Finite Group Databasebeta

← Group #13168572

Character table — Group #13168572

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order12223336666666663334666666666443666121212121212121212121212122444466121212121212121212124466612121212121212121212121212121244444121212121212441212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-111-111-1-1111111-1-1-1-111111-1-1111-1-1-1-111111-1-11-111-1-1-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-111-11-1-11111-1-11111-1-1-1-1-11-1111-1-111111111-11-1-11-1-111-1-1-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-111-1-111-1-1-11-1-1-11-1-1-1-1-1-11111-1-11-1-1-1-1-1-11111-1-111
χ511111111111111111111111111111-1-11111111111111111111-1111111-1-111-1-11111111-1111-1111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11-1
χ611111111111111111111111111111-1-1111111111111111111-1-11-111-1-1-1-111-1-1-1-1-1-1111-11-1-1-111-1-1-1-1-1-1-1-1-11-1-11-1-111-1-111-11-11
χ711111111111111111111111111111-1-111111111111111111-11-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-11111-1-1-1-11-1-11-111-1-1-1-1111-1-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1111111111-1-1-11-1-1-1-1-11111-1-1-1-1-111-1-1-1-1111111-1-1
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-1-111-1-1-1-1111-1-11-1-1-1-111-1-111-1-1-1111-1-1-111-1-1-1-11-111
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111111111-1-1-1-1-1-11-11-111-1-11111-1-11-11-1111-1-1-1-1-1-1-1111
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1-1-111-1-11111-1-111-1-111-1-1-111111111-1-1-1-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111-1-1-1111111-1-1-1-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111111-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1-1-1-1111-11-1111-1-1-1-111-111-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-111-1-1-1-1-111-11111-1-111-1-111-1111-1-1-111-1-1111-11-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-1-1-111-1-1-1111-111111-1-1-1-111-1-1-111-1-1-1-111-1-111-11
χ17222222-1222-1-1-12222-1-122-1-1-1-12-12-122-1-1-1-1-122-1-1-1-122-1-1-1-1202202200-1-1-1-1220000-1-1-1-12002-1-10000-1-1-1-120020-1-1000000-1000
χ18222222-1222-1-1-12222-1-122-1-1-1-12-12-122-1-1-1-1-122-1-1-1-122-1-1-1-1-202-20-2-200-1-111220000111-1-2002110000-1-1-1-1-200-20110000001000
χ19222222-1222-1-1-12222-1-122-1-1-1-12-12-1-2-2-1-1-1-1-122-1-1-1-122-1-1-1-120-220220011-1-1-2-20000-1-1-11200-2-1-100001111-200-20110000001000
χ20222222-1222-1-1-12222-1-122-1-1-1-12-12-1-2-2-1-1-1-1-122-1-1-1-122-1-1-1-1-20-2-20-2-2001111-2-200001111-200-2110000111120020-1-1000000-1000
χ21222222-1222-1-1-12222-1-1-22-1-1-1-12-12-122-1-1-1-11-2-21111-2-2111120-2-202200-1-111220000-1-1-11-200-2110000-1-111-2002011000000-1000
χ22222222-1222-1-1-12222-1-1-22-1-1-1-12-12-122-1-1-1-11-2-21111-2-21111-20-220-2-200-1-1-1-12200001111200-2-1-10000-1-111200-20-1-10000001000
χ23222222-1222-1-1-12222-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-2-21111-2-21111202-2022001111-2-20000-1-1-1-1-200211000011-1-1200-20-1-10000001000
χ24222222-1222-1-1-12222-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-2-21111-2-21111-20220-2-20011-1-1-2-20000111-12002-1-1000011-1-1-2002011000000-1000
χ2522222-12-12-122222-1-12-12-12-12-1-1-1-1200-1-1-1-122-122-1-1-1-1-1-1-1-122022-1-122002200-1-1222-1-10-1-120-1-1-1-1-1-10000002000000-1-10000-10
χ2622222-12-12-122222-1-12-12-12-12-1-1-1-1200-1-1-1-122-122-1-1-1-1-1-1-1-12-202-2-1-1-2-200220011-2-22-1-10-11-20-1-11111000000-200000011000010
χ2722222-12-12-122222-1-12-12-12-12-1-1-1-1200-1-1-1-122-122-1-1-1-1-1-1-1-1-220-22112200-2-200-1-1-2-2-21101-12011-1-1-1-1000000-200000011000010
χ2822222-12-12-122222-1-12-12-12-12-1-1-1-1200-1-1-1-122-122-1-1-1-1-1-1-1-1-2-20-2-211-2-200-2-2001122-211011-201111110000002000000-1-10000-10
χ2922222-12-12-122222-1-12-1-2-12-12-1-1-1-1200-1-1-1-1-2-21-2-211111111220-2-2-1-1-2-200-2-200-1-1222-1-1011201111-1-1000000-2000000-1-1000010
χ3022222-12-12-122222-1-12-1-2-12-12-1-1-1-1200-1-1-1-1-2-21-2-2111111112-20-22-1-12200-2-20011-2-22-1-101-1-2011-1-1110000002000000110000-10
χ3122222-12-12-122222-1-12-1-2-12-12-1-1-1-1200-1-1-1-1-2-21-2-211111111-2202-211-2-2002200-1-1-2-2-2110-1120-1-111-1-10000002000000110000-10
χ3222222-12-12-122222-1-12-1-2-12-12-1-1-1-1200-1-1-1-1-2-21-2-211111111-2-202211220022001122-2110-1-1-20-1-1-1-111000000-2000000-1-1000010
χ332222-1222-12222-1-12-1-122-1-12-12-12-1-122-1-1-1-12-12-1-122-1-1-1-1-1-10220200-1-12200-1-12200000202-1-100-1-1-1-1-1-1-1-10200200-1-100000-100
χ342222-1222-12222-1-12-1-122-1-12-12-12-1-122-1-1-1-12-12-1-122-1-1-1-1-1-10-220-200112200-1-1-2-20000020-21-1001111-1-1-1-10-200-2001100000100
χ352222-1222-12222-1-12-1-122-1-12-12-12-1-1-2-2-1-1-1-12-12-1-122-1-1-1-1-1-102-20200-1-1-2-200112200000-202-1100-1-1-1-111110-200-2001100000100
χ362222-1222-12222-1-12-1-122-1-12-12-12-1-1-2-2-1-1-1-12-12-1-122-1-1-1-1-1-10-2-20-20011-2-20011-2-200000-20-21100111111110200200-1-100000-100
χ372222-1222-12222-1-12-1-12-2-1-12-12-12-1-122-1-1-1-1-21-211-2-211111102-20-200112200-1-12200000-20-2-110011-1-1-1-1110-2002001100000-100
χ382222-1222-12222-1-12-1-12-2-1-12-12-12-1-122-1-1-1-1-21-211-2-21111110-2-20200-1-12200-1-1-2-200000-2021100-1-111-1-1110200-200-1-100000100
χ392222-1222-12222-1-12-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-21-211-2-21111110220-20011-2-20011220000020-2-1-10011-1-111-1-10200-200-1-100000100
χ402222-1222-12222-1-12-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-21-211-2-21111110-220200-1-1-2-20011-2-2000002021-100-1-11111-1-10-2002001100000-100
χ4122-2-2222-2-2-2-22-22-222220-2-2-222-2-22-22i−2i2-2-2200000000000000000000002i−2i002i−2i002-2000000000000002i−2i000000000002-22i−2i0000
χ4222-2-2222-2-2-2-22-22-222220-2-2-222-2-22-22i−2i2-2-2200000000000000000000002i−2i002i−2i00-22000000000000002i−2i00000000000-22−2i2i0000
χ4322-2-2222-2-2-2-22-22-222220-2-2-222-2-22-2−2i2i2-2-220000000000000000000000−2i2i00−2i2i002-200000000000000−2i2i000000000002-2−2i2i0000
χ4422-2-2222-2-2-2-22-22-222220-2-2-222-2-22-2−2i2i2-2-220000000000000000000000−2i2i00−2i2i00-2200000000000000−2i2i00000000000-222i−2i0000
χ4544444-2-2-24-2-2-2-244-2-2-214-2-21-21-21-2-2001111-24-2-2-211-2-2111140040-2-20000-2-2000000-2110-2000110000000000000000000000000
χ4644444-2-2-24-2-2-2-244-2-2-214-2-21-21-21-2-2001111-24-2-2-211-2-21111-400-40220000220000002-1-102000-1-10000000000000000000000000
χ4744444-2-2-24-2-2-2-244-2-2-21-4-2-21-21-21-2-20011112-4222-1-122-1-1-1-1400-40-2-2000022000000-21102000-1-10000000000000000000000000
χ4844444-2-2-24-2-2-2-244-2-2-21-4-2-21-21-21-2-20011112-4222-1-122-1-1-1-1-40040220000-2-20000002-1-10-2000110000000000000000000000000
χ494444-24-24-24-2-2-2-2-24-21-24-21-21-2-2-2-21441111-2-2411-2-2-2-21111004000000-2-200-2-20000000-2000-2000000111100000000000000000
χ504444-24-24-24-2-2-2-2-24-21-24-21-21-2-2-2-21-4-41111-2-2411-2-2-2-2111100-4000000220022000000020002000000-1-1-1-100000000000000000
χ514444-24-24-24-2-2-2-2-24-21-2-4-21-21-2-2-2-2144111122-4-1-12222-1-1-1-100-4000000-2-200-2-200000002000200000011-1-100000000000000000
χ524444-24-24-24-2-2-2-2-24-21-2-4-21-21-2-2-2-21-4-4111122-4-1-12222-1-1-1-10040000002200220000000-2000-2000000-1-11100000000000000000
χ534444-2-24-2-2-2444-2-2-21-2-241-2-2-2-21-21-20011114-2-2-2-2-2-21111110400400-2-2000000-2-20000000-2-20001111000000000000000000000
χ544444-2-24-2-2-2444-2-2-21-2-241-2-2-2-21-21-20011114-2-2-2-2-2-21111110-400-4002200000022000000022000-1-1-1-1000000000000000000000
χ554444-2-24-2-2-2444-2-2-21-2-2-41-2-2-2-21-21-2001111-4222222-1-1-1-1-1-10400-40022000000-2-200000002-2000-1-111000000000000000000000
χ564444-2-24-2-2-2444-2-2-21-2-2-41-2-2-2-21-21-2001111-4222222-1-1-1-1-1-10-400400-2-2000000220000000-2200011-1-1000000000000000000000
χ5744-4-444-2-4-4-42-224-444-2-20-422-2-2-42424i−4i-222-20000000000000000000000−2i2i004i−4i000000000000000000−2i2i0000000000000000000
χ5844-4-444-2-4-4-42-224-444-2-20-422-2-2-4242−4i4i-222-200000000000000000000002i−2i00−4i4i0000000000000000002i−2i0000000000000000000
χ5944-4-44-242-42-44-44-4-2-24-202-424-222-2-400-222-20000000000000000000000000000004-4000000000000000000000000000-22000000
χ6044-4-44-242-42-44-44-4-2-24-202-424-222-2-400-222-2000000000000000000000000000000-440000000000000000000000000002-2000000
χ6144-4-4-244-42-4-44-4-224-2-24022-4-242-4-224i−4i-222-200000000000000000000004i−4i00−2i2i000000000000000000−2i2i0000000000000000000
χ6244-4-4-244-42-4-44-4-224-2-24022-4-242-4-22−4i4i-222-20000000000000000000000−4i4i002i−2i0000000000000000002i−2i0000000000000000000
χ6344-4-4-24-2-42-42-22-224-21-202-121-222-2-14i−4i1-1-110003-3000033-3-3000000000−2i2i00−2i2i000000000000000000i−i3i−3i00000000000000000
χ6444-4-4-24-2-42-42-22-224-21-202-121-222-2-14i−4i1-1-11000-330000-3-333000000000−2i2i00−2i2i000000000000000000i−i−3i3i00000000000000000
χ6544-4-4-24-2-42-42-22-224-21-202-121-222-2-1−4i4i1-1-110003-3000033-3-30000000002i−2i002i−2i000000000000000000−ii−3i3i00000000000000000
χ6644-4-4-24-2-42-42-22-224-21-202-121-222-2-1−4i4i1-1-11000-330000-3-3330000000002i−2i002i−2i000000000000000000−ii3i−3i00000000000000000
χ674-44-44444-4-44-4-4-44-444404-44-4-4-4-4-440044-4-40000000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-24-4-4-222-44-44-2-2042-222-42-4-200-2-22200000000000000000000000023−230000000000000023−230000000000000000000000000
χ694-44-444-24-4-4-222-44-44-2-2042-222-42-4-200-2-222000000000000000000000000−232300000000000000−23230000000000000000000000000
χ704-44-44-24-2-424-4-4-442-24-20-2-4-2-42222400-2-222000000000000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ714-44-44-24-2-424-4-4-442-24-20-2-4-2-42222400-2-2220000000000000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ724-44-44-2-2-2-42-222-442-2-210-2212-12-12-20011-1-1000003i−3i003i−3i3i−3i00000−2i32i3000023−230000000i3−i300000−330000000000000000000000000
χ734-44-44-2-2-2-42-222-442-2-210-2212-12-12-20011-1-1000003i−3i003i−3i3i−3i000002i3−2i30000−23230000000−i3i3000003−30000000000000000000000000
χ744-44-44-2-2-2-42-222-442-2-210-2212-12-12-20011-1-100000−3i3i00−3i3i−3i3i00000−2i32i30000−23230000000i3−i3000003−30000000000000000000000000
χ754-44-44-2-2-2-42-222-442-2-210-2212-12-12-20011-1-100000−3i3i00−3i3i−3i3i000002i3−2i3000023−230000000−i3i300000−330000000000000000000000000
χ764-44-4-24442-44-4-42-2-4-2-240-2242-42-42-200-2-22200000000000000000000000000000000000000000000000000000000023−2300000000
χ774-44-4-24442-44-4-42-2-4-2-240-2242-42-42-200-2-222000000000000000000000000000000000000000000000000000000000−232300000000
χ784-4-44444-444-4-44-4-4-44440-44-4-4-444-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-44422-2-4-4-44-2-20-4-22224-2-4200-22-22000000000000000000000000000000000000000000000000000000023−230000000000
χ804-4-4444-2-44422-2-4-4-44-2-20-4-22224-2-4200-22-220000000000000000000000000000000000000000000000000000000−23230000000000
χ814-4-444-2424-2-4-44-4-42-24-20242-42-2-22-400-22-22000000000000000000000000000023−230000000000000023−23000000000000000000000
χ824-4-444-2424-2-4-44-4-42-24-20242-42-2-22-400-22-220000000000000000000000000000−232300000000000000−2323000000000000000000000
χ834-4-44-244-4-24-4-4422-4-2-2402-2-42-4-242200-22-2200000000000000000000−2i32i300000000000000000000−2i32i300000000000000000000000
χ844-4-44-244-4-24-4-4422-4-2-2402-2-42-4-242200-22-22000000000000000000002i3−2i3000000000000000000002i3−2i300000000000000000000000
χ854-4-44-2-242-2-2-4-442221-2-20-1-22221-2-12001-11-100000003i−3i3i−3i−3i3i0000000−2i32i300000023−23000000000000i3−i3−33000000000000000000000
χ864-4-44-2-242-2-2-4-442221-2-20-1-22221-2-12001-11-100000003i−3i3i−3i−3i3i00000002i3−2i3000000−2323000000000000−i3i33−3000000000000000000000
χ874-4-44-2-242-2-2-4-442221-2-20-1-22221-2-12001-11-10000000−3i3i−3i3i3i−3i0000000−2i32i3000000−2323000000000000i3−i33−3000000000000000000000
χ884-4-44-2-242-2-2-4-442221-2-20-1-22221-2-12001-11-10000000−3i3i−3i3i3i−3i00000002i3−2i300000023−23000000000000−i3i3−33000000000000000000000
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
χ9188-8-88-4-44-844-448-8-4-4-42044-2-424-2-44002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48444-88-8-44-42-4-40-244-4-4-2424002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44444-44-44-42220-2-2-222-2-22-200-111-10006-60000-3-333000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44444-44-44-42220-2-2-222-2-22-200-111-1000-66000033-3-3000000000000000000000000000000000000000000000000000000
χ958-88-8-48-484-8-4444-4-8-42-40-4-2-4-2444420022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-48-4448-8-84-442-4-4024-444-24-2-40022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-444-4444-4422202-22-2-2-2-2-2200-1-111000006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-444-4444-4422202-22-2-2-2-2-2200-1-11100000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-888-4-448-444-4-8-84-4-4204-4-24-2-4244002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-4-8-4844-444-8-42-40424-24-4-44-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-4-444-44442220-22-2-2-222-2-200-11-1100000006i−6i−3i3i3i−3i000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-4-444-44442220-22-2-2-222-2-200-11-110000000−6i6i3i−3i−3i3i000000000000000000000000000000000000000000000000000000

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