Finite Group Databasebeta

← Group #13169186

Character table — Group #13169186

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order12223336666666663334666666666121244366612121212121212121212121224444661212121212124466612121212121212121212121212121212122244466121212121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-11111-1-111-1-11111-1-1111-11111-1-111-1-1-1-1-111-1-1-1-1-1-111-1-1-11-1
χ31111111111111111111111111111111111111111111111111-111-11-1-1111111-1-1-1-1-11111-1-1111-1-111111111-1-1-111-1-1-1-1-1-1-1-11-1-1
χ41111111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-11111-1-1-11-1-11-1-1-111-1-1-1-111-1-1-1-11-1-1-1-11111-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-11111-1-111-1-111111-111-1111-1-11111-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1111-11
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-111-1-111-1-1-111-1-1-1-1-1-11111-111
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1111-11-1-1-1-11-1-1-1-11111-1-11-111-1-1-111-1-111-1-11-11
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111111111-1-11-1-1-1-1-1-1-1-1-1-11111-11-11-111-1-1111111-1-1-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-1-1-11-1-1111-1-1111111-1-11-1-1-11-1-1-1-111-1-11111-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11-111-1-1-111-1-11111-111-111111-1-1-1-1-1-1-111
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-111111-11-1-1111-1-111-1-1-1-1-111-111111-1-1-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-111-1-1111111-111-1-1-111-1-1-1-1-1-1111-1-1-11-1-1-1-111-1-1-1-1111
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-1-111-11111111111-1-1-1-1-11-11-111-1-11111-1-1-1-11
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-11-11111-11111-1-1-1-1111-111-1-1-111-1-111111-1-1
χ17222222-12-1-122-1222-1-122-1-122-1-12-1-12222-1-1-1-1-1222-1-1-1-1-1-1-1-10220200-1-1-1-12200000-1-122002-1-100-1-1-1-1-1-122000-1-100000000-100
χ18222222-12-1-122-1222-1-122-1-122-1-12-1-12222-1-1-1-1-1222-1-1-1-1-1-1-1-10-220-200-1-1112200000-11-2200-2-1-10011-1-111-2-20001100000000100
χ19222222-12-1-122-1222-1-122-1-122-1-12-1-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-102-2020011-1-1-2-2000001-12-20021100-1-111-1-1-2-20001100000000100
χ20222222-12-1-122-1222-1-122-1-122-1-12-1-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-20-2001111-2-20000011-2-200-2110011111122000-1-100000000-100
χ21222222-12-1-122-1222-1-12-2-1-122-1-12-1-1-2-222-1-1-1-11-2-2-21111111102-20-200-1-11122000001-1-2-20021100-1-1-1-1112-20001100000000-100
χ22222222-12-1-122-1222-1-12-2-1-122-1-12-1-1-2-222-1-1-1-11-2-2-2111111110-2-20200-1-1-1-12200000112-200-2110011-1-1-1-1-22000-1-100000000100
χ23222222-12-1-122-1222-1-12-2-1-122-1-12-1-1-2-2-2-2-1-1-1-11-2-2-2111111110220-2001111-2-200000-1-1-22002-1-100-1-11111-22000-1-100000000100
χ24222222-12-1-122-1222-1-12-2-1-122-1-12-1-1-2-2-2-2-1-1-1-11-2-2-2111111110-22020011-1-1-2-200000-112200-2-1-1001111-1-12-20001100000000-100
χ2522222-12222-122-1-122-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1220222200220022-1-1-102-102-1-100-1-1-1-100-1-10020000-1-1-1-10000000
χ2622222-12222-122-1-122-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-12-202-22200-2-200-2-2-1-1-10-2102-1100-1-111001100-2000011110000000
χ2722222-12222-122-1-122-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1-220-22-2-2002200-2-211102-10-21-10011-1-100-1-100-2000011110000000
χ2822222-12222-122-1-122-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1-2-20-2-2-2-200-2-200221110-210-21100111100110020000-1-1-1-10000000
χ2922222-12222-122-1-122-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-2111111220-2-22200-2-200-2-2-1-1-10210-21-10011-1-100110020000-1-1110000000
χ3022222-12222-122-1-122-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-21111112-20-222200220022-1-1-10-2-10-21100111100-1-100-2000011-1-10000000
χ3122222-12222-122-1-122-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-2111111-2202-2-2-200-2-2002211102102-1-100-1-1-1-1001100-2000011-1-10000000
χ3222222-12222-122-1-122-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-2111111-2-2022-2-2002200-2-21110-2-102-1100-1-11100-1-10020000-1-1110000000
χ332222-122-1222-1222-1-12-12-12-1-1-12-1-122222-1-1-1-12-1-1-1-1-122-1-1-1-120220-1-12200-1-1002-1-1200-1-120-1-1-1-100-1-10000022000000-1-1000-10
χ342222-122-1222-1222-1-12-12-12-1-1-12-1-122222-1-1-1-12-1-1-1-1-122-1-1-1-1-202-20112200-1-100-211200-11-20-1-11100-1-100000-2-20000001100010
χ352222-122-1222-1222-1-12-12-12-1-1-12-1-1222-2-2-1-1-1-12-1-1-1-1-122-1-1-1-120-220-1-1-2-20011002-1-1-2001-12011-1-1001100000-2-20000001100010
χ362222-122-1222-1222-1-12-12-12-1-1-12-1-1222-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2-2011-2-2001100-211-20011-20111100110000022000000-1-1000-10
χ372222-122-1222-1222-1-12-1-2-12-1-1-12-1-12-2-222-1-1-1-1-211111-2-2111120-2-20-1-12200-1-1002-1-1-20011-20111100-1-1000002-2000000-1-100010
χ382222-122-1222-1222-1-12-1-2-12-1-1-12-1-12-2-222-1-1-1-1-211111-2-21111-20-220112200-1-100-211-2001-12011-1-100-1-100000-2200000011000-10
χ392222-122-1222-1222-1-12-1-2-12-1-1-12-1-12-2-2-2-2-1-1-1-1-211111-2-21111202-20-1-1-2-20011002-1-1200-11-20-1-111001100000-2200000011000-10
χ402222-122-1222-1222-1-12-1-2-12-1-1-12-1-12-2-2-2-2-1-1-1-1-211111-2-21111-2022011-2-2001100-211200-1-120-1-1-1-10011000002-2000000-1-100010
χ412-22-2222-22-2-22-22-2-22220-22-2-22-22-2-2002i−2i22-2-200000000000000000002i−2i002i−2i2i−2i00000000000000002i−2i000000000002i−2i002-2000
χ422-22-2222-22-2-22-22-2-22220-22-2-22-22-2-2002i−2i22-2-200000000000000000002i−2i002i−2i−2i2i00000000000000002i−2i00000000000−2i2i00-22000
χ432-22-2222-22-2-22-22-2-22220-22-2-22-22-2-200−2i2i22-2-20000000000000000000−2i2i00−2i2i2i−2i0000000000000000−2i2i000000000002i−2i00-22000
χ442-22-2222-22-2-22-22-2-22220-22-2-22-22-2-200−2i2i22-2-20000000000000000000−2i2i00−2i2i−2i2i0000000000000000−2i2i00000000000−2i2i002-2000
χ4544444-2-24-2-2-24-2-2-24-21-24-21-2-2-21-2-21-2-2001111-24-2-2-2-2111111040040000-2-200000000-2-2000-20000110011000000000000000000
χ4644444-2-24-2-2-24-2-2-24-21-24-21-2-2-21-2-21-2-2001111-24-2-2-2-21111110-400-4000022000000002200020000-1-100-1-1000000000000000000
χ4744444-2-24-2-2-24-2-2-24-21-2-4-21-2-2-21-2-21220011112-42222-1-1-1-1-1-10400-400002200000000-22000-200001100-1-1000000000000000000
χ4844444-2-24-2-2-24-2-2-24-21-2-4-21-2-2-21-2-21220011112-42222-1-1-1-1-1-10-40040000-2-2000000002-200020000-1-10011000000000000000000
χ494444-24-2-2-2-24-2-244-21-2-241-2-2-21-2-21-244441111-2-2-2-211-2-211110040000-2-200-2-200000-200-20001100001100000000000000000000
χ504444-24-2-2-2-24-2-244-21-2-241-2-2-21-2-21-244-4-41111-2-2-2-211-2-2111100-40000220022000002002000-1-10000-1-100000000000000000000
χ514444-24-2-2-2-24-2-244-21-2-2-41-2-2-21-2-21-2-4-44411112222-1-122-1-1-1-100-40000-2-200-2-2000002002000-1-100001100000000000000000000
χ524444-24-2-2-2-24-2-244-21-2-2-41-2-2-21-2-21-2-4-4-4-411112222-1-122-1-1-1-1004000022002200000-200-2000110000-1-100000000000000000000
χ534444-2-24-244-2-24-2-2-2-2-214-2-211-2-21-2-2-2-20011114-211-2-2-2-2111140040-2-200000000-2110000-2-200011000000000000000000000000
χ544444-2-24-244-2-24-2-2-2-2-214-2-211-2-21-2-2-2-20011114-211-2-2-2-21111-400-4022000000002-1-1000022000-1-1000000000000000000000000
χ554444-2-24-244-2-24-2-2-2-2-21-4-2-211-2-21-2-222001111-42-1-12222-1-1-1-1400-40-2-200000000-211000022000-1-1000000000000000000000000
χ564444-2-24-244-2-24-2-2-2-2-21-4-2-211-2-21-2-222001111-42-1-12222-1-1-1-1-4004022000000002-1-10000-2-200011000000000000000000000000
χ5744-4-44444-44-4-4-4-44-444404-44-4-44-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-242-2-4-42-44-4-2-240-224-42-2-4220000-22-2200000000000000000000023−23000000000000000000000023−23000000000000000000
χ5944-4-444-242-2-4-42-44-4-2-240-224-42-2-4220000-22-22000000000000000000000−23230000000000000000000000−2323000000000000000000
χ6044-4-44-244-442-4-42-2-44-2-2042-22-4-22-4223−2300-22-220023−230023−232323−23−2300000000000000000000000000000000000000000000000000000
χ6144-4-44-244-442-4-42-2-44-2-2042-22-4-22-42−232300-22-2200−232300−2323−23−23232300000000000000000000000000000000000000000000000000000
χ6244-4-44-2-242-22-422-2-4-21-20-2-1-222122-123−23001-11-10023−2300−33−3−33300000000023−230000000000000000003-300−33000000000000000000
χ6344-4-44-2-242-22-422-2-4-21-20-2-1-222122-123−23001-11-10023−2300−33−3−333000000000−2323000000000000000000-33003−3000000000000000000
χ6444-4-44-2-242-22-422-2-4-21-20-2-1-222122-1−2323001-11-100−2323003−333−3−300000000023−23000000000000000000-3300−33000000000000000000
χ6544-4-44-2-242-22-422-2-4-21-20-2-1-222122-1−2323001-11-100−2323003−333−3−3000000000−23230000000000000000003-3003−3000000000000000000
χ6644-4-4-244-2-44-42-4-442-24-20-2-4-222422-40000-22-2200000000000000000−2i32i3000000000−2i32i300000000000000000000000000000000000
χ6744-4-4-244-2-44-42-4-442-24-20-2-4-222422-40000-22-22000000000000000002i3−2i30000000002i3−2i300000000000000000000000000000000000
χ6844-4-4-2-24-2-4422-42-22-2-210-221-12-2-12223−23001-11-100−330023−23−3−33300000−2i32i3000000000i3−i30000000003i−3i000000000000000000000000
χ6944-4-4-2-24-2-4422-42-22-2-210-221-12-2-12223−23001-11-100−330023−23−3−333000002i3−2i3000000000−i3i3000000000−3i3i000000000000000000000000
χ7044-4-4-2-24-2-4422-42-22-2-210-221-12-2-122−2323001-11-1003−300−232333−3−300000−2i32i3000000000i3−i3000000000−3i3i000000000000000000000000
χ7144-4-4-2-24-2-4422-42-22-2-210-221-12-2-122−2323001-11-1003−300−232333−3−3000002i3−2i3000000000−i3i30000000003i−3i000000000000000000000000
χ724-44-444-2-4-22-4424-4-4-2-2402-2-4-4-22422004i−4i-2-2220000000000000000000−2i2i004i−4i000000000000000000−2i2i00000000000000000000
χ734-44-444-2-4-22-4424-4-4-2-2402-2-4-4-2242200−4i4i-2-22200000000000000000002i−2i00−4i4i0000000000000000002i−2i00000000000000000000
χ744-44-44-24-44-424-4-22-44-2-20-4-22242-2-420000-2-22200000000000000000000000004i−4i00000000000000000000000000000−2i2i0000000
χ754-44-44-24-44-424-4-22-44-2-20-4-22242-2-420000-2-2220000000000000000000000000−4i4i000000000000000000000000000002i−2i0000000
χ764-44-4-24424-4-4-2-44-42-24-202422-2-4-22-4004i−4i-2-22200000000000000000004i−4i00−2i2i000000000000000000−2i2i00000000000000000000
χ774-44-4-24424-4-4-2-44-42-24-202422-2-4-22-400−4i4i-2-2220000000000000000000−4i4i002i−2i0000000000000000002i−2i00000000000000000000
χ784-44-4-24-22-22-4-224-421-2-20-1-22212-2-12004i−4i11-1-100003i−3i003i−3i3i−3i0000000−2i2i00−2i2i0000000000003-30000i−i00000000000000000000
χ794-44-4-24-22-22-4-224-421-2-20-1-22212-2-12004i−4i11-1-10000−3i3i00−3i3i−3i3i0000000−2i2i00−2i2i000000000000-330000i−i00000000000000000000
χ804-44-4-24-22-22-4-224-421-2-20-1-22212-2-1200−4i4i11-1-100003i−3i003i−3i3i−3i00000002i−2i002i−2i000000000000-330000−ii00000000000000000000
χ814-44-4-24-22-22-4-224-421-2-20-1-22212-2-1200−4i4i11-1-10000−3i3i00−3i3i−3i3i00000002i−2i002i−2i0000000000003-30000−ii00000000000000000000
χ824-4-44444-4-4-44-44-4-444440-4-4-44-4-4-44400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-2-4224-4-2-4-44-2-24022-4422-4-2-20000-222-20000000000000000000000000000000000000000000000000000−2i32i300000000000
χ844-4-4444-2-4224-4-2-4-44-2-24022-4422-4-2-20000-222-200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ854-4-444-24-4-4-4-2-442244-2-20-422-2-4224-20000-222-200000000000000000000000000000000000000000000000000000023−23000000000
χ864-4-444-24-4-4-4-2-442244-2-20-422-2-4224-20000-222-2000000000000000000000000000000000000000000000000000000−2323000000000
χ874-4-44-2442-4-4424-4-4-2-24-202-42-22-42-240000-222-20000000000000000000000000000000000000000000000000000000000−2i32i300000
χ884-4-44-2442-4-4424-4-4-2-24-202-42-22-42-240000-222-200000000000000000000000000000000000000000000000000000000002i3−2i300000
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
χ9188-8-8-48-4-44-4-844-8842-4-4024-44-2-44-2400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-44-44444-4422202-22-2-22-2-2-243−4300-11-1100−232300−232333−3−300000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-44444-4422202-22-2-22-2-2-2−434300-11-110023−230023−23−3−33300000000000000000000000000000000000000000000000000000
χ948-88-88-4-4-8-44484-44-8-42-404244-4-2-44-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-4-4848-84-4-8-444-4-4204-4-2-2-44244000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-44-444-44-4442220-22-2-22-22-2-20000-1-11100006i−6i00−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-444-44-4442220-22-2-22-22-2-20000-1-1110000−6i6i003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-844-4-8-4448-42-404-24-44-24-4200002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-444484-4-8-8-42-4-40-244-4-2442-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-8-8-44844-4-4-42044-2244-2-4-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-44-444-42220-2-2-22-2-2-2220000-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-44-444-42220-2-2-22-2-2-2220000-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000000000000

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