Finite Group Databasebeta

← Group #13169251

Character table — Group #13169251

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order122233366666666633346666666664436661212121212121212121212121222444666612121212121212124466666612121212121212121212121244444121212121212221212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-11111-1-11111-1-1-1-11111111-1-1111-1-111-1-11-1-1-1111-1-1-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-1-111-1-1-1-11-1
χ4111111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11-1-1111-1-111-1-1-1-1-11-1-1-111-1-111-11-11
χ511111111111111111111111111111-1-111111111111111111111-11111111-1-1-1-11111111111-111-1-1-111-1-111-1-1-11-1-1-111-1-1-1-1-11-1-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ711111111111111111111111111111-1-111111111111111111-1-11-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-111-1-1111-1-1-1111-1-1-1-1111-1-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1111-111-1-1-11-1-1-1-11111-1-1-11-1-1111111111-1-1-1-1
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-1111111-1-11-111-1-1-1-11-1-1-1-1-11111-1-111111-1-1-1-1-1-1-1111
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-111-11-1-1-1-11111-1-111-11-1-1-1-1-111-1-111-11
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-111111111-11-1-111-1-11-1-1-1-1-111111-11-1-1-1-111-1-1111-11-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-111-1-111-1-1-1-1-1-1111-111-1-111-111111-1-1-1-11-11-1-1-1-111-1-1-1-11-111
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-11-111-1-11-11111-1-1-1-11111-11-1-1-1-1-1111111-1-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-111111-1-1-1-1-1-111111-1-1-1-111-111-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-11111-11-1-1111-11111-1-1-1-111-11-1-11111111-1-1-1-1-11
χ17222222-122-122-12-122-1-122-1-1-1-12-12-100-1-1-1-122-1-1-122-1-1-1-1-1-12220222-1-1220000-1-122-12-1-1-1-10-12000-1-100-1-10002000-1-100000-100
χ18222222-122-122-12-122-1-122-1-1-1-12-12-100-1-1-1-122-1-1-122-1-1-1-1-1-122-20-222-1-1-2-2000011-2-2-12-1-1-1-101-2000110011000-20001100000100
χ19222222-122-122-12-122-1-122-1-1-1-12-12-100-1-1-1-122-1-1-122-1-1-1-1-1-1-2-2202-2-211220000-1-1-2-21-211110-12000-1-100-1-1000-20001100000100
χ20222222-122-122-12-122-1-122-1-1-1-12-12-100-1-1-1-122-1-1-122-1-1-1-1-1-1-2-2-20-2-2-211-2-2000011221-2111101-20001100110002000-1-100000-100
χ21222222-122-122-12-122-1-1-22-1-1-1-12-12-100-1-1-1-1-2-2111-2-21111112-220-222112200001122-1-2-1-1110-1-2000-1-10011000-2000-1-100000100
χ22222222-122-122-12-122-1-1-22-1-1-1-12-12-100-1-1-1-1-2-2111-2-21111112-2-2022211-2-20000-1-1-2-2-1-2-1-1110120001100-1-100020001100000-100
χ23222222-122-122-12-122-1-1-22-1-1-1-12-12-100-1-1-1-1-2-2111-2-2111111-2220-2-2-2-1-122000011-2-21211-1-10-1-2000-1-1001100020001100000-100
χ24222222-122-122-12-122-1-1-22-1-1-1-12-12-100-1-1-1-1-2-2111-2-2111111-22-202-2-2-1-1-2-20000-1-1221211-1-10120001100-1-1000-2000-1-100000100
χ2522222-122-122-12-122-12-12-12-1-1-1-12-1222-1-1-1-12-12-1-1-1-122-1-1-1-122020-1-1220022-1-100002-1-1-1-1-1-1002-1-100-1-10020002-1-1000000-1000
χ2622222-122-122-12-122-12-12-12-1-1-1-12-1222-1-1-1-12-12-1-1-1-122-1-1-1-1-2-202011-2-20022-1-10000-211111-1002-1-100-1-100-2000-2110000001000
χ2722222-122-122-12-122-12-12-12-1-1-1-12-12-2-2-1-1-1-12-12-1-1-1-122-1-1-1-1220-20-1-12200-2-21100002-1-1-1-1-1100-211001100-2000-2110000001000
χ2822222-122-122-12-122-12-12-12-1-1-1-12-12-2-2-1-1-1-12-12-1-1-1-122-1-1-1-1-2-20-2011-2-200-2-2110000-211111100-21100110020002-1-1000000-1000
χ2922222-122-122-12-122-12-1-2-12-1-1-1-12-1222-1-1-1-1-21-21111-2-211112-20-20-1-1-2-20022-1-1000021-1-111100-21100-1-100-20002-1-10000001000
χ3022222-122-122-12-122-12-1-2-12-1-1-1-12-1222-1-1-1-1-21-21111-2-21111-220-2011220022-1-10000-2-111-1-1100-21100-1-1002000-211000000-1000
χ3122222-122-122-12-122-12-1-2-12-1-1-1-12-12-2-2-1-1-1-1-21-21111-2-211112-2020-1-1-2-200-2-211000021-1-111-1002-1-10011002000-211000000-1000
χ3222222-122-122-12-122-12-1-2-12-1-1-1-12-12-2-2-1-1-1-1-21-21111-2-21111-22020112200-2-2110000-2-111-1-1-1002-1-1001100-20002-1-10000001000
χ332222-122-122-12222-1-1-122-1-1222-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1002220000-1-1-1-122220000000022-1-1-1-1-1-1-1-1-1-1022000000-1-10000-10
χ342222-122-122-12222-1-1-122-1-1222-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-100-22-2000011-1-122-2-2000000002-21-1-1-111-1-1110-2-200000011000010
χ352222-122-122-12222-1-1-122-1-1222-1-1-1-1-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-1002-220000-1-111-2-22200000000-22-1111-1-111-1-10-2-200000011000010
χ362222-122-122-12222-1-1-122-1-1222-1-1-1-1-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-2-200001111-2-2-2-200000000-2-21111111111022000000-1-10000-10
χ372222-122-122-12222-1-1-12-2-1-1222-1-1-1-122-1-1-1-11-2-2-2-211111111002-2-20000-1-1-1-122-2-200000000-221111-1-1-1-11102-2000000-1-1000010
χ382222-122-122-12222-1-1-12-2-1-1222-1-1-1-122-1-1-1-11-2-2-2-21111111100-2-22000011-1-1222200000000-2-2-111111-1-1-1-10-22000000110000-10
χ392222-122-122-12222-1-1-12-2-1-1222-1-1-1-1-2-2-1-1-1-11-2-2-2-2111111110022-20000-1-111-2-2-2-200000000221-1-1-1-1-111110-22000000110000-10
χ402222-122-122-12222-1-1-12-2-1-1222-1-1-1-1-2-2-1-1-1-11-2-2-2-21111111100-22200001111-2-222000000002-2-1-1-1-11111-1-102-2000000-1-1000010
χ412-22-2222-22-2-2-22-2-222220-222-2-22-2-2-22i−2i22-2-20000000000000000000000002i−2i2i−2i002i−2i000000000000002i−2i0000000002i−2i002-20000
χ422-22-2222-22-2-2-22-2-222220-222-2-22-2-2-22i−2i22-2-20000000000000000000000002i−2i2i−2i00−2i2i000000000000002i−2i000000000−2i2i00-220000
χ432-22-2222-22-2-2-22-2-222220-222-2-22-2-2-2−2i2i22-2-2000000000000000000000000−2i2i−2i2i002i−2i00000000000000−2i2i0000000002i−2i00-220000
χ442-22-2222-22-2-2-22-2-222220-222-2-22-2-2-2−2i2i22-2-2000000000000000000000000−2i2i−2i2i00−2i2i00000000000000−2i2i000000000−2i2i002-20000
χ4544444-2-24-2-24-2-2-2-24-2-214-2-2111-2-2-2-20011114-2-211-2-2-2-2111144000-2-2-2-20000000000-2-2111100000000000000000000000000000
χ4644444-2-24-2-24-2-2-2-24-2-214-2-2111-2-2-2-20011114-2-211-2-2-2-21111-4-40002222000000000022-1-1-1-100000000000000000000000000000
χ4744444-2-24-2-24-2-2-2-24-2-21-4-2-2111-2-2-2-2001111-422-1-12222-1-1-1-14-4000-2-2220000000000-2211-1-100000000000000000000000000000
χ4844444-2-24-2-24-2-2-2-24-2-21-4-2-2111-2-2-2-2001111-422-1-12222-1-1-1-1-4400022-2-200000000002-2-1-11100000000000000000000000000000
χ494444-24-2-24-2-24-24-2-2-21-24-21-2-2-2-21-21001111-24-2-2-2-2-2111111004040000-2-20000-2-2000000000-2-200011001100000000000000000
χ504444-24-2-24-2-24-24-2-2-21-24-21-2-2-2-21-21001111-24-2-2-2-2-211111100-40-400002200002200000000022000-1-100-1-100000000000000000
χ514444-24-2-24-2-24-24-2-2-21-2-4-21-2-2-2-21-210011112-422222-1-1-1-1-1-10040-40000-2-2000022000000000-220001100-1-100000000000000000
χ524444-24-2-24-2-24-24-2-2-21-2-4-21-2-2-2-21-210011112-422222-1-1-1-1-1-100-4040000220000-2-20000000002-2000-1-1001100000000000000000
χ534444-2-24-2-24-2-24-24-21-2-241-2-2-2-21-21-2441111-2-24-2-211-2-2111100040000000-2-2-2-20000000000-200-21100110000000000000000000
χ544444-2-24-2-24-2-24-24-21-2-241-2-2-2-21-21-2-4-41111-2-24-2-211-2-21111000-40000000222200000000002002-1-100-1-10000000000000000000
χ554444-2-24-2-24-2-24-24-21-2-2-41-2-2-2-21-21-244111122-422-1-122-1-1-1-1000-40000000-2-2-2-200000000002002-1-100110000000000000000000
χ564444-2-24-2-24-2-24-24-21-2-2-41-2-2-2-21-21-2-4-4111122-422-1-122-1-1-1-10004000000022220000000000-200-21100-1-10000000000000000000
χ5744-4-44444-44-44-4-4-4-444404-4-44-4-44-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-4-2-442-42-44-2-20422-22-4-2-4200-22-22000000000000000000000000000023−2300000000000000000023−2300000000000000000
χ5944-4-444-24-4-2-442-42-44-2-20422-22-4-2-4200-22-220000000000000000000000000000−2323000000000000000000−232300000000000000000
χ6044-4-44-24424-4-2-42-4-4-24-20-2-42-22242-400-22-22000000000000000000000000000000000000000000000000000000023−230000000000
χ6144-4-44-24424-4-2-42-4-4-24-20-2-42-22242-400-22-220000000000000000000000000000000000000000000000000000000−23230000000000
χ6244-4-4-244-2-4424-4-4-42-2-240-22-44-42-22200-22-220000000000000000000000−2i32i300000000000000000000−2i32i3000000000000000000000
χ6344-4-4-244-2-4424-4-4-42-2-240-22-44-42-22200-22-2200000000000000000000002i3−2i3000000000000000000002i3−2i3000000000000000000000
χ6444-4-4-24-2-2-4-2242-422-21-20-2-12-22212-1001-11-100000003i−3i3i3i−3i−3i000000000−2i32i3000023−2300000000000000i3−i300−3300000000000000000
χ6544-4-4-24-2-2-4-2242-422-21-20-2-12-22212-1001-11-100000003i−3i3i3i−3i−3i0000000002i3−2i30000−232300000000000000−i3i3003−300000000000000000
χ6644-4-4-24-2-2-4-2242-422-21-20-2-12-22212-1001-11-10000000−3i3i−3i−3i3i3i000000000−2i32i30000−232300000000000000i3−i3003−300000000000000000
χ6744-4-4-24-2-2-4-2242-422-21-20-2-12-22212-1001-11-10000000−3i3i−3i−3i3i3i0000000002i3−2i3000023−2300000000000000−i3i300−3300000000000000000
χ684-44-444-2-442-4-4-2-4244-2-20-4-2-22242-4200-2-2220000000000000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ694-44-444-2-442-4-4-2-4244-2-20-4-2-22242-4200-2-222000000000000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ704-44-44-24-4-2-4-4242-44-24-2024-222-2-42-44i−4i-2-2220000000000000000000000004i−4i−2i2i000000000000000000−2i2i0000000000000000000
χ714-44-44-24-4-2-4-4242-44-24-2024-222-2-42-4−4i4i-2-222000000000000000000000000−4i4i2i−2i0000000000000000002i−2i0000000000000000000
χ724-44-4-24424-42-44-4-4-2-2-2402-24-4-4-22224i−4i-2-222000000000000000000000000−2i2i4i−4i000000000000000000−2i2i0000000000000000000
χ734-44-4-24424-42-44-4-4-2-2-2402-24-4-4-2222−4i4i-2-2220000000000000000000000002i−2i−4i4i0000000000000000002i−2i0000000000000000000
χ744-44-4-2-242-2-42242-4-21-2-20-1-2-22212-124i−4i11-1-1000003i−3i003i−3i3i−3i00000000000−2i2i−2i2i000000000000003-300i−i0000000000000000000
χ754-44-4-2-242-2-42242-4-21-2-20-1-2-22212-124i−4i11-1-100000−3i3i00−3i3i−3i3i00000000000−2i2i−2i2i00000000000000-3300i−i0000000000000000000
χ764-44-4-2-242-2-42242-4-21-2-20-1-2-22212-12−4i4i11-1-1000003i−3i003i−3i3i−3i000000000002i−2i2i−2i00000000000000-3300−ii0000000000000000000
χ774-44-4-2-242-2-42242-4-21-2-20-1-2-22212-12−4i4i11-1-100000−3i3i00−3i3i−3i3i000000000002i−2i2i−2i000000000000003-300−ii0000000000000000000
χ784-4-44444-4-4-44-4-444-44440-4-4-4-44-4-444004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-424-424-2-44-2-20-4222-2-424-200-222-200000000000000000000−2i32i300000000000000−2i32i300000000000000000000000000000
χ804-4-4444-2-4-424-424-2-44-2-20-4222-2-424-200-222-2000000000000000000002i3−2i3000000000000002i3−2i300000000000000000000000000000
χ814-4-444-24-42-442-4-24-4-24-202-422-22-4-2400-222-2000000000000000000−2i32i300000000000000−2i32i30000000000000000000000000000000
χ824-4-444-24-42-442-4-24-4-24-202-422-22-4-2400-222-20000000000000000002i3−2i3000000000000002i3−2i30000000000000000000000000000000
χ834-4-444-2-2-422422-2-2-4-2-21022-1-1122-2-2001-1-110003-300003-3-3300000−2i32i3−2i32i3000000000000i3−i3i3−i300000000000000000000000000000
χ844-4-444-2-2-422422-2-2-4-2-21022-1-1122-2-2001-1-110003-300003-3-33000002i3−2i32i3−2i3000000000000−i3i3−i3i300000000000000000000000000000
χ854-4-444-2-2-422422-2-2-4-2-21022-1-1122-2-2001-1-11000-330000-333-300000−2i32i32i3−2i3000000000000i3−i3−i3i300000000000000000000000000000
χ864-4-444-2-2-422422-2-2-4-2-21022-1-1122-2-2001-1-11000-330000-333-3000002i3−2i3−2i32i3000000000000−i3i3i3−i300000000000000000000000000000
χ874-4-44-2442-4-4-2-4-4442-2-24022-4-4422-2-200-222-20000000000000000000000000000000000000000000000000000000000023−23000000
χ884-4-44-2442-4-4-2-4-4442-2-24022-4-4422-2-200-222-200000000000000000000000000000000000000000000000000000000000−2323000000
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
χ9188-8-88-4-484-4-8-4444-8-4-420-44-22-24-444002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-4484-4-84-842-4-40244-44-2-4-24002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-44-4444422202-2-22-2-22-2-200-11-1100000006i−6i−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-44-4444422202-2-22-2-22-2-200-11-110000000−6i6i3i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-88-4-4-8-44-84-4448-4-4204-42-2-2-44440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-44844-8-4-84-4-42-4042-444-4-24-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-4444-444-42220-222-2-22-2-2-200-1-111000006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44-4444-444-42220-222-2-22-2-2-200-1-11100000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-88-48-44-84-4-848-44-42-404-244-44-2-42002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-8-44-8-4842-4-40-2444-4-242-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-444-4-442220-2-2-2-22-2-22200-111-10006-60000-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-444-4-442220-2-2-2-22-2-22200-111-1000-6600003-3-33000000000000000000000000000000000000000000000000000000

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