Finite Group Databasebeta

← Group #13168569

Character table — Group #13168569

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order1222333666666666333466666666644366612121212121212121212121212244446612121212121212121212446661212121212121212121212121212122244466661212441212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-111-111111111-1-1-1-1-1-1111-11-11111-1-1-1-111111-1-11-1-1-111-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-111-11-1-111-1-1111111-1-1-1-1-11-1111-1-111111111-11-1-1111-1-1-1-1-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11-1-1-1-1-1-11111-1-111
χ511111111111111111111111111111-1-11111111111111111111-11111-1-111-1-1111111111111-1-1111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11-1
χ611111111111111111111111111111-1-1111111111111111111-1-11-111-1-111-1-1-1-1-1-1-1-1111-11-1-1-111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-11-11
χ711111111111111111111111111111-1-111111111111111111-11-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-1-1-11111-1-1-1-11-1-11-1-1-111-1-1111-1-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1111111-1-1
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-11111-1-1-1-1111-1-11-1-1-1-111-1-111-1-1-1111-111-1-1-1-1-1-11-111
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1111111-1-111-1-1-1-1-111-1-1-111-1-11111-1-11-11-11-1-111-1-1-1-1-1111
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1-1-111-1-11111-1-111-1-111-1-1-111111111-1-1-1-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111-1-1-1111111-1-1-1-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-1-1-1-1-111-1-1-1-1111-1-1111-1-111-1-1-1-1111-11-11-1-111-1-111-111-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-111-1-1-1-1-111-11111-1-111-1-111-1111-111-1-1-1-1111-11-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-111-1-1-1-111-1-111-11
χ17222222-122-122-1-1222-1-122-1-1-1-12-12-122-1-1-1-1-122-1-1-1-122-1-1-1-12022022-1-1-1-122000000-1-1-1020-12-1-10000-1-1-1-12002000-1-10000-1000
χ18222222-122-122-1-1222-1-122-1-1-1-12-12-122-1-1-1-1-122-1-1-1-122-1-1-1-1-202-20-2-2-1-111220000001110-20-12110000-1-1-1-1-200-20001100001000
χ19222222-122-122-1-1222-1-122-1-1-1-12-12-1-2-2-1-1-1-1-122-1-1-1-122-1-1-1-120-2202211-1-1-2-2000000-1-1-10201-2-1-100001111-200-20001100001000
χ20222222-122-122-1-1222-1-122-1-1-1-12-12-1-2-2-1-1-1-1-122-1-1-1-122-1-1-1-1-20-2-20-2-21111-2-20000001110-201-211000011112002000-1-10000-1000
χ21222222-122-122-1-1222-1-1-22-1-1-1-12-12-122-1-1-1-11-2-21111-2-2111120-2-2022-1-11122000000-1-1-10-201-2110000-1-111-2002000110000-1000
χ22222222-122-122-1-1222-1-1-22-1-1-1-12-12-122-1-1-1-11-2-21111-2-21111-20-220-2-2-1-1-1-1220000001110201-2-1-10000-1-111200-2000-1-100001000
χ23222222-122-122-1-1222-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-2-21111-2-21111202-20221111-2-2000000-1-1-10-20-1211000011-1-1200-2000-1-100001000
χ24222222-122-122-1-1222-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-2-21111-2-21111-20220-2-211-1-1-2-2000000111020-12-1-1000011-1-1-2002000110000-1000
χ2522222-122-12-1222-12-1-122-1-12-12-12-1-122-1-1-1-12-1222-1-1-1-1-1-1-1-102202002200-1-1-1-12200000-1022-100-1-1-1-1-1-1-1-102002-1-10000000-100
χ2622222-122-12-1222-12-1-122-1-12-12-12-1-122-1-1-1-12-1222-1-1-1-1-1-1-1-10-220-2002200-1-111-2-20000010-22-1001111-1-1-1-10-200-2110000000100
χ2722222-122-12-1222-12-1-122-1-12-12-12-1-1-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-102-20200-2-20011-1-12200000-102-2100-1-1-1-111110-200-2110000000100
χ2822222-122-12-1222-12-1-122-1-12-12-12-1-1-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-10-2-20-200-2-2001111-2-20000010-2-21001111111102002-1-10000000-100
χ2922222-122-12-1222-12-1-12-2-1-12-12-12-1-122-1-1-1-1-21-2-2-21111111102-20-2002200-1-1112200000-10-2-210011-1-1-1-1110-2002110000000-100
χ3022222-122-12-1222-12-1-12-2-1-12-12-12-1-122-1-1-1-1-21-2-2-2111111110-2-202002200-1-1-1-1-2-200000102-2100-1-111-1-1110200-2-1-10000000100
χ3122222-122-12-1222-12-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-21-2-2-2111111110220-200-2-20011112200000-10-22-10011-1-111-1-10200-2-1-10000000100
χ3222222-122-12-1222-12-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-21-2-2-2111111110-220200-2-20011-1-1-2-2000001022-100-1-11111-1-10-2002110000000-100
χ332222-122-1222-1222-1-12-12-12-12-1-1-1-1200-1-1-1-122-1-1-122-1-1-1-1-1-122022-1-100220022-1-1222-1-12-1-100-1-1-1-1-1-10000002000000-1-10000-10
χ342222-122-1222-1222-1-12-12-12-12-1-1-1-1200-1-1-1-122-1-1-122-1-1-1-1-1-12-202-2-1-1002200-2-211-2-22-1-1-2-1100-1-11111000000-200000011000010
χ352222-122-1222-1222-1-12-12-12-12-1-1-1-1200-1-1-1-122-1-1-122-1-1-1-1-1-1-220-221100-2-20022-1-1-2-2-21121-10011-1-1-1-1000000-200000011000010
χ362222-122-1222-1222-1-12-12-12-12-1-1-1-1200-1-1-1-122-1-1-122-1-1-1-1-1-1-2-20-2-21100-2-200-2-21122-211-211001111110000002000000-1-10000-10
χ372222-122-1222-1222-1-12-1-2-12-12-1-1-1-1200-1-1-1-1-2-2111-2-2111111220-2-2-1-100-2-200-2-2-1-1222-1-1211001111-1-1000000-2000000-1-1000010
χ382222-122-1222-1222-1-12-1-2-12-12-1-1-1-1200-1-1-1-1-2-2111-2-21111112-20-22-1-100-2-2002211-2-22-1-1-21-10011-1-1110000002000000110000-10
χ392222-122-1222-1222-1-12-1-2-12-12-1-1-1-1200-1-1-1-1-2-2111-2-2111111-2202-211002200-2-2-1-1-2-2-2112-1100-1-111-1-10000002000000110000-10
χ402222-122-1222-1222-1-12-1-2-12-12-1-1-1-1200-1-1-1-1-2-2111-2-2111111-2-202211002200221122-211-2-1-100-1-1-1-111000000-2000000-1-1000010
χ4122-2-2222-2-222-2-2-2-222220-2-2-222-2-22-22i−2i2-2-22000000000000000000002i−2i002i−2i00002-2000000000000002i−2i000000000002-22i−2i0000
χ4222-2-2222-2-222-2-2-2-222220-2-2-222-2-22-22i−2i2-2-22000000000000000000002i−2i002i−2i0000-22000000000000002i−2i00000000000-22−2i2i0000
χ4322-2-2222-2-222-2-2-2-222220-2-2-222-2-22-2−2i2i2-2-2200000000000000000000−2i2i00−2i2i00002-200000000000000−2i2i000000000002-2−2i2i0000
χ4422-2-2222-2-222-2-2-2-222220-2-2-222-2-22-2−2i2i2-2-2200000000000000000000−2i2i00−2i2i0000-2200000000000000−2i2i00000000000-222i−2i0000
χ4544444-2-24-2-2-24-2-2-24-21-24-21-21-2-2-2-21441111-2-24-2-211-2-211110040000-2-200-2-2000000000000-2-2000000111100000000000000000
χ4644444-2-24-2-2-24-2-2-24-21-24-21-21-2-2-2-21-4-41111-2-24-2-211-2-2111100-4000022002200000000000022000000-1-1-1-100000000000000000
χ4744444-2-24-2-2-24-2-2-24-21-2-4-21-21-2-2-2-2144111122-422-1-122-1-1-1-100-40000-2-200-2-20000000000002200000011-1-100000000000000000
χ4844444-2-24-2-2-24-2-2-24-21-2-4-21-21-2-2-2-21-4-4111122-422-1-122-1-1-1-10040000220022000000000000-2-2000000-1-11100000000000000000
χ494444-24-2-24-24-2-2-24-2-2-214-2-21-21-21-2-2001111-24-211-2-2-2-2111140040-2-200-2-200000000-2110-2000110000000000000000000000000
χ504444-24-2-24-24-2-2-24-2-2-214-2-21-21-21-2-2001111-24-211-2-2-2-21111-400-40220022000000002-1-102000-1-10000000000000000000000000
χ514444-24-2-24-24-2-2-24-2-2-21-4-2-21-21-21-2-20011112-42-1-12222-1-1-1-1400-40-2-2002200000000-21102000-1-10000000000000000000000000
χ524444-24-2-24-24-2-2-24-2-2-21-4-2-21-21-21-2-20011112-42-1-12222-1-1-1-1-400402200-2-2000000002-1-10-2000110000000000000000000000000
χ534444-2-24-2-24-2-244-2-21-2-241-2-2-2-21-21-20011114-2-2-2-2-2-21111110400400000000-2-2-2-200000-20-200001111000000000000000000000
χ544444-2-24-2-24-2-244-2-21-2-241-2-2-2-21-21-20011114-2-2-2-2-2-21111110-400-4000000002222000002020000-1-1-1-1000000000000000000000
χ554444-2-24-2-24-2-244-2-21-2-2-41-2-2-2-21-21-2001111-4222222-1-1-1-1-1-10400-40000000022-2-200000-2020000-1-111000000000000000000000
χ564444-2-24-2-24-2-244-2-21-2-2-41-2-2-2-21-21-2001111-4222222-1-1-1-1-1-10-400400000000-2-2220000020-2000011-1-1000000000000000000000
χ5744-4-444-2-4-4-24-422-444-2-20-422-2-2-42424i−4i-222-200000000000000000000−2i2i004i−4i00000000000000000000−2i2i0000000000000000000
χ5844-4-444-2-4-4-24-422-444-2-20-422-2-2-4242−4i4i-222-2000000000000000000002i−2i00−4i4i000000000000000000002i−2i0000000000000000000
χ5944-4-44-24-424-2-4-4-424-2-24022-4-242-4-224i−4i-222-2000000000000000000004i−4i00−2i2i00000000000000000000−2i2i0000000000000000000
χ6044-4-44-24-424-2-4-4-424-2-24022-4-242-4-22−4i4i-222-200000000000000000000−4i4i002i−2i000000000000000000002i−2i0000000000000000000
χ6144-4-44-2-2-42-2-2-42224-21-202-121-222-2-14i−4i1-1-11000003-30033-3-30000000−2i2i00−2i2i00000000000000000000i−i3i−3i00000000000000000
χ6244-4-44-2-2-42-2-2-42224-21-202-121-222-2-14i−4i1-1-1100000-3300-3-3330000000−2i2i00−2i2i00000000000000000000i−i−3i3i00000000000000000
χ6344-4-44-2-2-42-2-2-42224-21-202-121-222-2-1−4i4i1-1-11000003-30033-3-300000002i−2i002i−2i00000000000000000000−ii−3i3i00000000000000000
χ6444-4-44-2-2-42-2-2-42224-21-202-121-222-2-1−4i4i1-1-1100000-3300-3-33300000002i−2i002i−2i00000000000000000000−ii3i−3i00000000000000000
χ6544-4-4-2442-4442-4-4-4-2-24-202-424-222-2-400-222-20000000000000000000000000000004-4000000000000000000000000000-22000000
χ6644-4-4-2442-4442-4-4-4-2-24-202-424-222-2-400-222-2000000000000000000000000000000-440000000000000000000000000002-2000000
χ674-44-444444-4-4-44-4-4-44440444-4-4-4-4-4-40044-4-40000000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-2442-4-4-22-4-44-2-204-2-222-42-4200-2-222000000000000000000000023−23000000000000000023−230000000000000000000000000
χ694-44-444-2442-4-4-22-4-44-2-204-2-222-42-4200-2-2220000000000000000000000−23230000000000000000−23230000000000000000000000000
χ704-44-44-244-2-42-44-42-4-2-240-2-242-42-42200-2-2220000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ714-44-44-244-2-42-44-42-4-2-240-2-242-42-42200-2-22200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ724-44-4-244-24-4-424-4-42-24-20-24-2-42222-400-2-222000000000000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ734-44-4-244-24-4-424-4-42-24-20-24-2-42222-400-2-2220000000000000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ744-44-4-24-2-242-42-22-42-2-210-2-212-12-1220011-1-10003i−3i00003i−3i3i−3i00000−2i32i30023−23000000000i3−i300000−330000000000000000000000000
χ754-44-4-24-2-242-42-22-42-2-210-2-212-12-1220011-1-10003i−3i00003i−3i3i−3i000002i3−2i300−2323000000000−i3i3000003−30000000000000000000000000
χ764-44-4-24-2-242-42-22-42-2-210-2-212-12-1220011-1-1000−3i3i0000−3i3i−3i3i00000−2i32i300−2323000000000i3−i3000003−30000000000000000000000000
χ774-44-4-24-2-242-42-22-42-2-210-2-212-12-1220011-1-1000−3i3i0000−3i3i−3i3i000002i3−2i30023−23000000000−i3i300000−330000000000000000000000000
χ784-4-44444-4-4-4-44-444-44440-4-4-4-4-444-44004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-42-442-24-44-2-20-422224-2-4-200-22-22000000000000000000000000000000000000000000000000000000000−2i32i300000000
χ804-4-4444-2-4-42-442-24-44-2-20-422224-2-4-200-22-220000000000000000000000000000000000000000000000000000000002i3−2i300000000
χ814-4-444-24-42-424-44-2-4-2-24022-42-4-242-200-22-2200000000000000000000000000−2i32i300000000000000−2i32i300000000000000000000000
χ824-4-444-24-42-424-44-2-4-2-24022-42-4-242-200-22-22000000000000000000000000002i3−2i3000000000000002i3−2i300000000000000000000000
χ834-4-44-2442-4-4-4-2-4442-24-202-42-42-2-22400-22-22000000000000000000000000000023−230000000000000023−23000000000000000000000
χ844-4-44-2442-4-4-4-2-4442-24-202-42-42-2-22400-22-220000000000000000000000000000−232300000000000000−2323000000000000000000000
χ854-4-44-2-2422-42-2-44-221-2-20-122221-2-1-2001-11-100000003i−3i3i−3i−3i3i0000000000000−2i32i323−23000000000000i3−i3−33000000000000000000000
χ864-4-44-2-2422-42-2-44-221-2-20-122221-2-1-2001-11-100000003i−3i3i−3i−3i3i00000000000002i3−2i3−2323000000000000−i3i33−3000000000000000000000
χ874-4-44-2-2422-42-2-44-221-2-20-122221-2-1-2001-11-10000000−3i3i−3i3i3i−3i0000000000000−2i32i3−2323000000000000i3−i33−3000000000000000000000
χ884-4-44-2-2422-42-2-44-221-2-20-122221-2-1-2001-11-10000000−3i3i−3i3i3i−3i00000000000002i3−2i323−23000000000000−i3i3−33000000000000000000000
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
χ9188-8-8-48-44-8-48444-8-4-4-42044-2-424-2-44002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48448-44-8-84-42-4-40-244-4-4-2424002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-444-4-44444-42220-2-2-222-2-22-200-111-1000006-600-3-333000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-444-4-44444-42220-2-2-222-2-22-200-111-100000-660033-3-3000000000000000000000000000000000000000000000000000000
χ958-88-88-4-48-444-8-444-8-42-40-42-4-24444-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-48-4-4-8448-8442-4-402-4-444-24-240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-4-4444-44442220222-2-2-2-2-2-200-1-1110006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4-4444-44442220222-2-2-2-2-2-200-1-111000−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-844484-4-4-8-42-404-24-24-4-442002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-44-84-8-44-484-4-42044-24-2-424-4002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44444-44-4-442220-2-2-2-2-222-2200-11-1100000006i−6i−3i3i3i−3i000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44444-44-4-442220-2-2-2-2-222-2200-11-110000000−6i6i3i−3i−3i3i000000000000000000000000000000000000000000000000000000

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