Finite Group Databasebeta

← Group #13169173

Character table — Group #13169173

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order122233366666666633346666666664436661212121212121212121212121224444661212121212121212121244666121212121212121212121212121212244446612121212441212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-111-1-1111111-1-1-1-1111-1-111111-1-1-1-11111-1-11-11-1-111-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-11-111-1-111-1-1111111-1-1-1-1-11111-1-1-1111111111-1-11-111-1-1-1-1-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111111-1-1111111111111111111-1111111111-1-1-1-1111111111-1-11111111-1-1-1-1-11-1-1-1-1-1-1-111-1-1-1-11-1
χ611111111111111111111111111111-1-1111111111111111111-11-1-111-1-111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11-1-11-111-1-1-1-111-11-11
χ711111111111111111111111111111-1-111111111111111111-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-11-11-1-111-1-1111-1-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111-1-1-1-111111111111-11-1-1-1-1-111-1-111-1-11-11-1-111111111-1-1-1-1
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1111-1-1-111-1-1-1-1-1111
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-1-1-11-1-111111-1-111-1-111-1-1111-1-1-1-1-1-11-111
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111111111-1-111-1-1-11-1-1-1111-1-11111-1-1-1-1-111-1-1-1-1111111-1-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-1-1-1-1-1-1-11111111-1111-1-1-111-1-1-1-111-1-1-111-1-1-1-111-1-111-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111-1-11111-1-1111-1-1-1-1111-11-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1111-1-1-111-1-111-111-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11111-1-1-1-1-1-111-1-1-11-111111-1-111-1-1111-11-1-1111111-1-1-1-1-11
χ17222222-12-12-12222-1-1-122-1-12-12-12-1-122-1-1-1-12-1222-1-1-1-1-1-1-1-10202200220022-1-1-1-100000-122-1000-1-1-1-1-1-1-1-120020-1-10000000-100
χ18222222-12-12-12222-1-1-122-1-12-12-12-1-122-1-1-1-12-1222-1-1-1-1-1-1-1-1020-2-200-2-20022-1-111000001-22-10001111-1-1-1-1-200-20110000000100
χ19222222-12-12-12222-1-1-122-1-12-12-12-1-1-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-10-2022002200-2-211-1-100000-12-21000-1-1-1-11111-200-20110000000100
χ20222222-12-12-12222-1-1-122-1-12-12-12-1-1-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-10-20-2-200-2-200-2-21111000001-2-210001111111120020-1-10000000-100
χ21222222-12-12-12222-1-1-12-2-1-12-12-12-1-122-1-1-1-1-21-2-2-2111111110-202-200-2-20022-1-1-1-10000012-21000-1-111-1-111200-20-1-10000000100
χ22222222-12-12-12222-1-1-12-2-1-12-12-12-1-122-1-1-1-1-21-2-2-2111111110-20-2200220022-1-11100000-1-2-2100011-1-1-1-111-20020110000000-100
χ23222222-12-12-12222-1-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-21-2-2-2111111110202-200-2-200-2-211-1-100000122-1000-1-11111-1-1-20020110000000-100
χ24222222-12-12-12222-1-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-21-2-2-211111111020-22002200-2-2111100000-1-22-100011-1-111-1-1200-20-1-10000000100
χ2522222-1222-12-122-122-1-122-1-12-1-1-1-1200-1-1-1-1-122-1-122-1-1-1-1-1-12022222-1-1-1-100002222-1-1-12-1002-1-1-1-1-1-10000020000000-1-10000-10
χ2622222-1222-12-122-122-1-122-1-12-1-1-1-1200-1-1-1-1-122-1-122-1-1-1-1-1-1202-2-22211-1-10000-2-2-2-2-1-1-1-21002-1-1111100000-2000000011000010
χ2722222-1222-12-122-122-1-122-1-12-1-1-1-1200-1-1-1-1-122-1-122-1-1-1-1-1-1-20-222-2-2-1-111000022-2-21112-100-211-1-1-1-100000-2000000011000010
χ2822222-1222-12-122-122-1-122-1-12-1-1-1-1200-1-1-1-1-122-1-122-1-1-1-1-1-1-20-2-2-2-2-211110000-2-222111-2100-21111110000020000000-1-10000-10
χ2922222-1222-12-122-122-1-1-22-1-12-1-1-1-1200-1-1-1-11-2-211-2-211111120-22-222111100002222-1-1-1-2-100-211-1-11100000-20000000-1-1000010
χ3022222-1222-12-122-122-1-1-22-1-12-1-1-1-1200-1-1-1-11-2-211-2-211111120-2-2222-1-1110000-2-2-2-2-1-1-12100-21111-1-10000020000000110000-10
χ3122222-1222-12-122-122-1-1-22-1-12-1-1-1-1200-1-1-1-11-2-211-2-2111111-2022-2-2-211-1-1000022-2-2111-2-1002-1-1-1-1110000020000000110000-10
χ3222222-1222-12-122-122-1-1-22-1-12-1-1-1-1200-1-1-1-11-2-211-2-2111111-202-22-2-2-1-1-1-10000-2-22211121002-1-111-1-100000-20000000-1-1000010
χ332222-122-12222-1-122-12-12-12-1-1-12-12-122-1-1-1-122-1-1-1-1-122-1-1-1-122200-1-10022-1-12200002-1-100-12-1-1-10000-1-1-1-10020200-1-10000-1000
χ342222-122-12222-1-122-12-12-12-1-1-12-12-122-1-1-1-122-1-1-1-1-122-1-1-1-1-22-2001100-2-2-1-1220000-21100-121110000-1-1-1-100-20-2001100001000
χ352222-122-12222-1-122-12-12-12-1-1-12-12-1-2-2-1-1-1-122-1-1-1-1-122-1-1-1-12-2200-1-1002211-2-200002-1-1001-2-1-1-10000111100-20-2001100001000
χ362222-122-12222-1-122-12-12-12-1-1-12-12-1-2-2-1-1-1-122-1-1-1-1-122-1-1-1-1-2-2-2001100-2-211-2-20000-211001-2111000011110020200-1-10000-1000
χ372222-122-12222-1-122-12-1-2-12-1-1-12-12-122-1-1-1-1-2-211111-2-211112-2-200-1-100-2-2-1-12200002-1-1001-21110000-1-1110020-200-1-100001000
χ382222-122-12222-1-122-12-1-2-12-1-1-12-12-122-1-1-1-1-2-211111-2-21111-2-2200110022-1-1220000-211001-2-1-1-10000-1-11100-20200110000-1000
χ392222-122-12222-1-122-12-1-2-12-1-1-12-12-1-2-2-1-1-1-1-2-211111-2-2111122-200-1-100-2-211-2-200002-1-100-12111000011-1-100-20200110000-1000
χ402222-122-12222-1-122-12-1-2-12-1-1-12-12-1-2-2-1-1-1-1-2-211111-2-21111-2220011002211-2-20000-21100-12-1-1-1000011-1-10020-200-1-100001000
χ412-2-22222-2-222-22-2-2-22220-2-2-222-2-22-22i−2i2-2-220000000000000000000000002i−2i2i−2i002i−2i000000000000002i−2i000000000002i−2i2-20000
χ422-2-22222-2-222-22-2-2-22220-2-2-222-2-22-22i−2i2-2-220000000000000000000000002i−2i2i−2i00−2i2i000000000000002i−2i00000000000−2i2i-220000
χ432-2-22222-2-222-22-2-2-22220-2-2-222-2-22-2−2i2i2-2-22000000000000000000000000−2i2i−2i2i002i−2i00000000000000−2i2i000000000002i−2i-220000
χ442-2-22222-2-222-22-2-2-22220-2-2-222-2-22-2−2i2i2-2-22000000000000000000000000−2i2i−2i2i00−2i2i00000000000000−2i2i00000000000−2i2i2-20000
χ4544444-2-24-2-2-2-244-2-2-21-24-21-2-2-21-21-2001111-2-24-2-2-2-21111110004400-2-2000000-2-200000-2-2000001111000000000000000000000
χ4644444-2-24-2-2-2-244-2-2-21-24-21-2-2-21-21-2001111-2-24-2-2-2-2111111000-4-4002200000022000002200000-1-1-1-1000000000000000000000
χ4744444-2-24-2-2-2-244-2-2-21-2-4-21-2-2-21-21-200111122-42222-1-1-1-1-1-10004-40022000000-2-2000002-20000011-1-1000000000000000000000
χ4844444-2-24-2-2-2-244-2-2-21-2-4-21-2-2-21-21-200111122-42222-1-1-1-1-1-1000-4400-2-20000002200000-2200000-1-111000000000000000000000
χ494444-24-2-2-24-24-2-24-21-2-241-2-21-2-2-2-214411114-2-2-2-211-2-2111104000000000-2-2-2-2000000000-2-20000000111100000000000000000
χ504444-24-2-2-24-24-2-24-21-2-241-2-21-2-2-2-21-4-411114-2-2-2-211-2-211110-40000000002222000000000220000000-1-1-1-100000000000000000
χ514444-24-2-2-24-24-2-24-21-2-2-41-2-21-2-2-2-21441111-42222-1-122-1-1-1-10-4000000000-2-2-2-200000000022000000011-1-100000000000000000
χ524444-24-2-2-24-24-2-24-21-2-2-41-2-21-2-2-2-21-4-41111-42222-1-122-1-1-1-1040000000002222000000000-2-20000000-1-11100000000000000000
χ534444-2-24-24-24-2-2-2-24-2-214-2-21-21-21-2-2001111-24-211-2-2-2-2111140400-2-200-2-200000000-2110000-2110000000000000000000000000
χ544444-2-24-24-24-2-2-2-24-2-214-2-21-21-21-2-2001111-24-211-2-2-2-21111-40-400220022000000002-1-100002-1-10000000000000000000000000
χ554444-2-24-24-24-2-2-2-24-2-21-4-2-21-21-21-2-20011112-42-1-12222-1-1-1-140-400-2-2002200000000-21100002-1-10000000000000000000000000
χ564444-2-24-24-24-2-2-2-24-2-21-4-2-21-21-21-2-20011112-42-1-12222-1-1-1-1-404002200-2-2000000002-1-10000-2110000000000000000000000000
χ5744-4-444444-4-4-4-4-44-44440444-4-4-4-4-4-40044-4-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-2-42-4-4-442-2-240-2-242-42-42200-2-2220000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ5944-4-444-24-2-42-4-4-442-2-240-2-242-42-42200-2-22200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ6044-4-44-24442-42-4-4-2-44-2-204-2-2-42222-400-2-222000000000000000000000023−23000000000000000023−230000000000000000000000000
χ6144-4-44-24442-42-4-4-2-44-2-204-2-2-42222-400-2-2220000000000000000000000−23230000000000000000−23230000000000000000000000000
χ6244-4-4-244-24-4-4-4224-4-24-20-24-222-42-4200-2-222000000000000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ6344-4-4-244-24-4-4-4224-4-24-20-24-222-42-4200-2-2220000000000000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ6444-4-4-2-24-242-4222-2-4-2-210-2-212-12-1220011-1-10003i−3i00003i3i−3i−3i00000−2i32i30023−23000000000i3−i300000−330000000000000000000000000
χ6544-4-4-2-24-242-4222-2-4-2-210-2-212-12-1220011-1-10003i−3i00003i3i−3i−3i000002i3−2i300−2323000000000−i3i3000003−30000000000000000000000000
χ6644-4-4-2-24-242-4222-2-4-2-210-2-212-12-1220011-1-1000−3i3i0000−3i−3i3i3i00000−2i32i300−2323000000000i3−i3000003−30000000000000000000000000
χ6744-4-4-2-24-242-4222-2-4-2-210-2-212-12-1220011-1-1000−3i3i0000−3i−3i3i3i000002i3−2i30023−23000000000−i3i300000−330000000000000000000000000
χ684-44-4444-4-4-4-44-44-444440-4-4-4-4-444-44004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ694-44-444-2-42-424-44-4-2-2-24022-42-4-242-200-22-220000000000000000000000000000−2i32i3000000000000−2i32i300000000000000000000000
χ704-44-444-2-42-424-44-4-2-2-24022-42-4-242-200-22-2200000000000000000000000000002i3−2i30000000000002i3−2i300000000000000000000000
χ714-44-44-24-4-42-4-2-44244-2-20-422-42-2-22400-22-220000000000000000000023−23000000000000000000000023−23000000000000000000000
χ724-44-44-24-4-42-4-2-44244-2-20-422-42-2-22400-22-2200000000000000000000−23230000000000000000000000−2323000000000000000000000
χ734-44-44-2-2-4222-2-442-2-21-202-12221-2-1-2001-11-100000003i−3i3i−3i3i−3i000000023−23000000−2i32i3000000000000i3−i3−33000000000000000000000
χ744-44-44-2-2-4222-2-442-2-21-202-12221-2-1-2001-11-100000003i−3i3i−3i3i−3i0000000−23230000002i3−2i3000000000000−i3i33−3000000000000000000000
χ754-44-44-2-2-4222-2-442-2-21-202-12221-2-1-2001-11-10000000−3i3i−3i3i−3i3i000000023−230000002i3−2i3000000000000−i3i3−33000000000000000000000
χ764-44-44-2-2-4222-2-442-2-21-202-12221-2-1-2001-11-10000000−3i3i−3i3i−3i3i0000000−2323000000−2i32i3000000000000i3−i33−3000000000000000000000
χ774-44-4-2442-4-4-442-2-44-24-202-42224-2-4-200-22-22000000000000000000000000000000000000000000000000000000000−2i32i300000000
χ784-44-4-2442-4-4-442-2-44-24-202-42224-2-4-200-22-220000000000000000000000000000000000000000000000000000000002i3−2i300000000
χ794-4-4444-2-424-2-44-4-42-2-24022-4-242-4-224i−4i-222-20000000000000000000000004i−4i−2i2i000000000000000000−2i2i0000000000000000000
χ804-4-4444-2-424-2-44-4-42-2-24022-4-242-4-22−4i4i-222-2000000000000000000000000−4i4i2i−2i0000000000000000002i−2i0000000000000000000
χ814-4-444-24-4-4-2424-42-44-2-20-4224-222-2-400-222-20000000000000000000000000000004i−4i000000000000000000000000000−2i2i000000
χ824-4-444-24-4-4-2424-42-44-2-20-4224-222-2-400-222-2000000000000000000000000000000−4i4i0000000000000000000000000002i−2i000000
χ834-4-44-2442-444-4-22-4-4-24-202-42-2-2-42424i−4i-222-2000000000000000000000000−2i2i4i−4i000000000000000000−2i2i0000000000000000000
χ844-4-44-2442-444-4-22-4-4-24-202-42-2-2-4242−4i4i-222-20000000000000000000000002i−2i−4i4i0000000000000000002i−2i0000000000000000000
χ854-4-44-24-2224-2-4-22-421-2-20-1221-222-2-14i−4i1-1-11000003-3003-3-3300000000000−2i2i−2i2i000000000000000000i−i3i−3i00000000000000000
χ864-4-44-24-2224-2-4-22-421-2-20-1221-222-2-14i−4i1-1-1100000-3300-333-300000000000−2i2i−2i2i000000000000000000i−i−3i3i00000000000000000
χ874-4-44-24-2224-2-4-22-421-2-20-1221-222-2-1−4i4i1-1-11000003-3003-3-33000000000002i−2i2i−2i000000000000000000−ii−3i3i00000000000000000
χ884-4-44-24-2224-2-4-22-421-2-20-1221-222-2-1−4i4i1-1-1100000-3300-333-3000000000002i−2i2i−2i000000000000000000−ii3i−3i00000000000000000
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
χ9188-8-88-4-48-4444-8-8-44-42-40-42-444-24-240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-4-4-84-844842-4-402-4-4-24444-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-4-444444-442220222-2-2-2-2-2-200-1-1110006i−6i0000−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-4-444444-442220222-2-2-2-2-2-200-1-111000−6i6i00003i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-8-48-444-8484-4-8-42-4-40-244-24-4-442002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-484-84-8-44-448-4-42044-24-2-424-4002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44444-44-44-42220-2-2-2-2-222-2200-11-1100000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44444-44-44-42220-2-2-2-2-222-2200-11-110000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-84-4-448-844-42-404-24-4-4-2424002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-8-484-444-8-4-42044-2-424-2-44002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-4-44-44442220-2-2-222-2-22-200-111-1000006-600-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-4-44-44442220-2-2-222-2-22-200-111-100000-66003-3-33000000000000000000000000000000000000000000000000000000

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