Finite Group Databasebeta

← Group #13168121

Character table — Group #13168121

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121236661212121212121212121212122224446666121212122244446666666666121212121212121212122446612121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111-1-111-1-1-1-111111111111-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-1-11111-1-1-1-111-1-111-1-111-11-1-11111-1111-1-11111-11-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111-111
χ511111111111111111111111111111111111111111111111-1-11111-1-1111111-1-1-1-111-1-11-111-1-1-1-111111111111-1-1-1-1-1-1-1-1111-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11-111-1-1-1-11-1-1-111-1-1-1-1-11-1-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1111-1-1-1-1-1-1-1111
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
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11111-1-11111-1-1-1-11-11-11111-1-1-11-1-1-1-111-1-111-11111-1-1-1-11-1-11
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111111-1-1-1-11111111-11-11111-1-1-1-111-1-1-1-111-1-1-111-1-11111-1-11-1
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-1-11111-1-1-1-1111-1-1-1-1-111-1-111-1-11111-1-1-111-1-111-1-111-111-1
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1111-1-111-1-1-1-111-1-11-1-1-1-1-111-1-11-11111-1-1111-11-1-1-1-111-1-111-11
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-1-111-1-111-1-1-111111-1-111-11-1-1-1-111-1-11-11-1-1-1-111-1-1111-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-1-1-1-1-1-111-111111-1-111-1-111-1-1-1-111-111-1-111-1-111-11-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-11111111111-11-11-1-1-1-11111-1-11111-1-1-1-1-111-1-11111-1-1-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111-1-111-1-1-1-1-11-11-1-1-1-1111-11111-1-11111-11111-1-1-1-11-11-1
χ17222222-1-12-122222-12-1-1222-1-1-1-1-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1222200-1-1-1-12200220000222-1-1-1-1-1-1-1-1000-1-10000002-1-10000000-100
χ18222222-1-12-122222-12-1-1222-1-1-1-1-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-122-2-200-1-111-2-200-2-2000022-2-111-1-1-1-1100011000000-2110000000100
χ19222222-1-12-122222-12-1-1222-1-1-1-1-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2220011-1-12200-2-20000-2-221-1-11111-1000-1-1000000-2110000000100
χ20222222-1-12-122222-12-1-1222-1-1-1-1-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-2-2001111-2-200220000-2-2-211111111000110000002-1-10000000-100
χ21222222-1-12-122222-12-1-1-222-1-1-1-1-1-12-2-2-1-1-1-11-21111-2-211112-22-200-1-1-1-1-2-2002200002-221-1-1-1-111100011000000-2-1-10000000100
χ22222222-1-12-122222-12-1-1-222-1-1-1-1-1-12-2-2-1-1-1-11-21111-2-211112-2-2200-1-1112200-2-200002-2-2111-1-111-1000-1-10000002110000000-100
χ23222222-1-12-122222-12-1-1-222-1-1-1-1-1-12-2-2-1-1-1-11-21111-2-21111-222-20011-1-1-2-200-2-20000-222-1-1-111-1-11000110000002110000000-100
χ24222222-1-12-122222-12-1-1-222-1-1-1-1-1-12-2-2-1-1-1-11-21111-2-21111-22-220011112200220000-22-2-11111-1-1-1000-1-1000000-2-1-10000000100
χ2522222-122-122-122-12-1-122-1-1-122-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-10022220022-1-1-1-100002200-10-1-10000222-1-1-1-1-1-1-1200000000-1-1-1000
χ2622222-122-122-122-12-1-122-1-1-122-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-10022-2-20022-1-1110000-2-200-10-1-100002-2-21-1-11111-200000000111000
χ2722222-122-122-122-12-1-122-1-1-122-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-100-2-22200-2-211-1-10000-2-20010110000-222-111-1-1-1-1-200000000111000
χ2822222-122-122-122-12-1-122-1-1-122-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-100-2-2-2-200-2-211110000220010110000-2-2-21111111200000000-1-1-1000
χ2922222-122-122-122-12-1-12-2-1-1-122-12-1-1-2-2-1-1-1-1-21-2-211111111002-22-2002211-1-10000-2-200-10-1-10000-22-2111-1-11120000000011-1000
χ3022222-122-122-122-12-1-12-2-1-1-122-12-1-1-2-2-1-1-1-1-21-2-211111111002-2-220022111100002200-10-1-10000-2-22-11111-1-1-200000000-1-11000
χ3122222-122-122-122-12-1-12-2-1-1-122-12-1-1-2-2-1-1-1-1-21-2-21111111100-222-200-2-2-1-1-1-1000022001011000022-21-1-1-1-111-200000000-1-11000
χ3222222-122-122-122-12-1-12-2-1-1-122-12-1-1-2-2-1-1-1-1-21-2-21111111100-22-2200-2-2-1-1110000-2-200101100002-22-1-1-111-1-120000000011-1000
χ332222-122222-12-1-122-12-12-1-12-1-12-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-122002222000022002200-1-10200-1-1-1-10-1-1200-1-1-1-102000-1-1-1-1000000
χ342222-122222-12-1-122-12-12-1-12-1-12-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-12200-2-2220000-2-200-2-200-1-10200-1-1-1-1011-20011110-20001111000000
χ352222-122222-12-1-122-12-12-1-12-1-12-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-2-20022-2-200002200-2-200110-20011110-1-1200-1-1-1-10-20001111000000
χ362222-122222-12-1-122-12-12-1-12-1-12-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-2-200-2-2-2-20000-2-2002200110-2001111011-200111102000-1-1-1-1000000
χ372222-122222-12-1-122-12-1-2-1-12-1-12-12-111-1-1-1-1-2-211-2-21111112-2002-22200002200-2-200-110-200-1-1110-11-200-1-11102000-1-111000000
χ382222-122222-12-1-122-12-1-2-1-12-1-12-12-111-1-1-1-1-2-211-2-21111112-200-22220000-2-2002200-110-200-1-11101-120011-1-10-200011-1-1000000
χ392222-122222-12-1-122-12-1-2-1-12-1-12-12-111-1-1-1-1-2-211-2-2111111-22002-2-2-20000220022001-1020011-1-10-11-200-1-1110-200011-1-1000000
χ402222-122222-12-1-122-12-1-2-1-12-1-12-12-111-1-1-1-1-2-211-2-2111111-2200-22-2-20000-2-200-2-2001-1020011-1-101-120011-1-102000-1-111000000
χ4122-2-2222-222-2-22-2-2-222202-2-22-2-2-22-20022-2-2000000000000000000000000002-22i−2i2i−2i000000000000000000000002-2002i−2i2i−2i0000
χ4222-2-2222-222-2-22-2-2-222202-2-22-2-2-22-20022-2-2000000000000000000000000002-2−2i2i−2i2i000000000000000000000002-200−2i2i−2i2i0000
χ4322-2-2222-222-2-22-2-2-222202-2-22-2-2-22-20022-2-200000000000000000000000000-222i−2i−2i2i00000000000000000000000-22002i−2i−2i2i0000
χ4422-2-2222-222-2-22-2-2-222202-2-22-2-2-22-20022-2-200000000000000000000000000-22−2i2i2i−2i00000000000000000000000-2200−2i2i2i−2i0000
χ4544444-2-2-2-2-24-244-2-2-21-24-2-21-2-21-21-2441111-2-2-2-211-2-2111100440000-2-2-2-20000000000-20110000-2000110000000000000000000
χ4644444-2-2-2-2-24-244-2-2-21-24-2-21-2-21-21-2441111-2-2-2-211-2-2111100-4-400002222000000000020-1-100002000-1-10000000000000000000
χ4744444-2-2-2-2-24-244-2-2-21-2-4-2-21-2-21-21-2-4-411112222-1-122-1-1-1-1004-40000-2-2220000000000-201100002000-1-10000000000000000000
χ4844444-2-2-2-2-24-244-2-2-21-2-4-2-21-2-21-21-2-4-411112222-1-122-1-1-1-100-44000022-2-2000000000020-1-10000-2000110000000000000000000
χ494444-24-2-24-2-24-2-24-2-2-214-2-2-211-21-2-2-2-21111-2411-2-2-2-21111440000-2-2000000000000-2-20-20011110000000000000000000000000
χ504444-24-2-24-2-24-2-24-2-2-214-2-2-211-21-2-2-2-21111-2411-2-2-2-21111-4-4000022000000000000220200-1-1-1-10000000000000000000000000
χ514444-24-2-24-2-24-2-24-2-2-21-4-2-2-211-21-2-22211112-4-1-12222-1-1-1-14-40000-2-2000000000000-22020011-1-10000000000000000000000000
χ524444-24-2-24-2-24-2-24-2-2-21-4-2-2-211-21-2-22211112-4-1-12222-1-1-1-1-440000220000000000002-20-200-1-1110000000000000000000000000
χ534444-2-244-24-2-2-2-2-241-2-2411-2-2-2-2-2-21-2-211114-2-2-2-2-2111111000044000000-2-200000000000000000-2-2-2001111000000000000000
χ544444-2-244-24-2-2-2-2-241-2-2411-2-2-2-2-2-21-2-211114-2-2-2-2-21111110000-4-4000000220000000000000000022200-1-1-1-1000000000000000
χ554444-2-244-24-2-2-2-2-241-2-2-411-2-2-2-2-2-21221111-422222-1-1-1-1-1-100004-4000000-2-200000000000000000-2220011-1-1000000000000000
χ564444-2-244-24-2-2-2-2-241-2-2-411-2-2-2-2-2-21221111-422222-1-1-1-1-1-10000-4400000022000000000000000002-2-200-1-111000000000000000
χ5744-4-444-224-2-4-44-4-424-2-204-42-2222-2-400-2-222000000000000000000000000004-4000000000000000000000000000-220000000000
χ5844-4-444-224-2-4-44-4-424-2-204-42-2222-2-400-2-22200000000000000000000000000-440000000000000000000000000002-20000000000
χ5944-4-44-24-4-24-424-42-4-2-240-2224-42-4-2200-2-2220000000000000000000000000000004i−4i00000000000000000000000000000−2i2i0000
χ6044-4-44-24-4-24-424-42-4-2-240-2224-42-4-2200-2-222000000000000000000000000000000−4i4i000000000000000000000000000002i−2i0000
χ6144-4-4-244-4442-4-22-4-4-24-20-22-4-22-424200-2-22200000000000000000000000000004i−4i00000000000000000000000000000−2i2i000000
χ6244-4-4-244-4442-4-22-4-4-24-20-22-4-22-424200-2-2220000000000000000000000000000−4i4i000000000000000000000000000002i−2i000000
χ634-44-44444-4-444-4-4-4-44440-4-4-4-4-444-44004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ644-44-444-2-2-4244-4-4-424-2-20-4-4222-2-22400-222-2000000000000000000−2i32i3000000000000000000−2i32i3000000000000000000000000000
χ654-44-444-2-2-4244-4-4-424-2-20-4-4222-2-22400-222-20000000000000000002i3−2i30000000000000000002i3−2i3000000000000000000000000000
χ664-44-44-2442-44-2-4-42-4-2-240222-4-4-242-200-222-2000000000000000000000000−2i32i30000000000000000000000−2i32i300000000000000000
χ674-44-44-2442-44-2-4-42-4-2-240222-4-4-242-200-222-20000000000000000000000002i3−2i300000000000000000000002i3−2i300000000000000000
χ684-44-4-2444-4-4-2422-4-4-24-2022-4224-2-4-2−2i32i3-222-200−2i32i300−2i32i3−2i3−2i32i32i30000000000000000000000000000000000000000000000000000000
χ694-44-4-2444-4-4-2422-4-4-24-2022-4224-2-4-22i3−2i3-222-2002i3−2i3002i3−2i32i32i3−2i3−2i30000000000000000000000000000000000000000000000000000000
χ704-44-4-24-2-2-42-2422-42-2-210222-1-1-212-2−2i32i31-1-1100i3−i300−2i32i3i3i3−i3−i3000000−2i32i3000000000000000000i3−i33-30000000000000000000000000
χ714-44-4-24-2-2-42-2422-42-2-210222-1-1-212-2−2i32i31-1-1100i3−i300−2i32i3i3i3−i3−i30000002i3−2i3000000000000000000−i3i3-330000000000000000000000000
χ724-44-4-24-2-2-42-2422-42-2-210222-1-1-212-22i3−2i31-1-1100−i3i3002i3−2i3−i3−i3i3i3000000−2i32i3000000000000000000i3−i3-330000000000000000000000000
χ734-44-4-24-2-2-42-2422-42-2-210222-1-1-212-22i3−2i31-1-1100−i3i3002i3−2i3−i3−i3i3i30000002i3−2i3000000000000000000−i3i33-30000000000000000000000000
χ744-44-4-2-2442-4-2-2222-41-2-20-1-1222-2-221−2i32i31-1-1100−2i32i300i3−i3i3i3−i3−i3000000000000−2i32i30000000000000000000000i3−i33-3000000000000000
χ754-44-4-2-2442-4-2-2222-41-2-20-1-1222-2-221−2i32i31-1-1100−2i32i300i3−i3i3i3−i3−i30000000000002i3−2i30000000000000000000000−i3i3-33000000000000000
χ764-44-4-2-2442-4-2-2222-41-2-20-1-1222-2-2212i3−2i31-1-11002i3−2i300−i3i3−i3−i3i3i3000000000000−2i32i30000000000000000000000i3−i3-33000000000000000
χ774-44-4-2-2442-4-2-2222-41-2-20-1-1222-2-2212i3−2i31-1-11002i3−2i300−i3i3−i3−i3i3i30000000000002i3−2i30000000000000000000000−i3i33-3000000000000000
χ784-4-44444-4-4-4-4-4-44444440-444-44-4-4-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-22-42-4-4-444-24-2-20-44-22-2222-400-22-2200000000000000000000−2i32i300000000000000−2i32i300000000000000000000000000000
χ804-4-4444-22-42-4-4-444-24-2-20-44-22-2222-400-22-22000000000000000000002i3−2i3000000000000002i3−2i300000000000000000000000000000
χ814-4-444-24-42-4-42-44-24-2-2402-2-2-442-42200-22-22000000000000000000000023−23000000000000000000000023−230000000000000000000
χ824-4-444-24-42-4-42-44-24-2-2402-2-2-442-42200-22-220000000000000000000000−23230000000000000000000000−23230000000000000000000
χ834-4-444-2-2222-42-44-2-2-21-202-212-2-12-12001-11-100003i−3i003i−3i3i−3i00000000−2i32i323−23000000000000i3−i300000000−330000000000000000000
χ844-4-444-2-2222-42-44-2-2-21-202-212-2-12-12001-11-100003i−3i003i−3i3i−3i000000002i3−2i3−2323000000000000−i3i3000000003−30000000000000000000
χ854-4-444-2-2222-42-44-2-2-21-202-212-2-12-12001-11-10000−3i3i00−3i3i−3i3i00000000−2i32i3−2323000000000000i3−i3000000003−30000000000000000000
χ864-4-444-2-2222-42-44-2-2-21-202-212-2-12-12001-11-10000−3i3i00−3i3i−3i3i000000002i3−2i323−23000000000000−i3i300000000−330000000000000000000
χ874-4-44-244-4-4-42-42-244-24-202-242-2-42-4200-22-2200000000000000000000000000000000000000000000000000000000023−2300000000
χ884-4-44-244-4-4-42-42-244-24-202-242-2-42-4200-22-22000000000000000000000000000000000000000000000000000000000−232300000000
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
χ9188-8-88-4-44-4-4-848-844-42-40-44-2-44-24240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-448-44-8-44-84-4-420-4442-24-2-440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-48-8-4844-444-82-4-402-24-4444-4-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-4-444-444422202-2-22-2-2-22-200-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-44-4-444-444422202-2-22-2-2-22-200-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000
χ968-88-88-4-4-4448-4-8-844-42-4044-2442-4-2-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-444-4-444442220-2-2-2-2-222-22−4i34i3-111-1002i3−2i3002i3−2i3−i3−i3i3i30000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-444-4-444442220-2-2-2-2-222-224i3−4i3-111-100−2i32i300−2i32i3i3i3−i3−i30000000000000000000000000000000000000000000000000000000
χ998-8-88-48-44-844-84-48-4-4-4204-4-4-224-244002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-84-8444-4-482-4-40-22-44-4444-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444444-4-4-42220-222-22-2-2-2-200-11-1100006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444444-4-4-42220-222-22-2-2-2-200-11-110000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000

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