Finite Group Databasebeta

← Group #13168295

Character table — Group #13168295

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order1222333666666666333466666666622366612121212121212121212121212444446666121212121212121244661212121212121212121212121212121244444121212121212441212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111-1-111111-11-1111111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11-1
χ31111111111111111111111111111111111111111111111111-1-1111111-1-11111-1-1-1-1111-111-1111-1-1-1-111111-1-11-1-1-111-1-1-1-11-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-11-11
χ511111111111111111111111111111-1-111111111111111111-11111-1-1-1-11111111111-1-1-11-1111-1-111111111-1-1-1-1111-1-1-1-1-1-1-11-1-1
χ611111111111111111111111111111-1-111111111111111111-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11-1-11-1-1-11111-1-1-1-11-1-11-1-1-111-1-1111-1-11
χ711111111111111111111111111111-1-111111111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-11111-111-1-1-1-1-1-11111-1-111
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111111111-1-1-1-1-1-111-11-1-1-11-1-111-1-111-1-1-11-111-1-111-1-1-1-1-1111
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-111-1-11111-11-11-1-1-1-111-1-1-1-11111-1-1-111-1-1-1-1111-11-1
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111-111111111-1-1-1-1
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-11111-1-111-1-1-111-1-1-1-1-111-1-1111-11-11-1-1-1-111-1-111-11
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111111-1-111-1-11-11-11-1-1-1-1111111-1-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-111-1-111-1-111-1-11111-1-11111-1-1-1-111-1-111-1111111-1-1-1-1-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-111-1-11111-1-11-11-11111-1-11111-1-111-1-1-111-1-1-1-1-1-11-111
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-1-1-1-11111-1-1-1-11-1111-111-1-111-1-111-11-111-1-111-1-111-111-1
χ17222222-12-1222-1-1222-1-122-1-1-1-12-12-122-1-1-1-1-122-1-122-1-1-1-1-1-12002222-1-100-1-1220000-1-120-1-102-1-10000-1-1-1-12002000-1-10000-1000
χ18222222-12-1222-1-1222-1-122-1-1-1-12-12-122-1-1-1-1-122-1-122-1-1-1-1-1-1200-2-222-1-10011-2-20000-1-120-110-2-1-100001111-200-20001100001000
χ19222222-12-1222-1-1222-1-122-1-1-1-12-12-1-2-2-1-1-1-1-122-1-122-1-1-1-1-1-1-20022-2-21100-1-122000011-201-102110000-1-1-1-1-200-20001100001000
χ20222222-12-1222-1-1222-1-122-1-1-1-12-12-1-2-2-1-1-1-1-122-1-122-1-1-1-1-1-1-200-2-2-2-2110011-2-2000011-20110-211000011112002000-1-10000-1000
χ21222222-12-1222-1-1222-1-1-22-1-1-1-12-12-122-1-1-1-11-2-211-2-2111111-2002-222-1-100-1-1-2-20000-1-1-201102110000-1-111-2002000-1-100001000
χ22222222-12-1222-1-1222-1-1-22-1-1-1-12-12-122-1-1-1-11-2-211-2-2111111-200-2222-1-10011220000-1-1-201-10-211000011-1-1200-2000110000-1000
χ23222222-12-1222-1-1222-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-2-211-2-21111112002-2-2-21100-1-1-2-200001120-1102-1-10000-1-111200-2000110000-1000
χ24222222-12-1222-1-1222-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-2-211-2-2111111200-22-2-21100112200001120-1-10-2-1-1000011-1-1-2002000-1-100001000
χ2522222-12-122-12222-1-12-12-122-1-1-1-1-1222-1-1-1-122-1-1-1-1-122-1-1-1-122200-1-122220000-1-100-1-1-1-12020-1-1-1-1-1-10000022000000-1-10000-10
χ2622222-12-122-12222-1-12-12-122-1-1-1-1-1222-1-1-1-122-1-1-1-1-122-1-1-1-12-2-200-1-122-2-200001100-1-1-1120-20-1-1111100000-2-200000011000010
χ2722222-12-122-12222-1-12-12-122-1-1-1-1-12-2-2-1-1-1-122-1-1-1-1-122-1-1-1-1-2220011-2-2220000-1-100111-1-202011-1-1-1-100000-2-200000011000010
χ2822222-12-122-12222-1-12-12-122-1-1-1-1-12-2-2-1-1-1-122-1-1-1-1-122-1-1-1-1-2-2-20011-2-2-2-2000011001111-20-201111110000022000000-1-10000-10
χ2922222-12-122-12222-1-12-1-2-122-1-1-1-1-1222-1-1-1-1-2-211111-2-21111-22-200-1-1222200001100-1-11-1-20-2011-1-111000002-2000000110000-10
χ3022222-12-122-12222-1-12-1-2-122-1-1-1-1-1222-1-1-1-1-2-211111-2-21111-2-2200-1-122-2-20000-1-100-1-111-20201111-1-100000-22000000-1-1000010
χ3122222-12-122-12222-1-12-1-2-122-1-1-1-1-12-2-2-1-1-1-1-2-211111-2-2111122-20011-2-2220000110011-1-120-20-1-1-1-11100000-22000000-1-1000010
χ3222222-12-122-12222-1-12-1-2-122-1-1-1-1-12-2-2-1-1-1-1-2-211111-2-211112-220011-2-2-2-20000-1-10011-112020-1-111-1-1000002-2000000110000-10
χ332222-12222-12-122-12-1-122-1-1-122-12-1-100-1-1-1-12-1222-1-1-1-1-1-1-1-1022220000-1-122-1-12222000202-1-100-1-1-1-1-1-1-1-100002-1-10000000-100
χ342222-12222-12-122-12-1-122-1-1-122-12-1-100-1-1-1-12-1222-1-1-1-1-1-1-1-1022-2-20000-1-1-2-21122-2-200020-2-1100-1-1-1-111110000-2110000000100
χ352222-12222-12-122-12-1-122-1-1-122-12-1-100-1-1-1-12-1222-1-1-1-1-1-1-1-10-2-22200001122-1-1-2-2-2-2000-2021-1001111-1-1-1-10000-2110000000100
χ362222-12222-12-122-12-1-122-1-1-122-12-1-100-1-1-1-12-1222-1-1-1-1-1-1-1-10-2-2-2-2000011-2-211-2-222000-20-211001111111100002-1-10000000-100
χ372222-12222-12-122-12-1-12-2-1-1-122-12-1-100-1-1-1-1-21-2-2-21111111102-22-20000-1-12211-2-2-2-200020-21-100-1-111-1-11100002110000000-100
χ382222-12222-12-122-12-1-12-2-1-1-122-12-1-100-1-1-1-1-21-2-2-21111111102-2-220000-1-1-2-2-1-1-2-2220002021100-1-11111-1-10000-2-1-10000000100
χ392222-12222-12-122-12-1-12-2-1-1-122-12-1-100-1-1-1-1-21-2-2-2111111110-222-200001122112222000-20-2-1-10011-1-1-1-1110000-2-1-10000000100
χ402222-12222-12-122-12-1-12-2-1-1-122-12-1-100-1-1-1-1-21-2-2-2111111110-22-22000011-2-2-1-122-2-2000-202-110011-1-111-1-100002110000000-100
χ4122-2-222222-2-22-2-2-2-2222022-22-2-2-2-2-22-222-2-20000000000000000002-22-2000000002-22-20000000000000000000002-200002-20000
χ4222-2-222222-2-22-2-2-2-2222022-22-2-2-2-2-22-222-2-20000000000000000002-22-200000000-222-2000000000000000000000-220000-220000
χ4322-2-222222-2-22-2-2-2-2222022-22-2-2-2-2-2-2222-2-2000000000000000000-22-22000000002-2-220000000000000000000002-20000-220000
χ4422-2-222222-2-22-2-2-2-2222022-22-2-2-2-2-2-2222-2-2000000000000000000-22-2200000000-22-22000000000000000000000-2200002-20000
χ4544444-2-2-2-24-24-2-24-2-2-214-2-2-211-21-2-2441111-24-211-2-2-2-2111140000-2-2-2-2000000000011-20-2000110000000000000000000000000
χ4644444-2-2-2-24-24-2-24-2-2-214-2-2-211-21-2-2-4-41111-24-211-2-2-2-21111-4000022220000000000-1-1202000-1-10000000000000000000000000
χ4744444-2-2-2-24-24-2-24-2-2-21-4-2-2-211-21-2-24411112-42-1-12222-1-1-1-1-40000-2-2-2-2000000000011202000-1-10000000000000000000000000
χ4844444-2-2-2-24-24-2-24-2-2-21-4-2-2-211-21-2-2-4-411112-42-1-12222-1-1-1-14000022220000000000-1-1-20-2000110000000000000000000000000
χ494444-24-24-2-24-2-2-2-24-21-24-211-2-2-2-2-21001111-2-24-2-2-2-211111100044000000-2-2-2-2000000000-20-2000000111100000000000000000
χ504444-24-24-2-24-2-2-2-24-21-24-211-2-2-2-2-21001111-2-24-2-2-2-2111111000-4-40000002222000000000202000000-1-1-1-100000000000000000
χ514444-24-24-2-24-2-2-2-24-21-2-4-211-2-2-2-2-2100111122-42222-1-1-1-1-1-10004-4000000-2-22200000000020-200000011-1-100000000000000000
χ524444-24-24-2-24-2-2-2-24-21-2-4-211-2-2-2-2-2100111122-42222-1-1-1-1-1-1000-4400000022-2-2000000000-202000000-1-11100000000000000000
χ534444-2-24-24-2-2-244-2-21-2-241-2-2-2-21-21-20011114-2-2-2-211-2-21111044000000-2-20000-2-200000-200-20001111000000000000000000000
χ544444-2-24-24-2-2-244-2-21-2-241-2-2-2-21-21-20011114-2-2-2-211-2-211110-4-400000022000022000002002000-1-1-1-1000000000000000000000
χ554444-2-24-24-2-2-244-2-21-2-2-41-2-2-2-21-21-2001111-42222-1-122-1-1-1-104-4000000-2-200002200000-200200011-1-1000000000000000000000
χ564444-2-24-24-2-2-244-2-21-2-2-41-2-2-2-21-21-2001111-42222-1-122-1-1-1-10-44000000220000-2-200000200-2000-1-111000000000000000000000
χ5744-4-444-24-2-4-4422-4-44-2-204-22-22-42-424-4-2-2220000000000000000004-4-220000000000-22000000000000000000000000000000000
χ5844-4-444-24-2-4-4422-4-44-2-204-22-22-42-42-44-2-222000000000000000000-442-200000000002-2000000000000000000000000000000000
χ5944-4-44-24-24-424-4-4-42-24-20-24-4-22222-44-4-2-222000000000000000000-224-40000000000-22000000000000000000000000000000000
χ6044-4-44-24-24-424-4-4-42-24-20-24-4-22222-4-44-2-2220000000000000000002-2-4400000000002-2000000000000000000000000000000000
χ6144-4-44-2-2-2-2-42422-42-2-210-2-221-12-1224-411-1-10003i−3i00003i3i−3i−3i00000-22-2200000000001-10000003i−3i0000000000000000000000000
χ6244-4-44-2-2-2-2-42422-42-2-210-2-221-12-1224-411-1-1000−3i3i0000−3i−3i3i3i00000-22-2200000000001-1000000−3i3i0000000000000000000000000
χ6344-4-44-2-2-2-2-42422-42-2-210-2-221-12-122-4411-1-10003i−3i00003i3i−3i−3i000002-22-20000000000-11000000−3i3i0000000000000000000000000
χ6444-4-44-2-2-2-2-42422-42-2-210-2-221-12-122-4411-1-1000−3i3i0000−3i−3i3i3i000002-22-20000000000-110000003i−3i0000000000000000000000000
χ6544-4-4-244442-4-2-4-42-4-2-240-2-224-42-42200-2-2220000000000000000000000000000004-400000000000000000000000-220000000000
χ6644-4-4-244442-4-2-4-42-4-2-240-2-224-42-42200-2-222000000000000000000000000000000-44000000000000000000000002-20000000000
χ674-44-4444-4-444-44-4-4-44440-4-44-4-444-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-4244-4-22-4-44-2-20-42-2224-2-4200-22-2200000000000000000000000000000000000000000000000000000000023−2300000000
χ694-44-444-2-4244-4-22-4-44-2-20-42-2224-2-4200-22-22000000000000000000000000000000000000000000000000000000000−232300000000
χ704-44-44-242-44-2-44-4-42-24-202-4422-2-22-400-22-22000000000000000000000000000023−230000000000000023−23000000000000000000000
χ714-44-44-242-44-2-44-4-42-24-202-4422-2-22-400-22-220000000000000000000000000000−232300000000000000−2323000000000000000000000
χ724-44-4-244-4-4-2424-42-4-2-24022-2-4-4-242200-22-220000000000000000000000−2i32i3000000000000000000−2i32i300000000000000000000000
χ734-44-4-244-4-4-2424-42-4-2-24022-2-4-4-242200-22-2200000000000000000000002i3−2i30000000000000000002i3−2i300000000000000000000000
χ744-44-4-2-242-4-2-224-4221-2-20-12-2221-2-12001-11-1000003i−3i003i−3i3i−3i000000000−2i32i3000023−23000000000000i3−i3−33000000000000000000000
χ754-44-4-2-242-4-2-224-4221-2-20-12-2221-2-12001-11-1000003i−3i003i−3i3i−3i0000000002i3−2i30000−2323000000000000−i3i33−3000000000000000000000
χ764-44-4-2-242-4-2-224-4221-2-20-12-2221-2-12001-11-100000−3i3i00−3i3i−3i3i000000000−2i32i30000−2323000000000000i3−i33−3000000000000000000000
χ774-44-4-2-242-4-2-224-4221-2-20-12-2221-2-12001-11-100000−3i3i00−3i3i−3i3i0000000002i3−2i3000023−23000000000000−i3i3−33000000000000000000000
χ784-4-44444-4-4-4-4-4-44444440-4-4-4-44-4-444004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-42-4-4-42-2444-2-20-4222-2-424-200-222-2000000000000000000000000−2i32i300000000000000000000−2i32i30000000000000000000
χ804-4-4444-2-42-4-4-42-2444-2-20-4222-2-424-200-222-20000000000000000000000002i3−2i3000000000000000000002i3−2i30000000000000000000
χ814-4-444-242-4-42-4-444-2-24-202-4-42-222-2400-222-200000000000000000000000000000000000000000000000000000000000−2i32i3000000
χ824-4-444-242-4-42-4-444-2-24-202-4-42-222-2400-222-2000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ834-4-44-244-4-42-42-44-24-2-240222-442-4-2-200-222-200000000000000000000000000−2i32i300000000000000000000−2i32i300000000000000000
χ844-4-44-244-4-42-42-44-24-2-240222-442-4-2-200-222-2000000000000000000000000002i3−2i3000000000000000000002i3−2i300000000000000000
χ854-4-44-24-2-422-422-2-24-21-202-1-12-222-21001-1-1100000003-33-3-3300000000000−2i32i3−2i32i3000000000000000000i3−i3i3−i300000000000000000
χ864-4-44-24-2-422-422-2-24-21-202-1-12-222-21001-1-1100000003-33-3-33000000000002i3−2i32i3−2i3000000000000000000−i3i3−i3i300000000000000000
χ874-4-44-24-2-422-422-2-24-21-202-1-12-222-21001-1-110000000-33-333-300000000000−2i32i32i3−2i3000000000000000000i3−i3−i3i300000000000000000
χ884-4-44-24-2-422-422-2-24-21-202-1-12-222-21001-1-110000000-33-333-3000000000002i3−2i3−2i32i3000000000000000000−i3i3i3−i300000000000000000
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
χ9188-8-8-48-48-44-8-4444-8-42-40-42-2-44444-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-4844-4-8-8442-4-402-44-44-24-240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-4-444-44444222022-22-2-2-2-2-200-1-1110006i−6i0000−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-4-444-44444222022-22-2-2-2-2-200-1-111000−6i6i00003i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-88-4-4448-4-8-44-84-4-42044-4-2-2-4244002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-4-84-484-444-8-42-404-2244-4-44-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-444-4-44-44442220-2-22-2-222-2-200-11-11000006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-444-4-44-44442220-2-22-2-222-2-200-11-1100000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-888-4-444-84-84-48-4-4-420444-224-2-4-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-8444-88-4-42-4-40-2444-4-242-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444444-4-4-42220-2-2-2-22-2-22200-111-100000006-6-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444444-4-4-42220-2-2-2-22-2-22200-111-10000000-663-3-33000000000000000000000000000000000000000000000000000000

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