Finite Group Databasebeta

← Group #13172264

Character table — Group #13172264

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666662333666666666663666666666666666444444121212121212121244444412121212121212121212121212121212121212124441212121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-111-111-1-111-1-1-1-1-1-111111-11-11111111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-111-111111-1-11111-1-1-1-11-1-11111-11111-1-1-1-11111-11-111-1-1-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-111-1-1-1-1-1-1-1-111-1-11-1-1-11-11-11111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111-111-111-1-1111111-1-111-1-1-1111-11-11-1-1-1-1111111111-1-1-1-111-1-1-1-1-11-1-1
χ611111111111111111111111111111111111111111111111-11-1-11-1-1-1-1-111-1-111-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-11-111-1-1-1-1-1-11-111
χ711111111111111111111111111111111111111111111111-1-11-1-11-1-111-1-111-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-11111-1-111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-111-1-111-1-1-1-1-111-1-1111-1
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11-1-11111-1-111111111-111-1-1-111-1-111-1-1-1-111-1-1-1111111-1-1-1-1-11
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1-1-1-1-1-1-111-1-111-1-11-11-111-1111-1-1-1-11111-1-1-111-1-111-1-1111-1-11
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111-1-111-1-1-1-111-1-1-1-11-1111-1-1111-1-1-1-111-1-1111-1111-1-1-1-111-111-1
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1111111-1-1-1-1-11-1-1-111-1-1-11111-1-111-1-11-1111-1-1-1-111-11-11
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-11111111-1-1-1-111-1-1-11-11-1-11-1-1-11111-1-1-1-111-111-1-111-1-1111-11-1
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-111-1-1-1-111111111-1-11-1-1111-1-111-1-11111-1-1-1-1-1111111-1-1-1-11-1
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-111-1-111-11
χ17222222-1222-122-1-1222-1-1222-1-122-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-102202200-1-1-1-12200220002-120-1020000-1-1-1-1-1-1-1-120000-1-100000-100
χ18222222-1222-122-1-1222-1-1222-1-122-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-102-202-20011-1-1-2-200-2-20002-1-201020000-1-1-1-11111-200001100000100
χ19222222-1222-122-1-1222-1-1222-1-122-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-10-220-2200-1-1112200-2-2000-2120-10-200001111-1-1-1-1-200001100000100
χ20222222-1222-122-1-1222-1-1222-1-122-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-10-2-20-2-2001111-2-20022000-21-2010-200001111111120000-1-100000-100
χ21222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-1-1-21-2-21111-1-1-111110220-2-20011-1-12200-2-200021-20-10-20000-1-111-1-111200001100000-100
χ22222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-1-1-21-2-21111-1-1-1111102-20-2200-1-1-1-1-2-20022000212010-20000-1-11111-1-1-20000-1-100000100
χ23222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-1-1-21-2-21111-1-1-111110-2202-2001111220022000-2-1-20-102000011-1-1-1-111-20000-1-100000100
χ24222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-1-1-21-2-21111-1-1-111110-2-202200-1-111-2-200-2-2000-2-120102000011-1-111-1-1200001100000-100
χ2522222-1222-12-1-12222-12-122-12-1-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1-1202202-1-12200-1-1220000200-1-1220-1-1-1-10000-1-1-1-1020-1-1000000-1000
χ2622222-1222-12-1-12222-12-122-12-1-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1-120-220-2-1-1-2-20011-2-200002001-1-220-1-1-1-1000011110-20110000001000
χ2722222-1222-12-1-12222-12-122-12-1-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1-1-202-202112200-1-1-2-20000-200-112-2011110000-1-1-1-10-20110000001000
χ2822222-1222-12-1-12222-12-122-12-1-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1-1-20-2-20-211-2-20011220000-20011-2-20111100001111020-1-1000000-1000
χ2922222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-1-11-211-2-211-1-1-11111202-20-211-2-200-1-1-2-200002001-12-20-1-1110000-1-11102011000000-1000
χ3022222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-1-11-211-2-211-1-1-1111120-2-20211220011220000200-1-1-2-20-1-111000011-1-10-20-1-10000001000
χ3122222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-1-11-211-2-211-1-1-11111-20220-2-1-1-2-200-1-1220000-2001122011-1-10000-1-1110-20-1-10000001000
χ3222222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-1-11-211-2-211-1-1-11111-20-2202-1-1220011-2-20000-200-11-22011-1-1000011-1-102011000000-1000
χ332222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-122-122-1-1-1-122-1-1-1-1-1-1-122022022002200000022-1-12020-1-1-1-1-1-1-1-1-1-100000020000-1-1-1-10000
χ342222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-122-122-1-1-1-122-1-1-1-1-1-1-12-202-202200-2-2000000-2-2-11-2020-11-1-1-1-11111000000-2000011110000
χ352222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-122-122-1-1-1-122-1-1-1-1-1-1-1-220-220-2-20022000000-2-21-120-201-11111-1-1-1-1000000-2000011110000
χ362222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-122-122-1-1-1-122-1-1-1-1-1-1-1-2-20-2-20-2-200-2-20000002211-20-20111111111100000020000-1-1-1-10000
χ372222-122-1-1222222-1-2-1-1211-1-12-1-1-1-122-1-2-21111-2-2-1-1-11111220-2-20-2-2002200000022-1-1-202011-1-111-1-111000000-20000-1-1110000
χ382222-122-1-1222222-1-2-1-1211-1-12-1-1-1-122-1-2-21111-2-2-1-1-111112-20-220-2-200-2-2000000-2-2-1120201-1-1-11111-1-10000002000011-1-10000
χ392222-122-1-1222222-1-2-1-1211-1-12-1-1-1-122-1-2-21111-2-2-1-1-11111-2202-20220022000000-2-21-1-20-20-1111-1-1-1-1110000002000011-1-10000
χ402222-122-1-1222222-1-2-1-1211-1-12-1-1-1-122-1-2-21111-2-2-1-1-11111-2-202202200-2-2000000221120-20-1-111-1-111-1-1000000-20000-1-1110000
χ412-2-22222-2-222-2-2-2-22022200-2-2-22-22-22-22000000002-2-20000000000000000002i−2i2i−2i2-2000000000000000000000002i−2i2i−2i2-2000000
χ422-2-22222-2-222-2-2-2-22022200-2-2-22-22-22-22000000002-2-20000000000000000002i−2i−2i2i-22000000000000000000000002i−2i−2i2i-22000000
χ432-2-22222-2-222-2-2-2-22022200-2-2-22-22-22-22000000002-2-2000000000000000000−2i2i2i−2i-2200000000000000000000000−2i2i2i−2i-22000000
χ442-2-22222-2-222-2-2-2-22022200-2-2-22-22-22-22000000002-2-2000000000000000000−2i2i−2i2i2-200000000000000000000000−2i2i−2i2i2-2000000
χ4544444-2-244-2-2-2-2-2-244-2-2144-2-21-2-2-2-2111-2-2-2-2-2-211111111100400400-2-200-2-2000000000-20-200000000001111000000000000000
χ4644444-2-244-2-2-2-2-2-244-2-2144-2-21-2-2-2-2111-2-2-2-2-2-211111111100-400-4002200220000000002020000000000-1-1-1-1000000000000000
χ4744444-2-244-2-2-2-2-2-24-4-2-21-4-4-2-21-2-2-2-2111222222-1-1111-1-1-1-100400-4002200-2-200000000020-2000000000011-1-1000000000000000
χ4844444-2-244-2-2-2-2-2-24-4-2-21-4-4-2-21-2-2-2-2111222222-1-1111-1-1-1-100-400400-2-20022000000000-2020000000000-1-111000000000000000
χ494444-24-2-2-24-244-2-2-24-21-2-2-2-21-2-2-211-2-214-2-2-211-2-211111110400400000-2-2000000000-2-20000-2000011110000000000000000000
χ504444-24-2-2-24-244-2-2-24-21-2-2-2-21-2-2-211-2-214-2-2-211-2-211111110-400-4000002200000000022000020000-1-1-1-10000000000000000000
χ514444-24-2-2-24-244-2-2-2-4-21-222-21-2-2-211-2-21-4222-1-122111-1-1-1-10400-400000-2-2000000000-2200002000011-1-10000000000000000000
χ524444-24-2-2-24-244-2-2-2-4-21-222-21-2-2-211-2-21-4222-1-122111-1-1-1-10-400400000220000000002-20000-20000-1-1110000000000000000000
χ534444-2-24-2-2-24-2-244-241-2-2-2-21-2-211-2-2-2-21-2411-2-2-2-21111111400400-2-2000000000000-2000-20-20111100000000000000000000000
χ544444-2-24-2-2-24-2-244-241-2-2-2-21-2-211-2-2-2-21-2411-2-2-2-21111111-400-4002200000000000020002020-1-1-1-100000000000000000000000
χ554444-2-24-2-2-24-2-244-2-41-2-2221-2-211-2-2-2-212-4-1-12222111-1-1-1-1400-40022000000000000-2000-202011-1-100000000000000000000000
χ564444-2-24-2-2-24-2-244-2-41-2-2221-2-211-2-2-2-212-4-1-12222111-1-1-1-1-400400-2-2000000000000200020-20-1-11100000000000000000000000
χ5744-4-4444-44-4-44-44-4-4044400-4-44-44-44-4-4400000000-44-400000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-44-424-4-22-404-2-200-42-2-442-222-2000000002-2200000000000023−23000000000000000000000000000023−23000000000000000
χ5944-4-444-2-44-424-4-22-404-2-200-42-2-442-222-2000000002-22000000000000−23230000000000000000000000000000−2323000000000000000
χ6044-4-44-24-442-4-224-4-40-24-2002-4-22-2-4422-2000000002-22000000000000000023−23000000000000000000000023−2300000000000000000
χ6144-4-44-24-442-4-224-4-40-24-2002-4-22-2-4422-2000000002-220000000000000000−23230000000000000000000000−232300000000000000000
χ6244-4-44-2-2-4422-22-22-40-2-21002212-22-2-1-110000003-3-11-133-3-30000000023−230023−230000000000000000000000−33−33000000000000000
χ6344-4-44-2-2-4422-22-22-40-2-21002212-22-2-1-110000003-3-11-133-3-300000000−232300−232300000000000000000000003−33−3000000000000000
χ6444-4-44-2-2-4422-22-22-40-2-21002212-22-2-1-11000000-33-11-1-3-3330000000023−2300−232300000000000000000000003−3−33000000000000000
χ6544-4-44-2-2-4422-22-22-40-2-21002212-22-2-1-11000000-33-11-1-3-33300000000−23230023−230000000000000000000000−333−3000000000000000
χ6644-4-4-2442-2-4-44-44-420-2-24002242-22-2-4-4-2000000002-220000000000000000000000000000000000000000000000000000023−230000
χ6744-4-4-2442-2-4-44-44-420-2-24002242-22-2-4-4-2000000002-2200000000000000000000000000000000000000000000000000000−23230000
χ684-44-44444-4-4-4-44-44-404440044-4-4-4-4-4-44400000000-4-4400000000000000000000000000000000000000000000000000000000000
χ694-44-444-24-4-42-442-2-404-2-2004-22-4-4222-2-20000000022-20000000000000023−230000000000000000000023−23000000000000000000000
χ704-44-444-24-4-42-442-2-404-2-2004-22-4-4222-2-20000000022-200000000000000−232300000000000000000000−2323000000000000000000000
χ714-44-44-244-42-42-2-44-40-24-200-24222-4-42-2-20000000022-2000000000023−23000000000000000000000023−2300000000000000000000000
χ724-44-44-244-42-42-2-44-40-24-200-24222-4-42-2-20000000022-20000000000−23230000000000000000000000−232300000000000000000000000
χ734-44-4-244-22-4-4-44-4420-2-24−2i32i3-2-2-42222-44-200−2i32i3−2i32i30022-2−2i32i3−2i32i30000000000000000000000000000000000000000000000000000000
χ744-44-4-244-22-4-4-44-4420-2-242i3−2i3-2-2-42222-44-2002i3−2i32i3−2i30022-22i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000
χ754-44-4-24-2-22-42-442-220-21-2−2i32i3-21222-1-12-2100−2i32i3i3−i300-1-11i3−i3i3−i3000000000023−2300000000000000000000−333i−3i0000000000000000000
χ764-44-4-24-2-22-42-442-220-21-2−2i32i3-21222-1-12-2100−2i32i3i3−i300-1-11i3−i3i3−i30000000000−2323000000000000000000003−3−3i3i0000000000000000000
χ774-44-4-24-2-22-42-442-220-21-22i3−2i3-21222-1-12-21002i3−2i3−i3i300-1-11−i3i3−i3i3000000000023−2300000000000000000000−33−3i3i0000000000000000000
χ784-44-4-24-2-22-42-442-220-21-22i3−2i3-21222-1-12-21002i3−2i3−i3i300-1-11−i3i3−i3i30000000000−2323000000000000000000003−33i−3i0000000000000000000
χ794-44-4-2-24-222-42-2-44201-2-2−2i32i31-22-1-1222-2100i3−i3−2i32i300-1-11i3−i3i3−i300000023−23000000000000000000003i−3i−3300000000000000000000000
χ804-44-4-2-24-222-42-2-44201-2-2−2i32i31-22-1-1222-2100i3−i3−2i32i300-1-11i3−i3i3−i3000000−232300000000000000000000−3i3i3−300000000000000000000000
χ814-44-4-2-24-222-42-2-44201-2-22i3−2i31-22-1-1222-2100−i3i32i3−2i300-1-11−i3i3−i3i300000023−2300000000000000000000−3i3i−3300000000000000000000000
χ824-44-4-2-24-222-42-2-44201-2-22i3−2i31-22-1-1222-2100−i3i32i3−2i300-1-11−i3i3−i3i3000000−2323000000000000000000003i−3i3−300000000000000000000000
χ834-4-4444-2-4-44-2-4-422404-2-200-4224-4-22-22-200000000-222000000000000000000004i−4i000000000000000000000000000−2i2i00000000
χ844-4-4444-2-4-44-2-4-422404-2-200-4224-4-22-22-200000000-22200000000000000000000−4i4i0000000000000000000000000002i−2i00000000
χ854-4-444-24-4-4-2422-4-440-24-2002-42-224-4-22-200000000-2220000000000000000004i−4i000000000000000000000000000−2i2i0000000000
χ864-4-444-24-4-4-2422-4-440-24-2002-42-224-4-22-200000000-222000000000000000000−4i4i0000000000000000000000000002i−2i0000000000
χ874-4-44-2442244-4-4-4-4-20-2-240022-4-22-224-4-200000000-22200000000000000000000004-4000000000000000000000000000-22000000
χ884-4-44-2442244-4-4-4-4-20-2-240022-4-22-224-4-200000000-2220000000000000000000000-440000000000000000000000000002-2000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000
χ9188-8-8-48-44-4-848-8-4440-42-4004-2-44-4-2244200000000-22-200000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-484-44-8-448-8402-4-400-24-4-224-444200000000-22-200000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-444-44-444022200-2-22-22-22-2-2-10000006-61-11-3-3330000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-444-44-444022200-2-22-22-22-2-2-1000000-661-1133-3-30000000000000000000000000000000000000000000000000000000
χ958-88-88-4-48-8444-44-4-80-4-4200-4-4-24444-22200000000-2-2200000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4-44444-44-440222−4i34i322-2-2-2-2-2-22-1002i3−2i32i3−2i30011-1−i3i3−i3i30000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-44444-44-4402224i3−4i322-2-2-2-2-2-22-100−2i32i3−2i32i30011-1i3−i3i3−i30000000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-8-8-4-4444480-4-420044-2-44-442-22000000002-2-200000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4448-4-8-844-40-42-4004-24-442-2-442000000002-2-200000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-4844-8-8-402-4-400-2442-2-44-442000000002-2-200000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-4-44444-4022200-2-2-22-22-22-2-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-4-44444-4022200-2-2-22-22-22-2-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000

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