Finite Group Databasebeta

← Group #13168590

Character table — Group #13168590

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order1222333666666666333466666666644366612121212121212121212121212222446666661212121212124466666666612121212121212121244444121212121212441212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-1-1-11111-1-11111-1-111-1-1-1111111-111-1-11111-1-1-1-1-111-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-1-111111-1-1-1-1111111-1-1-1-1111-1-1-1-1111111111-1-111-1-1-1-1-111-1-1-1-11-1
χ4111111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-1111-1-1-1-111-11-11
χ511111111111111111111111111111-1-111111111111111111111-1111111111-1-1-1-111111111111-1-11-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-111
χ711111111111111111111111111111-1-111111111111111111-1-11-1111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-1-111-1-111-1-1-1-1-111-1-1111-1-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-1111111-1111111-1-1-1-1-1-1-1-1-111-111-1-111111111-1-1-1-1
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-111-1-1111111-1-1-11-1-1-111-1-1-1-11-1-11111-11-111-1-111-1-1-1-1-1111
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-11-1111-1-111-1-1-1-1-1-1-1111-11-11-1-1-1-111-1-111-11
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111111-1-1-1-1-1-111-1-11-1-111111-1-11-111-1-1-1-1111-11-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-11111-1-1-1-1-1-1-1-111-1111111-1-111-111-1-1-1-11-1-11-111-1-1-1-1-1-11-111
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-1-1-1-1-1-11-1-1-111-1-11111111-1-11-11-11-1-1-1-1111111-1-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-1-1-1-1-1-1-11-1111-1-11111-111-1-1-1-1-11-111-1-111-1-111-111-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1111111111-1-1-111-1-1111111-1-1-1-1-11
χ17222222-12-1222-1-1222-1-122-1-1-1-1-12-1200-1-1-1-1-122-1-1-1-122-1-1-1-1222022222-1-1-1-10000222-1-1-1-1-1-1-1-100200-1-10000002-1-10000000-100
χ18222222-12-1222-1-1222-1-122-1-1-1-1-12-1200-1-1-1-1-122-1-1-1-122-1-1-1-122-20-2-2-222-1-1110000-2-22-1111-1-1-1-100-20011000000-2110000000100
χ19222222-12-1222-1-1222-1-122-1-1-1-1-12-1200-1-1-1-1-122-1-1-1-122-1-1-1-1-2-220222-2-211-1-10000-2-2-21-1-1-1111100200-1-1000000-2110000000100
χ20222222-12-1222-1-1222-1-122-1-1-1-1-12-1200-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-20-2-2-2-2-21111000022-21111111100-200110000002-1-10000000-100
χ21222222-12-1222-1-1222-1-1-22-1-1-1-1-12-1200-1-1-1-11-2-21111-2-211112-220-222221111000022-2-1-1-1-1-1-11100-20011000000-2-1-10000000100
χ22222222-12-1222-1-1222-1-1-22-1-1-1-1-12-1200-1-1-1-11-2-21111-2-211112-2-202-2-22211-1-10000-2-2-2-1111-1-11100200-1-10000002110000000-100
χ23222222-12-1222-1-1222-1-1-22-1-1-1-1-12-1200-1-1-1-11-2-21111-2-21111-2220-222-2-2-1-1110000-2-221-1-1-111-1-100-200110000002110000000-100
χ24222222-12-1222-1-1222-1-1-22-1-1-1-1-12-1200-1-1-1-11-2-21111-2-21111-22-202-2-2-2-2-1-1-1-10000222111111-1-100200-1-1000000-2-1-10000000100
χ2522222-1222-12-122-12-12-12-12-1-12-1-12-122-1-1-1-12-1222-1-1-1-1-1-1-1-12202000-1-12200-1-12200-12000-1-1-1-1-120-1-100-1-12200000-1-10000-1000
χ2622222-1222-12-122-12-12-12-12-1-12-1-12-122-1-1-1-12-1222-1-1-1-1-1-1-1-1-2-20200011-2-200-1-122001-20001111-120-1-100-1-1-2-2000001100001000
χ2722222-1222-12-122-12-12-12-12-1-12-1-12-1-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-1220-2000-1-1220011-2-200-12000-1-1-1-11-20110011-2-2000001100001000
χ2822222-1222-12-122-12-12-12-12-1-12-1-12-1-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-1-2-20-200011-2-20011-2-2001-200011111-201100112200000-1-10000-1000
χ2922222-1222-12-122-12-12-1-2-12-1-12-1-12-122-1-1-1-1-21-2-2-2111111112-20-2000-1-1-2-200-1-1220012000-1-1111-201100-1-1-2200000-1-100001000
χ3022222-1222-12-122-12-12-1-2-12-1-12-1-12-122-1-1-1-1-21-2-2-211111111-220-2000112200-1-12200-1-200011-1-11-201100-1-12-200000110000-1000
χ3122222-1222-12-122-12-12-1-2-12-1-12-1-12-1-2-2-1-1-1-1-21-2-2-2111111112-202000-1-1-2-20011-2-20012000-1-111-120-1-100112-200000110000-1000
χ3222222-1222-12-122-12-12-1-2-12-1-12-1-12-1-2-2-1-1-1-1-21-2-2-211111111-220200011220011-2-200-1-200011-1-1-120-1-10011-2200000-1-100001000
χ332222-122-122-12222-1-1-122-1-122-12-1-1-122-1-1-1-122-1-1-122-1-1-1-1-1-100222-1-100002222-1-100002-1-100002-1-1-1-1-1-1-1-1002200000-1-10000-10
χ342222-122-122-12222-1-1-122-1-122-12-1-1-122-1-1-1-122-1-1-122-1-1-1-1-1-100-22-2110000-2-222-1-10000-21100002-11-1-111-1-100-2-20000011000010
χ352222-122-122-12222-1-1-122-1-122-12-1-1-1-2-2-1-1-1-122-1-1-122-1-1-1-1-1-1002-22-1-1000022-2-21100002-1-10000-21-111-1-11100-2-20000011000010
χ362222-122-122-12222-1-1-122-1-122-12-1-1-1-2-2-1-1-1-122-1-1-122-1-1-1-1-1-100-2-2-2110000-2-2-2-2110000-2110000-211111111002200000-1-10000-10
χ372222-122-122-12222-1-1-12-2-1-122-12-1-1-122-1-1-1-1-2-2111-2-2111111002-2-2-1-10000-2-222-1-100002-1-10000-2111111-1-1002-200000-1-1000010
χ382222-122-122-12222-1-1-12-2-1-122-12-1-1-122-1-1-1-1-2-2111-2-211111100-2-221100002222-1-10000-2110000-21-111-1-1-1-100-2200000110000-10
χ392222-122-122-12222-1-1-12-2-1-122-12-1-1-1-2-2-1-1-1-1-2-2111-2-21111110022-2-1-10000-2-2-2-21100002-1-100002-11-1-1111100-2200000110000-10
χ402222-122-122-12222-1-1-12-2-1-122-12-1-1-1-2-2-1-1-1-1-2-2111-2-211111100-22211000022-2-2110000-21100002-1-1-1-1-1-111002-200000-1-1000010
χ412-2-22222-2-222-2-22-2-22220-2-22-2-2-222-22i−2i22-2-2000000000000000000000000002i−2i2i−2i2-200000000000000002i−2i000002-200002i−2i0000
χ422-2-22222-2-222-2-22-2-22220-2-22-2-2-222-22i−2i22-2-2000000000000000000000000002i−2i2i−2i-2200000000000000002i−2i00000-220000−2i2i0000
χ432-2-22222-2-222-2-22-2-22220-2-22-2-2-222-2−2i2i22-2-200000000000000000000000000−2i2i−2i2i2-20000000000000000−2i2i000002-20000−2i2i0000
χ442-2-22222-2-222-2-22-2-22220-2-22-2-2-222-2−2i2i22-2-200000000000000000000000000−2i2i−2i2i-220000000000000000−2i2i00000-2200002i−2i0000
χ4544444-2-24-2-24-2-2-2-24-2-214-2-211-21-2-2-2001111-2-24-2-211-2-211114400000-2-2-2-200000000-2-2000111100000000000000000000000000
χ4644444-2-24-2-24-2-2-2-24-2-214-2-211-21-2-2-2001111-2-24-2-211-2-21111-4-40000022220000000022000-1-1-1-100000000000000000000000000
χ4744444-2-24-2-24-2-2-2-24-2-21-4-2-211-21-2-2-200111122-422-1-122-1-1-1-14-400000-2-222000000002-200011-1-100000000000000000000000000
χ4844444-2-24-2-24-2-2-2-24-2-21-4-2-211-21-2-2-200111122-422-1-122-1-1-1-1-440000022-2-200000000-22000-1-11100000000000000000000000000
χ494444-24-2-2-24-24-2-24-2-21-24-21-2-21-2-21-2001111-24-211-2-2-2-2111100404-2-20000-2-200000000-211000000-200110000000000000000000
χ504444-24-2-2-24-24-2-24-2-21-24-21-2-21-2-21-2001111-24-211-2-2-2-2111100-40-422000022000000002-1-1000000200-1-10000000000000000000
χ514444-24-2-2-24-24-2-24-2-21-2-4-21-2-21-2-21-20011112-42-1-12222-1-1-1-10040-4-2-200002200000000-211000000200-1-10000000000000000000
χ524444-24-2-2-24-24-2-24-2-21-2-4-21-2-21-2-21-20011112-42-1-12222-1-1-1-100-404220000-2-2000000002-1-1000000-200110000000000000000000
χ534444-2-24-24-2-2-244-2-21-2-241-2-2-2-2-21-214411114-2-2-2-2-2-21111110004000000000-2-2-2-200000000000-2-2011001100000000000000000
χ544444-2-24-24-2-2-244-2-21-2-241-2-2-2-2-21-21-4-411114-2-2-2-2-2-2111111000-4000000000222200000000000220-1-100-1-100000000000000000
χ554444-2-24-24-2-2-244-2-21-2-2-41-2-2-2-2-21-21441111-4222222-1-1-1-1-1-1000-4000000000-2-2-2-200000000000220-1-1001100000000000000000
χ564444-2-24-24-2-2-244-2-21-2-2-41-2-2-2-2-21-21-4-41111-4222222-1-1-1-1-1-10004000000000222200000000000-2-201100-1-100000000000000000
χ5744-4-444444-4-44-4-4-4-4444044-44-4-4-4-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-2-4-4422-4-44-2-204-22-222-42-400-22-2200000000000000000000000023−230000000000000000000023−230000000000000000000
χ5944-4-444-24-2-4-4422-4-44-2-204-22-222-42-400-22-22000000000000000000000000−232300000000000000000000−23230000000000000000000
χ6044-4-44-24442-4-2-4-42-4-24-20-242-2-422-4200-22-2200000000000000000000000000000000000000000000000000000000023−2300000000
χ6144-4-44-24442-4-2-4-42-4-24-20-242-2-422-4200-22-22000000000000000000000000000000000000000000000000000000000−232300000000
χ6244-4-4-244-24-424-4-4-42-2-240-2-2-442-422200-22-22000000000000000000−2i32i3000000000000000−2i32i3000000000000000000000000000000
χ6344-4-4-244-24-424-4-4-42-2-240-2-2-442-422200-22-220000000000000000002i3−2i30000000000000002i3−2i3000000000000000000000000000000
χ6444-4-4-24-2-2-2-42422-42-21-20-212-2-122-12001-11-10003i−3i00003i3i−3i−3i00000−2i32i3000023−23000000000i3−i3000000000−330000000000000000000
χ6544-4-4-24-2-2-2-42422-42-21-20-212-2-122-12001-11-10003i−3i00003i3i−3i−3i000002i3−2i30000−2323000000000−i3i30000000003−30000000000000000000
χ6644-4-4-24-2-2-2-42422-42-21-20-212-2-122-12001-11-1000−3i3i0000−3i−3i3i3i00000−2i32i30000−2323000000000i3−i30000000003−30000000000000000000
χ6744-4-4-24-2-2-2-42422-42-21-20-212-2-122-12001-11-1000−3i3i0000−3i−3i3i3i000002i3−2i3000023−23000000000−i3i3000000000−330000000000000000000
χ684-44-4444-4-4-4-4-44-4444440-4-4-4-444-4-44004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ694-44-444-2-42-4-4-4-22444-2-20-4222-2-2-42400-222-20000000000000000000000−2i32i3000000000000000−2i32i300000000000000000000000000
χ704-44-444-2-42-4-4-4-22444-2-20-4222-2-2-42400-222-200000000000000000000002i3−2i30000000000000002i3−2i300000000000000000000000000
χ714-44-44-24-4-42-424-4-24-24-202-4224-22-4-200-222-200000000000000000000−2i32i3000000000000000−2i32i30000000000000000000000000000
χ724-44-44-24-4-42-424-4-24-24-202-4224-22-4-200-222-2000000000000000000002i3−2i30000000000000002i3−2i30000000000000000000000000000
χ734-44-44-2-2-422-42-22-24-2-21022-1-1-2122-2001-1-11000003-3003-33-30000000−2i32i3−2i32i30000000000000i3−i3i3−i300000000000000000000000000
χ744-44-44-2-2-422-42-22-24-2-21022-1-1-2122-2001-1-11000003-3003-33-300000002i3−2i32i3−2i30000000000000−i3i3−i3i300000000000000000000000000
χ754-44-44-2-2-422-42-22-24-2-21022-1-1-2122-2001-1-1100000-3300-33-330000000−2i32i32i3−2i30000000000000i3−i3−i3i300000000000000000000000000
χ764-44-44-2-2-422-42-22-24-2-21022-1-1-2122-2001-1-1100000-3300-33-3300000002i3−2i3−2i32i30000000000000−i3i3i3−i300000000000000000000000000
χ774-44-4-2442-4-42-44-44-2-2-24022-4-4-2422-200-222-200000000000000000000000000000000000000000000000000000000000−2i32i3000000
χ784-44-4-2442-4-42-44-44-2-2-24022-4-4-2422-200-222-2000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ794-4-4444-2-4244-42-2-4-44-2-20-42-22224-2-400-2-2220000000000000000000000000000004-400000000000000000000000-220000000000
χ804-4-4444-2-4244-42-2-4-44-2-20-42-22224-2-400-2-222000000000000000000000000000000-44000000000000000000000002-20000000000
χ814-4-444-24-4-4-242-442-4-24-202-4-22-42-2424i−4i-2-22200000000000000000000000000−2i2i4i−4i000000000000000000−2i2i00000000000000000
χ824-4-444-24-4-4-242-442-4-24-202-4-22-42-242−4i4i-2-222000000000000000000000000002i−2i−4i4i0000000000000000002i−2i00000000000000000
χ834-4-44-2442-44-2-4-44-42-2-240224-42-4-2-224i−4i-2-222000000000000000000000000004i−4i−2i2i000000000000000000−2i2i00000000000000000
χ844-4-44-2442-44-2-4-44-42-2-240224-42-4-2-22−4i4i-2-22200000000000000000000000000−4i4i2i−2i0000000000000000002i−2i00000000000000000
χ854-4-44-2-242-4-2-22-44221-2-20-12-22221-2-14i−4i11-1-100000003i−3i3i−3i−3i3i0000000000000−2i2i−2i2i000000000000003-300i−i00000000000000000
χ864-4-44-2-242-4-2-22-44221-2-20-12-22221-2-14i−4i11-1-10000000−3i3i−3i3i3i−3i0000000000000−2i2i−2i2i00000000000000-3300i−i00000000000000000
χ874-4-44-2-242-4-2-22-44221-2-20-12-22221-2-1−4i4i11-1-100000003i−3i3i−3i−3i3i00000000000002i−2i2i−2i00000000000000-3300−ii00000000000000000
χ884-4-44-2-242-4-2-22-44221-2-20-12-22221-2-1−4i4i11-1-10000000−3i3i−3i3i3i−3i00000000000002i−2i2i−2i000000000000003-300−ii00000000000000000
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
χ9188-8-88-4-48-44-8-4444-8-4-420-4-4-224-2444002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-4844-4-8-8442-4-402-44-444-24-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-4-444-44444222022-22-2-2-2-2-200-11-110006i−6i0000−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-4-444-44444222022-22-2-2-2-2-200-11-11000−6i6i00003i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-8-48-444-84-8-448-4-42-404-2442-44-2-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-484-84448-8-4-42-4-40-2444-4-4-242002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-444444-44-4-42220-2-2-2-222-2-2200-111-1000006-600-33-33000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-444444-44-4-42220-2-2-2-222-2-2200-111-100000-66003-33-3000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-84-4844-44-8-4-420442-24-2-4-440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-4448-4-84-4-84-42-404-2-44-24-4240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-4-444-4442220-2-22-2-2-222-200-1-11100000006i−6i−3i3i3i−3i000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-4-444-4442220-2-22-2-2-222-200-1-1110000000−6i6i3i−3i−3i3i000000000000000000000000000000000000000000000000000000

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