000100
χ23222222-1-1222-1-12222-1-1-22-1-12-1-1-1-12-2-2-1-1-1-1-21-2-2-2111111112-200222-2-21111000000-1-1-1-2-12001111-1-10000-22000-1-10000000100
χ24222222-1-1222-1-12222-1-1-22-1-12-1-1-1-12-2-2-1-1-1-1-21-2-2-211111111-22002-2-2-2-211-1-10000001112-120011-1-1-1-100002-2000110000000-100
χ2522222-122-12-12222-1-12-12-12-1-1-12-12-100-1-1-1-1-122-1-1-1-122-1-1-1-122220-1-1000022-1-122222-1-1-1002-100-1-100-1-1-1-1002000000-1-100-1000
χ2622222-122-12-12222-1-12-12-12-1-1-12-12-100-1-1-1-1-122-1-1-1-122-1-1-1-122-2-20-1-100002211-2-2-2-22-1-1-100-2100-1-100111100-200000011001000
χ2722222-122-12-12222-1-12-12-12-1-1-12-12-100-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2220110000-2-2-1-122-2-2-2111002-1001100-1-1-1-100-200000011001000
χ2822222-122-12-12222-1-12-12-12-1-1-12-12-100-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-20110000-2-211-2-222-211100-210011001111002000000-1-100-1000
χ2922222-122-12-12222-1-12-1-2-12-1-1-12-12-100-1-1-1-11-2-21111-2-211112-22-20-1-10000-2-2-1-1-2-2222-1-110021001100-1-11100-2000000-1-1001000
χ3022222-122-12-12222-1-12-1-2-12-1-1-12-12-100-1-1-1-11-2-21111-2-211112-2-220-1-10000-2-21122-2-22-1-1100-2-100110011-1-10020000001100-1000
χ3122222-122-12-12222-1-12-1-2-12-1-1-12-12-100-1-1-1-11-2-21111-2-21111-222-2011000022-1-1-2-2-2-2-211-1002100-1-100-1-1110020000001100-1000
χ3222222-122-12-12222-1-12-1-2-12-1-1-12-12-100-1-1-1-11-2-21111-2-21111-22-22011000022112222-211-100-2-100-1-10011-1-100-2000000-1-1001000
χ332222-12222-1222-1-12-1-122-1-12-12-12-1-122-1-1-1-122-1-1-122-1-1-1-1-1-10022200-1-1220022-1-10000002-1-12-1-100-1-1-1-1-1-10002200-1-1000000-10
χ342222-12222-1222-1-12-1-122-1-12-12-12-1-122-1-1-1-122-1-1-122-1-1-1-1-1-100-2-2200-1-12200-2-2110000002-11-2-1-100-1-11111000-2-2001100000010
χ352222-12222-1222-1-12-1-122-1-12-12-12-1-1-2-2-1-1-1-122-1-1-122-1-1-1-1-1-10022-20011-2-20022-1-1000000-21-12110011-1-1-1-1000-2-2001100000010
χ362222-12222-1222-1-12-1-122-1-12-12-12-1-1-2-2-1-1-1-122-1-1-122-1-1-1-1-1-100-2-2-20011-2-200-2-211000000-211-211001111110002200-1-1000000-10
χ372222-12222-1222-1-12-1-12-2-1-12-12-12-1-122-1-1-1-1-2-2111-2-2111111002-2-200-1-122002211000000-21-1-2-1-10011-1-1110002-20011000000-10
χ382222-12222-1222-1-12-1-12-2-1-12-12-12-1-122-1-1-1-1-2-2111-2-211111100-22-200-1-12200-2-2-1-1000000-2112-1-1001111-1-1000-2200-1-100000010
χ392222-12222-1222-1-12-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-2-2111-2-2111111002-220011-2-20022110000002-1-1-21100-1-1-1-111000-2200-1-100000010
χ402222-12222-1222-1-12-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-2-2111-2-211111100-2220011-2-200-2-2-1-10000002-1121100-1-111-1-10002-20011000000-10
χ4122-2-2222-2-222-22-2-2-222202-2-2-2-222-2-22-222-2-2000000000000000000002-22-20000002i−2i000000002-2000000000000000002i−2i2i−2i0000
χ4222-2-2222-2-222-22-2-2-222202-2-2-2-222-2-22-222-2-2000000000000000000002-22-2000000−2i2i000000002-200000000000000000−2i2i−2i2i0000
χ4322-2-2222-2-222-22-2-2-222202-2-2-2-222-2-2-2222-2-200000000000000000000-22-220000002i−2i00000000-22000000000000000002i−2i−2i2i0000
χ4422-2-2222-2-222-22-2-2-222202-2-2-2-222-2-2-2222-2-200000000000000000000-22-22000000−2i2i00000000-2200000000000000000−2i2i2i−2i0000
χ4544444-2-2-2-24-2-2-244-2-2-214-2-21-21-21-2-2001111-2-24-2-211-2-2111144000-2-20000-2-2000000-211-20000001100000000000000000000000
χ4644444-2-2-2-24-2-2-244-2-2-214-2-21-21-21-2-2001111-2-24-2-211-2-21111-4-4000220000220000002-1-12000000-1-100000000000000000000000
χ4744444-2-2-2-24-2-2-244-2-2-21-4-2-21-21-21-2-200111122-422-1-122-1-1-1-14-4000-2-2000022000000-2112000000-1-100000000000000000000000
χ4844444-2-2-2-24-2-2-244-2-2-21-4-2-21-21-21-2-200111122-422-1-122-1-1-1-1-44000220000-2-20000002-1-1-20000001100000000000000000000000
χ494444-24-2-24-24-2-2-2-24-21-24-21-2-2-21-21-24411114-2-2-2-2-2-21111110000400-2-2-2-2000000000000-2-200110011000000000000000000000
χ504444-24-2-24-24-2-2-2-24-21-24-21-2-2-21-21-2-4-411114-2-2-2-2-2-21111110000-40022220000000000002200-1-100-1-1000000000000000000000
χ514444-24-2-24-24-2-2-2-24-21-2-4-21-2-2-21-21-2441111-4222222-1-1-1-1-1-10000-400-2-2-2-200000000000022001100-1-1000000000000000000000
χ524444-24-2-24-24-2-2-2-24-21-2-4-21-2-2-21-21-2-4-41111-4222222-1-1-1-1-1-100004002222000000000000-2-200-1-10011000000000000000000000
χ534444-2-244-2-2-244-2-2-21-2-241-2-21-2-2-2-21001111-24-211-2-2-2-211110044000000000-2-2-2-200000000-2-2000000111100000000000000000
χ544444-2-244-2-2-244-2-2-21-2-241-2-21-2-2-2-21001111-24-211-2-2-2-2111100-4-400000000022220000000022000000-1-1-1-100000000000000000
χ554444-2-244-2-2-244-2-2-21-2-2-41-2-21-2-2-2-210011112-42-1-12222-1-1-1-1004-4000000000-2-22200000000-2200000011-1-100000000000000000
χ564444-2-244-2-2-244-2-2-21-2-2-41-2-21-2-2-2-210011112-42-1-12222-1-1-1-100-4400000000022-2-2000000002-2000000-1-11100000000000000000
χ5744-4-444-22-4442-2-4-4-44-2-20422-42-2-22-44-4-2-222000000000000000000004-4-220000000000000000-220000000000000000000000000
χ5844-4-444-22-4442-2-4-4-44-2-20422-42-2-22-4-44-2-22200000000000000000000-442-200000000000000002-20000000000000000000000000
χ5944-4-44-24-424-2-44-4-42-24-20-2-42224-2-4200-2-2220000000000000000000000000000004i−4i000000000000000000000000000−2i2i000000
χ6044-4-44-24-424-2-44-4-42-24-20-2-42224-2-4200-2-222000000000000000000000000000000−4i4i0000000000000000000000000002i−2i000000
χ6144-4-4-244-4-4-24-4422-4-2-240-22-42-4-24224-4-2-22200000000000000000000-224-40000000000000000-220000000000000000000000000
χ6244-4-4-244-4-4-24-4422-4-2-240-22-42-4-2422-44-2-222000000000000000000002-2-4400000000000000002-20000000000000000000000000
χ6344-4-4-24-22-4-242-222-4-21-20-2-12221-2-124-411-1-100000003i−3i3i3i−3i−3i0000000-22-2200000000000000001-1003i−3i000000000000000000000
χ6444-4-4-24-22-4-242-222-4-21-20-2-12221-2-124-411-1-10000000−3i3i−3i−3i3i3i0000000-22-2200000000000000001-100−3i3i000000000000000000000
χ6544-4-4-24-22-4-242-222-4-21-20-2-12221-2-12-4411-1-100000003i−3i3i3i−3i−3i00000002-22-20000000000000000-1100−3i3i000000000000000000000
χ6644-4-4-24-22-4-242-222-4-21-20-2-12221-2-12-4411-1-10000000−3i3i−3i−3i3i3i00000002-22-20000000000000000-11003i−3i000000000000000000000
χ674-44-44444-4-4-4-4-4-4444440-444-4-4-4-4-44004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-2-4-4-422-4444-2-20-4-2-2-42222400-22-2200000000000000000000000023−23000000000000000023−2300000000000000000000000
χ694-44-444-2-2-4-4-422-4444-2-20-4-2-2-42222400-22-22000000000000000000000000−23230000000000000000−232300000000000000000000000
χ704-44-44-2442-42-4-4-44-2-24-2024-222-42-4-200-22-22000000000000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ714-44-44-2442-42-4-4-44-2-24-2024-222-42-4-200-22-220000000000000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ724-44-44-2-2-22-4222-44-2-2-2102-212-12-12-2001-11-1000003i−3i003i−3i3i−3i00000−2i32i3000023−230000000i3−i30000000−3300000000000000000000000
χ734-44-44-2-2-22-4222-44-2-2-2102-212-12-12-2001-11-1000003i−3i003i−3i3i−3i000002i3−2i30000−23230000000−i3i300000003−300000000000000000000000
χ744-44-44-2-2-22-4222-44-2-2-2102-212-12-12-2001-11-100000−3i3i00−3i3i−3i3i00000−2i32i30000−23230000000i3−i300000003−300000000000000000000000
χ754-44-44-2-2-22-4222-44-2-2-2102-212-12-12-2001-11-100000−3i3i00−3i3i−3i3i000002i3−2i3000023−230000000−i3i30000000−3300000000000000000000000
χ764-44-4-2444-42-4-4-42-24-2-2402-242-42-42-200-22-2200000000000000000000000000000000000000000000000000000000023−2300000000
χ774-44-4-2444-42-4-4-42-24-2-2402-242-42-42-200-22-22000000000000000000000000000000000000000000000000000000000−232300000000
χ784-4-44444-44-4-44-44-4-44440-4-4-444-4-44-4004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-224-4-4-224-4-44-2-20-4224-222-2-400-222-20000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ804-4-4444-224-4-4-224-4-44-2-20-4224-222-2-400-222-200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ814-4-444-24-4-2-424-44-42-24-202-42-2-2-424200-222-20000000000000000000000000023−2300000000000000000023−230000000000000000000
χ824-4-444-24-4-2-424-44-42-24-202-42-2-2-424200-222-200000000000000000000000000−2323000000000000000000−23230000000000000000000
χ834-4-44-244-442-44-4-22-4-2-24022-4-242-4-2200-222-2000000000000000000000000000023−2300000000000000000023−2300000000000000000
χ844-4-44-244-442-44-4-22-4-2-24022-4-242-4-2200-222-20000000000000000000000000000−2323000000000000000000−232300000000000000000
χ854-4-44-2-24-4-2224-4-2221-2-20-1221-222-2-1001-1-110003-300003-3-33000000000000023−2323−230000000000000000−33−3300000000000000000
χ864-4-44-2-24-4-2224-4-2221-2-20-1221-222-2-1001-1-110003-300003-3-330000000000000−2323−232300000000000000003−33−300000000000000000
χ874-4-44-2-24-4-2224-4-2221-2-20-1221-222-2-1001-1-11000-330000-333-3000000000000023−23−23230000000000000000−333−300000000000000000
χ884-4-44-2-24-4-2224-4-2221-2-20-1221-222-2-1001-1-11000-330000-333-30000000000000−232323−2300000000000000003−3−3300000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-4222822222222200-1-1-1-1-4-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222200-1-1-1-1444-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000
χ9188-8-88-4-4448-44-4-8-84-4-420-44-24-2-42440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-84-4-4-884442-4-40244-24-4-44-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-444-4-44-444422202-2-2-2-222-2-200-1-11100000006i−6i−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-444-4-44-444422202-2-2-2-222-2-200-1-1110000000−6i6i3i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-8-48-4-4-84-8444-48-42-4042-444-24-2-4002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-488444-8-84-4-42-4-40-2-4-4-244442002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-4444444-4-42220-222-2-2-2-2-2200-11-11000006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4444444-4-42220-222-2-2-2-2-2200-11-1100000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-888-4-44-4-84-448-84-4-42044-2-424-2-44002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-4484-8-44-44-8-42-404-24-4-4-2424002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-444-44-4442220-2-2-222-2-22-200-111-10006-60000-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-444-44-4442220-2-2-222-2-22-200-111-1000-6600003-3-33000000000000000000000000000000000000000000000000000000

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