Finite Group Databasebeta

← Group #13168568

Character table — Group #13168568

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order12223336666666663334666666666121212121212121244366612121212121212121224444661212121212121212121212121212121212124466612121212121212121212124444412124412121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111111111111-1-111111111-1-111111-1-1-111-1-1-1-1-11-1-11-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1111-1-1111111111111111111-1-1-1-1-1-1-1111-1-111111-11-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-11-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-111
χ51111111111111111111111111111111111111-1-111111111111111111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-11-111-1-1-1-1-1-11-1
χ61111111111111111111111111111111111111-1-1111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-1-11-11-1-1-1-111-1-111-11
χ71111111111111111111111111111111111111-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-11-1-11-1-11111-1-1-11
χ81111111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-11111-1-1-1-1-1-1111-1-11-11-1-111-1-1-1-1111-1-1-1-1-111-111
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11-111-1-111-1-111111111-1-1-1-111111-1-1-11-1-1-1-1-1111-1-1-111111-11-11-1-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1111-111111-1-1-111-1-111111-11-1-1-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111-11-111-1-11111-11-1-1-1-1-11-1-1111
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-111111-1-111-1-1-1-1-1-1-1-11111-1-1111-1-11-11-1-111-1-111-11-1-1-1111-1-111-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1111111-1-111-1-111-1-1-1-1111111111-1-1-11-1-1-1-1-111-111-1-111-1-11-11-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1111-111111-1-11-1-1-1111-1-1-11-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-111-11-111-1-111-1-1111-1-111-111-11-1
χ17222222-1222-1-1-12222-1-122-1-1-12-1-1-12-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-1220022222-1-1-1-12200-1-1-1-1-1-1-1-100-1-1-12-1000-1-10000020020000-1-10000
χ18222222-1222-1-1-12222-1-122-1-1-12-1-1-12-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-1-2-2002-2-222-1-1-1-12200-1-1-1-1-1-1-1-100111-210001100000-200-20000110000
χ19222222-1222-1-1-12222-1-122-1-1-12-1-1-12-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-12200-222-2-21111-2-2001111111100-1-1-12-1000-1-100000-200-20000110000
χ20222222-1222-1-1-12222-1-122-1-1-12-1-1-12-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1-2-200-2-2-2-2-21111-2-2001111111100111-21000110000020020000-1-10000
χ21222222-1222-1-1-12222-1-1-22-1-1-12-1-1-1211-2-2111122-1-1-1-1-211-2-211112-200-222-2-2-1-1112200-1-1-1-1111100-1-1-1-210001100000-200200001-10000
χ22222222-1222-1-1-12222-1-1-22-1-1-12-1-1-1211-2-2111122-1-1-1-1-211-2-21111-2200-2-2-2-2-2-1-1112200-1-1-1-11111001112-1000-1-100000200-20000-110000
χ23222222-1222-1-1-12222-1-1-22-1-1-12-1-1-1211-2-21111-2-2-1-1-1-1-211-2-211112-2002222211-1-1-2-2001111-1-1-1-100-1-1-1-210001100000200-20000-110000
χ24222222-1222-1-1-12222-1-1-22-1-1-12-1-1-1211-2-21111-2-2-1-1-1-1-211-2-21111-22002-2-22211-1-1-2-2001111-1-1-1-1001112-1000-1-100000-200200001-10000
χ2522222-12-12-122222-1-12-12-1-12-1-122-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-122220-1-100000000-1-100000000222-1-1-12-122-1-1-1-1-1-100020-1-1000000-10
χ2622222-12-12-122222-1-12-12-1-12-1-122-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-122-2-20-1-1000000001100000000-2-22-1-1-121-2-2-1-11111000-201100000010
χ2722222-12-12-122222-1-12-12-1-12-1-122-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22201100000000-1-100000000-2-2-2111-2-12211-1-1-1-1000-201100000010
χ2822222-12-12-122222-1-12-12-1-12-1-122-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-201100000000110000000022-2111-21-2-211111100020-1-1000000-10
χ2922222-12-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-200-1-1-1-11111111112-22-20-1-1000000001100000000-2-22-1-11-2-1-2211-1-1110002011000000-10
χ3022222-12-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-200-1-1-1-11111111112-2-220-1-100000000-1-100000000222-1-11-212-21111-1-1000-20-1-100000010
χ3122222-12-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-200-1-1-1-1111111111-222-201100000000110000000022-211-12-1-22-1-1-1-111000-20-1-100000010
χ3222222-12-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-200-1-1-1-1111111111-22-2201100000000-1-100000000-2-2-211-1212-2-1-111-1-10002011000000-10
χ332222-1222-12222-1-12-1-122-12-12-1-1-12-122-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-10022200-1-12222-1-122-1-1-1-1-1-1-1-100000002-1-100-1-1-1-120200000000-1-100
χ342222-1222-12222-1-12-1-122-12-12-1-1-12-122-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-100-2-2200-1-12222-1-1-2-2-1-1-1-1-1-1-1-10000000-211001111-20-2000000001100
χ352222-1222-12222-1-12-1-122-12-12-1-1-12-122-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-10022-20011-2-2-2-211221111111100000002-1-100-1-1-1-1-20-2000000001100
χ362222-1222-12222-1-12-1-122-12-12-1-1-12-122-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-100-2-2-20011-2-2-2-211-2-2111111110000000-21100111120200000000-1-100
χ372222-1222-12222-1-12-1-12-2-12-12-1-1-12-1-2-211111122-1-1-1-1-2-2-2111111002-2-2001122-2-2-1-1-2-2-1-1-1-11111000000021-100-1-111-20200000000-1100
χ382222-1222-12222-1-12-1-12-2-12-12-1-1-12-1-2-211111122-1-1-1-1-2-2-211111100-22-2001122-2-2-1-122-1-1-1-111110000000-2-110011-1-120-2000000001-100
χ392222-1222-12222-1-12-1-12-2-12-12-1-1-12-1-2-2111111-2-2-1-1-1-1-2-2-2111111002-2200-1-1-2-22211-2-21111-1-1-1-1000000021-100-1-11120-2000000001-100
χ402222-1222-12222-1-12-1-12-2-12-12-1-1-12-1-2-2111111-2-2-1-1-1-1-2-2-211111100-22200-1-1-2-22211221111-1-1-1-10000000-2-110011-1-1-20200000000-1100
χ412-22-2222-2-2-2-22-22-222220-2-222-2-2-2-22000000002i−2i2-2-220000000000000000002i−2i002i−2i002i2i−2i−2i00002-200000000000000000002-22i−2i000000
χ422-22-2222-2-2-2-22-22-222220-2-222-2-2-2-22000000002i−2i2-2-220000000000000000002i−2i002i−2i002i2i−2i−2i0000-220000000000000000000-22−2i2i000000
χ432-22-2222-2-2-2-22-22-222220-2-222-2-2-2-2200000000−2i2i2-2-22000000000000000000−2i2i00−2i2i00−2i−2i2i2i00002-200000000000000000002-2−2i2i000000
χ442-22-2222-2-2-2-22-22-222220-2-222-2-2-2-2200000000−2i2i2-2-22000000000000000000−2i2i00−2i2i00−2i−2i2i2i0000-220000000000000000000-222i−2i000000
χ4544444-2-2-24-2-2-2-244-2-2-214-21-21-2-2-21-2-2-244-2-2-2-2001111-211-2-2111144000-2-200000000000000000000-211-2-2000110000000000000000000
χ4644444-2-2-24-2-2-2-244-2-2-214-21-21-2-2-21-2-2-244-2-2-2-2001111-211-2-21111-4-400022000000000000000000002-1-122000-1-10000000000000000000
χ4744444-2-2-24-2-2-2-244-2-2-21-4-21-21-2-2-21-222-4-422220011112-1-122-1-1-1-14-4000-2-200000000000000000000-21122000-1-10000000000000000000
χ4844444-2-2-24-2-2-2-244-2-2-21-4-21-21-2-2-21-222-4-422220011112-1-122-1-1-1-1-4400022000000000000000000002-1-1-2-2000110000000000000000000
χ494444-24-24-24-2-2-2-2-24-21-24-2-21-2-211-2-2-2-2-2-211114411114-2-2-2-211110000400-2-2-2-2-2-2-2-200111111110000000000000000000000000000000
χ504444-24-24-24-2-2-2-2-24-21-24-2-21-2-211-2-2-2-2-2-21111-4-411114-2-2-2-211110000-4002222222200-1-1-1-1-1-1-1-10000000000000000000000000000000
χ514444-24-24-24-2-2-2-2-24-21-2-4-2-21-2-211-2-22222-1-1-1-1441111-42222-1-1-1-10000-40022-2-222-2-2001111-1-1-1-10000000000000000000000000000000
χ524444-24-24-24-2-2-2-2-24-21-2-4-2-21-2-211-2-22222-1-1-1-1-4-41111-42222-1-1-1-10000400-2-222-2-22200-1-1-1-111110000000000000000000000000000000
χ534444-2-24-2-2-2444-2-2-21-2-241-2-2-21-2-2-2144-2-2-2-2-2-2001111-2-2-2111111004400000000000-2-2000000000000000-2-2-2001111000000000000000
χ544444-2-24-2-2-2444-2-2-21-2-241-2-2-21-2-2-2144-2-2-2-2-2-2001111-2-2-211111100-4-4000000000002200000000000000022200-1-1-1-1000000000000000
χ554444-2-24-2-2-2444-2-2-21-2-2-41-2-2-21-2-2-21-4-4222222001111222-1-1-1-1-1-1004-40000000000022000000000000000-22-20011-1-1000000000000000
χ564444-2-24-2-2-2444-2-2-21-2-2-41-2-2-21-2-2-21-4-4222222001111222-1-1-1-1-1-100-4400000000000-2-20000000000000002-2200-1-111000000000000000
χ5744-4-4444-4-444-4-4-44-44440-4-4-4-444-44-4000000000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-4-44-222-44-44-2-20-42224-22-2-40000000000-2-2220000000000000000000023−23000000002323−23−230000000000000000000000000000000
χ5944-4-444-2-4-44-222-44-44-2-20-42224-22-2-40000000000-2-22200000000000000000000−232300000000−23−2323230000000000000000000000000000000
χ6044-4-44-242-4-24-4-4-442-24-2022-42-24-4-220000000000-2-22200000000000000000000000023−23000000000000000000000023−23000000000000000
χ6144-4-44-242-4-24-4-4-442-24-2022-42-24-4-220000000000-2-222000000000000000000000000−23230000000000000000000000−2323000000000000000
χ6244-4-4-244-4244-4-42-2-4-2-2402-42-4-2-22420023−232323−23−2300-2-22200023−232323−23−2300000000000000000000000000000000000000000000000000000000
χ6344-4-4-244-4244-4-42-2-4-2-2402-42-4-2-224200−2323−23−23232300-2-222000−2323−23−23232300000000000000000000000000000000000000000000000000000000
χ6444-4-4-24-2-424-2222-2-4-21-2022-12-21-1-220023−23−3−3330011-1-100023−23−3−3330000000000023−2300003-33-3−3−3330000000000000000000000000000000
χ6544-4-4-24-2-424-2222-2-4-21-2022-12-21-1-220023−23−3−3330011-1-100023−23−3−33300000000000−23230000-33-3333−3−30000000000000000000000000000000
χ6644-4-4-24-2-424-2222-2-4-21-2022-12-21-1-2200−232333−3−30011-1-1000−232333−3−30000000000023−230000-33-33−3−3330000000000000000000000000000000
χ6744-4-4-24-2-424-2222-2-4-21-2022-12-21-1-2200−232333−3−30011-1-1000−232333−3−300000000000−232300003-33-333−3−30000000000000000000000000000000
χ6844-4-4-2-2422-24-4-42-221-2-20-12221-22-2-10023−232323−23−230011-1-1000−33−3−33300000000000000023−23000000000000000000003-3−33000000000000000
χ6944-4-4-2-2422-24-4-42-221-2-20-12221-22-2-10023−232323−23−230011-1-1000−33−3−333000000000000000−232300000000000000000000-333−3000000000000000
χ7044-4-4-2-2422-24-4-42-221-2-20-12221-22-2-100−2323−23−2323230011-1-10003−333−3−300000000000000023−2300000000000000000000-33−33000000000000000
χ7144-4-4-2-2422-24-4-42-221-2-20-12221-22-2-100−2323−23−2323230011-1-10003−333−3−3000000000000000−2323000000000000000000003-33−3000000000000000
χ724-44-444-2-4-4-42-224-444-2-20-42-2-2-42224000000004i−4i-222-2000000000000000000−2i2i004i−4i00−2i−2i2i2i00000000000000000000000000000000000
χ734-44-444-2-4-4-42-224-444-2-20-42-2-2-4222400000000−4i4i-222-20000000000000000002i−2i00−4i4i002i2i−2i−2i00000000000000000000000000000000000
χ744-44-44-242-42-44-44-4-2-24-20224-22-4-42-20000000000-222-200000000000000000000000000000000004-40000000000000000000-2200000000
χ754-44-44-242-42-44-44-4-2-24-20224-22-4-42-20000000000-222-20000000000000000000000000000000000-4400000000000000000002-200000000
χ764-44-4-244-42-4-44-4-224-2-2402-4-24222-4-2000000004i−4i-222-20000000000000000004i−4i00−2i2i00−2i−2i2i2i00000000000000000000000000000000000
χ774-44-4-244-42-4-44-4-224-2-2402-4-24222-4-200000000−4i4i-222-2000000000000000000−4i4i002i−2i002i2i−2i−2i00000000000000000000000000000000000
χ784-44-4-24-2-42-42-22-224-21-20221-22-1-12-200003-33-34i−4i1-1-11000003-33-3000000000−2i2i00−2i2i00ii−i−i3i−3i3i−3i0000000000000000000000000000000
χ794-44-4-24-2-42-42-22-224-21-20221-22-1-12-200003-33-3−4i4i1-1-11000003-33-30000000002i−2i002i−2i00−i−iii−3i3i−3i3i0000000000000000000000000000000
χ804-44-4-24-2-42-42-22-224-21-20221-22-1-12-20000-33-334i−4i1-1-1100000-33-33000000000−2i2i00−2i2i00ii−i−i−3i3i−3i3i0000000000000000000000000000000
χ814-44-4-24-2-42-42-22-224-21-20221-22-1-12-20000-33-33−4i4i1-1-1100000-33-330000000002i−2i002i−2i00−i−iii3i−3i3i−3i0000000000000000000000000000000
χ824-4-4444444-4-4-44-4-4-4444044-4-4-4-44-4-400000000004-44-400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-244-422-2-4-4-44-2-204-222-42-22-423−230023−23−232300-22-22023−230023−23−232300000000000000000000000000000000000000000000000000000000
χ844-4-4444-244-422-2-4-4-44-2-204-222-42-22-4−232300−232323−2300-22-220−232300−232323−2300000000000000000000000000000000000000000000000000000000
χ854-4-444-24-242-4-44-4-42-24-20-2-2-422-44220000000000-22-2200000000000000−2i32i3000000000000000000000−2i32i300000000000000000000000000
χ864-4-444-24-242-4-44-4-42-24-20-2-2-422-44220000000000-22-22000000000000002i3−2i30000000000000000000002i3−2i300000000000000000000000000
χ874-4-444-2-2-24222-2-4-42-2-210-212-122-2-1223−230023−23−2323001-11-10−3300−333−300000−2i32i3000000000000000000000i3−i3000003i−3i0000000000000000000
χ884-4-444-2-2-24222-2-4-42-2-210-212-122-2-1223−230023−23−2323001-11-10−3300−333−3000002i3−2i3000000000000000000000−i3i300000−3i3i0000000000000000000
χ894-4-444-2-2-24222-2-4-42-2-210-212-122-2-12−232300−232323−23001-11-103−3003−3−3300000−2i32i3000000000000000000000i3−i300000−3i3i0000000000000000000
χ904-4-444-2-2-24222-2-4-42-2-210-212-122-2-12−232300−232323−23001-11-103−3003−3−33000002i3−2i3000000000000000000000−i3i3000003i−3i0000000000000000000
χ914-4-44-2444-2-4-4-4422-4-2-240-242-422-2-420000000000-22-220000000000000000−2i32i3000000000000−2i32i32i3−2i30000000000000000000000000000000
χ924-4-44-2444-2-4-4-4422-4-2-240-242-422-2-420000000000-22-2200000000000000002i3−2i30000000000002i3−2i3−2i32i30000000000000000000000000000000
χ934-4-44-24-24-2-422-222-4-21-20-2-2-122-112223−2300−333−3001-11-1023−2300−333−30000000−2i32i300000000−3i3i3i−3ii3−i3−i3i30000000000000000000000000000000
χ944-4-44-24-24-2-422-222-4-21-20-2-2-122-112223−2300−333−3001-11-1023−2300−333−300000002i3−2i3000000003i−3i−3i3i−i3i3i3−i30000000000000000000000000000000
χ954-4-44-24-24-2-422-222-4-21-20-2-2-122-1122−2323003−3−33001-11-10−2323003−3−330000000−2i32i3000000003i−3i−3i3ii3−i3−i3i30000000000000000000000000000000
χ964-4-44-24-24-2-422-222-4-21-20-2-2-122-1122−2323003−3−33001-11-10−2323003−3−3300000002i3−2i300000000−3i3i3i−3i−i3i3i3−i30000000000000000000000000000000
χ978888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-44-8-4-444-884-4-4204-24-2-4-4424000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-444-4-4444-442220-2-2-2-222-22-20043−43−23−23232300-1-111000−232333−3−300000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-444-4-4444-442220-2-2-2-222-22-200−43432323−23−2300-1-11100023−23−3−33300000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-44-844-448-8-4-4-4204-2-42444-2-400000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-48444-88-8-44-42-4-40-24-4-4-2444200000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44444-44-44-42220-2-222-2-2-2-2200006-66-600-111-100000-33-3300000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-44444-44-44-42220-2-222-2-2-2-220000-66-6600-111-1000003-33-300000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48-4-44-8-884442-4-402-444-24-44-200000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-4-4444-4444222022-2-2-2-22-2-243−4300−232323−2300-11-110−2323003−3−3300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-4-4444-4444222022-2-2-2-22-2-2−43430023−23−232300-11-11023−2300−333−300000000000000000000000000000000000000000000000000000000

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