Finite Group Databasebeta

← Group #13168549

Character table — Group #13168549

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order122233366666666633346666666661212443666121212121212121212121212244441212121212121212446666121212121212121212121212121212122244466121212121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-111-1-11111-1-111111-11-11-11111-1-111-1-111-1-1-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-11-111111111-1-1-1-1-1-1-1-111-111111-1-1111111-1-1-111-1-1-1-1-1-111-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-1-11-111-1-111-1-111-1-1-1-11-1-1-11-111-1-1-1-111-1-1-1-11-1-1-1-11111-1-111-1-11
χ51111111111111111111111111111111-1-11111111111111111111-11-1-111-1-111111111-1111-11-1-11111-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-11-1-1-1-1-1-1-1-111-1-11111-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-111-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111-1-1-1-11111-1-1-11-1-111-1-111-1-1-1-11-111-1-1-111-1-111-1-11-11
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-1111111-11-1-1-1111-1-1-1-1-1-1111-1-1-11-1-1-1-111-1-11111-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-11-11-111-1-1111111-1-1-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-1-111-1-111111-1-1-1-111-111-111111-1-1-1-1-1-1-111
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-1-1-1-1-1-111111-1-111-1-1-1-1-11111-1-1-111-111111-1-1-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-11-11-111-1-11111-1-1-1-11
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-11111-1-1-1-11-1111-1-1-1111111-1-11-1-1-11-1-1-1-111-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1111-111-1-111-1-111111-111-1-1-111-1-111111-1-1
χ17222222-1-1222-1-12222-1-122-1-1-12-1-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-1202202200-1-1-1-1002-1-1-1-102020-1-1-1-100-1-10022000-1-100000000-100
χ18222222-1-1222-1-12222-1-122-1-1-12-1-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-1-20-2202200-1-11100-2111-10-2020-1-11100-1-100-2-20001100000000100
χ19222222-1-1222-1-12222-1-122-1-1-12-1-12-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1202-20-2-20011-1-1002-1-1-11020-2011-1-1001100-2-20001100000000100
χ20222222-1-1222-1-12222-1-122-1-1-12-1-12-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-20-2-20-2-200111100-211110-20-20111100110022000-1-100000000-100
χ21222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-222-1-1-1-11-211-2-211111120-2-202200-1-111002-1-1-110-20-20-1-1110011002-20001100000000-100
χ22222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-222-1-1-1-11-211-2-2111111-202-202200-1-1-1-100-21111020-20-1-1-1-1001100-22000-1-100000000100
χ23222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-2-2-2-1-1-1-11-211-2-211111120-220-2-2001111002-1-1-1-10-2020111100-1-100-22000-1-100000000100
χ24222222-1-1222-1-12222-1-1-22-1-1-12-1-12-1-2-2-2-2-1-1-1-11-211-2-2111111-20220-2-20011-1-100-2111-10202011-1-100-1-1002-20001100000000-100
χ2522222-12222-122-1-12-12-12-12-1-1-12-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-1222020022002222-12-1-10-1-1-10200-1-1-1-100-1-10020000-1-1-1-10000000
χ2622222-12222-122-1-12-12-12-12-1-1-12-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-12-220-200-2-20022-2-2-12-1-101-110-200-1-111001100-2000011110000000
χ2722222-12222-122-1-12-12-12-12-1-1-12-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-1-22-202002200-2-2-2-21-2110-11-1020011-1-100-1-100-2000011110000000
χ2822222-12222-122-1-12-12-12-12-1-1-12-1-12-1-100-1-1-1-122-1-1-1-122-1-1-1-1-2-2-20-200-2-200-2-2221-21101110-200111100110020000-1-1-1-10000000
χ2922222-12222-122-1-12-12-1-2-12-1-1-12-1-121100-1-1-1-1-2-21111-2-2111122-20-2002200-2-2-2-2-12-1-1011-10-20011-1-100110020000-1-1110000000
χ3022222-12222-122-1-12-12-1-2-12-1-1-12-1-121100-1-1-1-1-2-21111-2-211112-2-20200-2-200-2-222-12-1-10-1110200111100-1-100-2000011-1-10000000
χ3122222-12222-122-1-12-12-1-2-12-1-1-12-1-121100-1-1-1-1-2-21111-2-21111-2220-200220022221-21101-1-10-200-1-1-1-1001100-2000011-1-10000000
χ3222222-12222-122-1-12-12-1-2-12-1-1-12-1-121100-1-1-1-1-2-21111-2-21111-2-220200-2-20022-2-21-2110-1-110200-1-11100-1-10020000-1-1110000000
χ332222-1222-1-122222-1-1-122-1-122-1-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-102022-1-1-1-122000000002202-1-1-1-100-1-1-1-1-1-100022000000-1-1000-10
χ342222-1222-1-122222-1-1-122-1-122-1-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-10-202-2-1-11122000000002-20-2-11-1-10011-1-111000-2-20000001100010
χ352222-1222-1-122222-1-1-122-1-122-1-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1020-2211-1-1-2-200000000-22021-11100-1-111-1-1000-2-20000001100010
χ362222-1222-1-122222-1-1-122-1-122-1-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-20-2-21111-2-200000000-2-20-211110011111100022000000-1-1000-10
χ372222-1222-1-122222-1-1-12-2-1-122-1-12-1-1-2-222-1-1-1-1-21-2-211111111020-2-2-1-1-1-12200000000-2-20211-1-100-1-111110002-2000000-1-100010
χ382222-1222-1-122222-1-1-12-2-1-122-1-12-1-1-2-222-1-1-1-1-21-2-2111111110-20-22-1-1112200000000-220-21-1-1-1001111-1-1000-2200000011000-10
χ392222-1222-1-122222-1-1-12-2-1-122-1-12-1-1-2-2-2-2-1-1-1-1-21-2-2111111110202-211-1-1-2-2000000002-202-111100-1-1-1-111000-2200000011000-10
χ402222-1222-1-122222-1-1-12-2-1-122-1-12-1-1-2-2-2-2-1-1-1-1-21-2-2111111110-20221111-2-200000000220-2-1-1110011-1-1-1-10002-2000000-1-100010
χ412-22-2222-22-2-2-222-2-222202-2-2-2-222-2-2002-222-2-2000000000000000002-2002-2002i−2i00000000002-2000000000000000002i−2i002i−2i000
χ422-22-2222-22-2-2-222-2-222202-2-2-2-222-2-2002-222-2-2000000000000000002-2002-200−2i2i00000000002-200000000000000000−2i2i00−2i2i000
χ432-22-2222-22-2-2-222-2-222202-2-2-2-222-2-200-2222-2-200000000000000000-2200-22002i−2i0000000000-22000000000000000002i−2i00−2i2i000
χ442-22-2222-22-2-2-222-2-222202-2-2-2-222-2-200-2222-2-200000000000000000-2200-2200−2i2i0000000000-2200000000000000000−2i2i002i−2i000
χ4544444-2-2-244-2-2-2-2-24-2-214-2-211-2-21-2-2-2-2001111-2411-2-2-2-2111140400000000-2-200-2-21100-20000011000000000000000000000000
χ4644444-2-2-244-2-2-2-2-24-2-214-2-211-2-21-2-2-2-2001111-2411-2-2-2-21111-40-400000000220022-1-100200000-1-1000000000000000000000000
χ4744444-2-2-244-2-2-2-2-24-2-21-4-2-211-2-21-2-2220011112-4-1-12222-1-1-1-140-4000000002200-2-21100200000-1-1000000000000000000000000
χ4844444-2-2-244-2-2-2-2-24-2-21-4-2-211-2-21-2-2220011112-4-1-12222-1-1-1-1-40400000000-2-20022-1-100-20000011000000000000000000000000
χ494444-24-2-2-2-24-2-244-2-21-24-21-2-2-21-2-2144441111-2-2-2-2-2-211111100040-2-200-2-200000000-2000-201100001100000000000000000000
χ504444-24-2-2-2-24-2-244-2-21-24-21-2-2-21-2-2144-4-41111-2-2-2-2-2-2111111000-4022002200000000200020-1-10000-1-100000000000000000000
χ514444-24-2-2-2-24-2-244-2-21-2-4-21-2-2-21-2-21-4-4441111222222-1-1-1-1-1-1000-40-2-200-2-200000000200020110000-1-100000000000000000000
χ524444-24-2-2-2-24-2-244-2-21-2-4-21-2-2-21-2-21-4-4-4-41111222222-1-1-1-1-1-10004022002200000000-2000-20-1-100001100000000000000000000
χ534444-2-244-2-2-244-2-2-21-2-241-2-2-21-2-21-2-2-20011114-2-2-211-2-211110400400-2-200000000000-20-20-20000110011000000000000000000
χ544444-2-244-2-2-244-2-2-21-2-241-2-2-21-2-21-2-2-20011114-2-2-211-2-211110-400-4002200000000000202020000-1-100-1-1000000000000000000
χ554444-2-244-2-2-244-2-2-21-2-2-41-2-2-21-2-21-222001111-4222-1-122-1-1-1-10400-400-2-20000000000020-20200001100-1-1000000000000000000
χ564444-2-244-2-2-244-2-2-21-2-2-41-2-2-21-2-21-222001111-4222-1-122-1-1-1-10-4004002200000000000-2020-20000-1-10011000000000000000000
χ5744-4-44444-44-4-4-4-44-44440-444-44-4-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-2-44-422-44-44-2-20-4-2-22422-420000-22-220000000000000000000000023−230000000000000023−23000000000000000000000000
χ5944-4-444-2-2-44-422-44-44-2-20-4-2-22422-420000-22-2200000000000000000000000−232300000000000000−2323000000000000000000000000
χ6044-4-44-244-442-4-42-2-4-24-2024-22-2-422-423−2300-22-220023−2323−23002323−23−2300000000000000000000000000000000000000000000000000000
χ6144-4-44-244-442-4-42-2-4-24-2024-22-2-422-4−232300-22-2200−2323−232300−23−23232300000000000000000000000000000000000000000000000000000
χ6244-4-44-2-2-2-442222-2-4-2-2102-21-1-22-12223−23001-11-100−3323−2300−3−3330000000000023−2300003-300000000−33000000000000000000000000
χ6344-4-44-2-2-2-442222-2-4-2-2102-21-1-22-12223−23001-11-100−3323−2300−3−33300000000000−23230000-33000000003−3000000000000000000000000
χ6444-4-44-2-2-2-442222-2-4-2-2102-21-1-22-122−2323001-11-1003−3−23230033−3−30000000000023−230000-3300000000−33000000000000000000000000
χ6544-4-44-2-2-2-442222-2-4-2-2102-21-1-22-122−2323001-11-1003−3−23230033−3−300000000000−232300003-3000000003−3000000000000000000000000
χ6644-4-4-24442-2-4-4-4-442-2-2402-24-4-22-4220000-22-220000000000000000000−2i32i300000000000000000000−2i32i30000000000000000000000
χ6744-4-4-24442-2-4-4-4-442-2-2402-24-4-22-4220000-22-2200000000000000000002i3−2i3000000000000000000002i3−2i30000000000000000000000
χ6844-4-4-2-2442-22-4-42-221-2-20-1-2-22122-1223−23001-11-10023−23−3300−3−3330000000−2i32i300000000000000000000i3−i3003i−3i000000000000000000
χ6944-4-4-2-2442-22-4-42-221-2-20-1-2-22122-1223−23001-11-10023−23−3300−3−33300000002i3−2i300000000000000000000−i3i300−3i3i000000000000000000
χ7044-4-4-2-2442-22-4-42-221-2-20-1-2-22122-12−2323001-11-100−23233−30033−3−30000000−2i32i300000000000000000000i3−i300−3i3i000000000000000000
χ7144-4-4-2-2442-22-4-42-221-2-20-1-2-22122-12−2323001-11-100−23233−30033−3−300000002i3−2i300000000000000000000−i3i3003i−3i000000000000000000
χ724-44-444-224-4-42-24-4-44-2-204222-4-2-2-42004-4-2-222000000000000000004-400-2200000000000000-2200000000000000000000000000
χ734-44-444-224-4-42-24-4-44-2-204222-4-2-2-4200-44-2-22200000000000000000-44002-2000000000000002-200000000000000000000000000
χ744-44-44-24-44-42-44-22-4-24-20-2-42224-22-40000-2-22200000000000000000000000004i−4i00000000000000000000000000000−2i2i0000000
χ754-44-44-24-44-42-44-22-4-24-20-2-42224-22-40000-2-2220000000000000000000000000−4i4i000000000000000000000000000002i−2i0000000
χ764-44-4-244-4-22-4-444-42-2-240-22-4-42-2422004-4-2-22200000000000000000-22004-400000000000000-2200000000000000000000000000
χ774-44-4-244-4-22-4-444-42-2-240-22-4-42-242200-44-2-222000000000000000002-200-44000000000000002-200000000000000000000000000
χ784-44-4-24-22-22-42-24-42-21-20-2-12221-22-1004-411-1-10000003i−3i3i−3i3i−3i00000-2200-22000000000000001-100003i−3i00000000000000000000
χ794-44-4-24-22-22-42-24-42-21-20-2-12221-22-1004-411-1-1000000−3i3i−3i3i−3i3i00000-2200-22000000000000001-10000−3i3i00000000000000000000
χ804-44-4-24-22-22-42-24-42-21-20-2-12221-22-100-4411-1-10000003i−3i3i−3i3i−3i000002-2002-200000000000000-110000−3i3i00000000000000000000
χ814-44-4-24-22-22-42-24-42-21-20-2-12221-22-100-4411-1-1000000−3i3i−3i3i−3i3i000002-2002-200000000000000-1100003i−3i00000000000000000000
χ824-4-44444-4-4-444-4-4-444440-4-4-44-4-4-44400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-22-4-44-22-4-444-2-20-422-2-4224-20000-222-20000000000000000000000000000000000000000000000000000−2i32i300000000000
χ844-4-4444-22-4-44-22-4-444-2-20-422-2-4224-20000-222-200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ854-4-444-24-4-4-4-24-4224-24-202-42-22-42-240000-222-200000000000000000000000000000000000000000000000000000023−23000000000
χ864-4-444-24-4-4-4-24-4224-24-202-42-22-42-240000-222-2000000000000000000000000000000000000000000000000000000−2323000000000
χ874-4-44-244-42244-4-4-4-2-2-24022-4422-4-2-20000-222-20000000000000000000000000000000000000000000000000000000000−2i32i300000
χ884-4-44-244-42244-4-4-4-2-2-24022-4422-4-2-20000-222-200000000000000000000000000000000000000000000000000000000002i3−2i300000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9188-8-8-48-4-44-4-844-884-42-4042-44-4-244-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-44-44444-442220-222-22-2-2-2-243−4300-11-1100−2323−23230033−3−300000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-44444-442220-222-22-2-2-2-2−434300-11-110023−2323−2300−3−33300000000000000000000000000000000000000000000000000000
χ948-88-88-4-448-844-4-44-8-4-420-44-2-24-4244000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-4-48-8-444-88-4442-4-402444-2-4-4-24000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-44-4444-4-44422202-2-2-2-222-2-20000-1-1110000006i−6i−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-4444-4-44422202-2-2-2-222-2-20000-1-111000000−6i6i3i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ988-8-888-4-44-8-8-4-44448-4-42044-2244-2-4-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-44448-44-8-8-4-42-404-24-44-24-4200002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-844-48-844-42-4-40-244-4-2442-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-4-4444-42220-2-2-22-2-2-2220000-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-4-4444-42220-2-2-22-2-2-2220000-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000000000000

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