Finite Group Databasebeta

← Group #13172254

Character table — Group #13172254

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order1222333666666666233366666666666443666666666666666444441212121212121212441212121212121212121212121212121212121212224446666121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-1111111-1-1-1-1111-11-11-111111111-1-1-1-11-1-11-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-111111-1-111-1-111-11-11-111111-1-1-1-11111-11-1-11-1-111-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-111-1-1-1-1111111-1-1111111-1-1-1-111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-1-1-1-1-111-1-1-1-1-1-11-11-11-1-1-1-1-11111-1-1-1-1-11-1-11-1-111-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-1-1-111-1-1-1-1-11-11-11-1-1-1-1-1-1-1-111111-1-11-111-1-1-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-111-1-1-1-1-111-1-1-1-111-1-11111-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111111-1-111-1-1-1-11-1-111-111-1-111-1-1-1-111-1111-1-1-111-1-111-1-11-11
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1111111-1-1-1-1-1-1-111-1-1111-1-1-1-11111-1-11-11-1111-1-1-1-111-1-1-111
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1111111-1-111-1-1-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-111-1-111-1-1-1111111-1-1-1-1-1-11
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1-1-1-1-1-111-1-1111-1-111-1-1-11111-1-1-1-1111-11-1111-1-1-1-11111-11-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-111-1-1-1-111-111-1-11-1-111-1-11111-1-1-1111-1-1-111-1-111111-1-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-111111111-1-111-1-1-1-111-1-111-1-111-1-1-111-1-1-1-111-1-1-1-1111
χ17222222-1222-1-122-1222-1-1222-1-122-1-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-10220222-1-100-1-1002-10-10202-1-1-1-10000-1-1-1-10200200-1-10000000-10
χ18222222-1222-1-122-1222-1-1222-1-122-1-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-10-220-222-1-10011002-1010-20-2-1-1-1-1000011110-200-20011000000010
χ19222222-1222-1-122-1222-1-1222-1-122-1-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-102-202-2-21100-1-100-210-1020211110000-1-1-1-10-200-20011000000010
χ20222222-1222-1-122-1222-1-1222-1-122-1-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-10-2-20-2-2-211001100-21010-20-21111000011110200200-1-10000000-10
χ21222222-1222-1-122-12-22-1-1-2-22-1-122-1-1-1-122-1-21-2-21111-1-1-1111102-20-222-1-1001100-210-10-202-1-1110000-1-1110-200200110000000-10
χ22222222-1222-1-122-12-22-1-1-2-22-1-122-1-1-1-122-1-21-2-21111-1-1-111110-2-20222-1-100-1-100-2101020-2-1-111000011-1-10200-200-1-1000000010
χ23222222-1222-1-122-12-22-1-1-2-22-1-122-1-1-1-1-2-2-1-21-2-21111-1-1-111110220-2-2-2110011002-10-10-20211-1-10000-1-1110200-200-1-1000000010
χ24222222-1222-1-122-12-22-1-1-2-22-1-122-1-1-1-1-2-2-1-21-2-21111-1-1-111110-2202-2-21100-1-1002-101020-211-1-1000011-1-10-200200110000000-10
χ2522222-122-1-1222-1222-12-122-12-1-1-122-1-122-1-12-1-122-1-1-1-1-1-1-1-1-120220-1-122-1-10000-12-102020-1-1-1-1-1-1-1-1000020020-1-100000000-100
χ2622222-122-1-1222-1222-12-122-12-1-1-122-1-122-1-12-1-122-1-1-1-1-1-1-1-1-1-202-20-1-122110000-1210-20-20-1-1-1-111110000-200-201100000000100
χ2722222-122-1-1222-1222-12-122-12-1-1-122-1-1-2-2-1-12-1-122-1-1-1-1-1-1-1-1-120-22011-2-2-1-100001-2-1020201111-1-1-1-10000-200-201100000000100
χ2822222-122-1-1222-1222-12-122-12-1-1-122-1-1-2-2-1-12-1-122-1-1-1-1-1-1-1-1-1-20-2-2011-2-21100001-210-20-2011111111000020020-1-100000000-100
χ2922222-122-1-1222-122-2-12-1-2-2-12-1-1-122-1-122-11-211-2-211-1-1-1111120-2-20-1-1221100001-2-10-2020-1-111-1-1110000-200201100000000-100
χ3022222-122-1-1222-122-2-12-1-2-2-12-1-1-122-1-122-11-211-2-211-1-1-11111-20-220-1-122-1-100001-21020-20-1-11111-1-10000200-20-1-100000000100
χ3122222-122-1-1222-122-2-12-1-2-2-12-1-1-122-1-1-2-2-11-211-2-211-1-1-11111202-2011-2-2110000-12-10-202011-1-1-1-1110000200-20-1-100000000100
χ3222222-122-1-1222-122-2-12-1-2-2-12-1-1-122-1-1-2-2-11-211-2-211-1-1-11111-2022011-2-2-1-10000-121020-2011-1-111-1-10000-200201100000000-100
χ332222-122-12222-122-12-1-12-1-1-1-12-1-1-1-12200-122-1-1-1-122-1-1-1-1-1-1-12202200002222220022-1-1-1-10000-1-1-1-1-1-1-1-1002000000-1-1-1-100000
χ342222-122-12222-122-12-1-12-1-1-1-12-1-1-1-12200-122-1-1-1-122-1-1-1-1-1-1-12-202-2000022-2-2-2-2002-2-11-110000-1-1-1-1111100-2000000111100000
χ352222-122-12222-122-12-1-12-1-1-1-12-1-1-1-12200-122-1-1-1-122-1-1-1-1-1-1-1-220-220000-2-222-2-200-221-11-100001111-1-1-1-100-2000000111100000
χ362222-122-12222-122-12-1-12-1-1-1-12-1-1-1-12200-122-1-1-1-122-1-1-1-1-1-1-1-2-20-2-20000-2-2-2-22200-2-21111000011111111002000000-1-1-1-100000
χ372222-122-12222-122-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-11111220-2-20000-2-2-2-222002211-1-10000-1-111-1-11100-2000000-1-11100000
χ382222-122-12222-122-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-111112-20-220000-2-222-2-2002-21-1-110000-1-11111-1-100200000011-1-100000
χ392222-122-12222-122-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-11111-2202-2000022-2-2-2-200-22-111-1000011-1-1-1-11100200000011-1-100000
χ402222-122-12222-122-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-11111-2-2022000022222200-2-2-1-111000011-1-111-1-100-2000000-1-11100000
χ4122-2-2222-22-22-2-2-2-22022200-2-222-22-2-2-22i−2i2000000002-2-20000000002i−2i2i−2i00002-2000000002i−2i00000000000000000002-2002i−2i000
χ4222-2-2222-22-22-2-2-2-22022200-2-222-22-2-2-22i−2i2000000002-2-20000000002i−2i2i−2i0000-22000000002i−2i0000000000000000000-2200−2i2i000
χ4322-2-2222-22-22-2-2-2-22022200-2-222-22-2-2-2−2i2i2000000002-2-2000000000−2i2i−2i2i00002-200000000−2i2i00000000000000000002-200−2i2i000
χ4422-2-2222-22-22-2-2-2-22022200-2-222-22-2-2-2−2i2i2000000002-2-2000000000−2i2i−2i2i0000-2200000000−2i2i0000000000000000000-22002i−2i000
χ4544444-2-24-2-2-2-24-2-244-2-2144-2-21-2-2-2-211441-2-2-2-2-2-211111111100400-2-2-2-2000000-2-2000000111100000000000000000000000000
χ4644444-2-24-2-2-2-24-2-244-2-2144-2-21-2-2-2-211-4-41-2-2-2-2-2-211111111100-400222200000022000000-1-1-1-100000000000000000000000000
χ4744444-2-24-2-2-2-24-2-24-4-2-21-4-4-2-21-2-2-2-211441222222-1-1111-1-1-1-100-400-2-2-2-20000002200000011-1-100000000000000000000000000
χ4844444-2-24-2-2-2-24-2-24-4-2-21-4-4-2-21-2-2-2-211-4-41222222-1-1111-1-1-1-1004002222000000-2-2000000-1-11100000000000000000000000000
χ494444-24-2-244-2-2-24-2-24-21-2-2-2-21-2-2-211-2-20014-2-2-211-2-2111111104004000000-2-200000-20-20-2000000001111000000000000000000
χ504444-24-2-244-2-2-24-2-24-21-2-2-2-21-2-2-211-2-20014-2-2-211-2-211111110-400-400000022000002020200000000-1-1-1-1000000000000000000
χ514444-24-2-244-2-2-24-2-2-4-21-222-21-2-2-211-2-2001-4222-1-122111-1-1-1-10400-40000002200000-2020-20000000011-1-1000000000000000000
χ524444-24-2-244-2-2-24-2-2-4-21-222-21-2-2-211-2-2001-4222-1-122111-1-1-1-10-4004000000-2-20000020-20200000000-1-111000000000000000000
χ534444-2-24-2-2-244-2-24-241-2-2-2-21-2-211-2-2-2-2001-2411-2-2-2-21111111400400000-2-2000000-20-20-20000011110000000000000000000000
χ544444-2-24-2-2-244-2-24-241-2-2-2-21-2-211-2-2-2-2001-2411-2-2-2-21111111-400-400000220000002020200000-1-1-1-10000000000000000000000
χ554444-2-24-2-2-244-2-24-2-41-2-2221-2-211-2-2-2-20012-4-1-12222111-1-1-1-1400-40000022000000-2020-20000011-1-10000000000000000000000
χ564444-2-24-2-2-244-2-24-2-41-2-2221-2-211-2-2-2-20012-4-1-12222111-1-1-1-1-400400000-2-200000020-20200000-1-1110000000000000000000000
χ5744-4-444-2-44-4-22-4-42404-2-200-42-24-4-22224i−4i-200000000-2220000000004i−4i−2i2i00000000000000−2i2i0000000000000000000000000000
χ5844-4-444-2-44-4-22-4-42404-2-200-42-24-4-2222−4i4i-200000000-222000000000−4i4i2i−2i000000000000002i−2i0000000000000000000000000000
χ5944-4-44-24-4-224-4-42-440-24-2002-4-2-224-4224i−4i-200000000-222000000000−2i2i4i−4i00000000000000−2i2i0000000000000000000000000000
χ6044-4-44-24-4-224-4-42-440-24-2002-4-2-224-422−4i4i-200000000-2220000000002i−2i−4i4i000000000000002i−2i0000000000000000000000000000
χ6144-4-44-2-2-4-22-22-42240-2-2100221-22-22-1-14i−4i10000003-31-1-133-3-300000−2i2i−2i2i00000000000000i−i3i−3i00000000000000000000000000
χ6244-4-44-2-2-4-22-22-42240-2-2100221-22-22-1-14i−4i1000000-331-1-1-3-33300000−2i2i−2i2i00000000000000i−i−3i3i00000000000000000000000000
χ6344-4-44-2-2-4-22-22-42240-2-2100221-22-22-1-1−4i4i10000003-31-1-133-3-3000002i−2i2i−2i00000000000000−ii−3i3i00000000000000000000000000
χ6444-4-44-2-2-4-22-22-42240-2-2100221-22-22-1-1−4i4i1000000-331-1-1-3-333000002i−2i2i−2i00000000000000−ii3i−3i00000000000000000000000000
χ6544-4-4-24424-44-42-4-4-20-2-2400224-22-22-4-400-200000000-222000000000000000004-400000000000000000000000000000-220000000
χ6644-4-4-24424-44-42-4-4-20-2-2400224-22-22-4-400-200000000-22200000000000000000-44000000000000000000000000000002-20000000
χ674-44-44444-44-44-4-4-4-404440044-4-4-4-4-44-400400000000-44-4000000000000000000000000000000000000000000000000000000000
χ684-44-444-24-442-2-4-42-404-2-2004-22-4-422-2200-2000000002-2200000000000000023−230000000000000000000023−23000000000000000000
χ694-44-444-24-442-2-4-42-404-2-2004-22-4-422-2200-2000000002-22000000000000000−232300000000000000000000−2323000000000000000000
χ704-44-44-2442-2-44-42-4-40-24-200-24222-4-4-2200-2000000002-22000000000000023−2300000000000000000023−230000000000000000000000
χ714-44-44-2442-2-44-42-4-40-24-200-24222-4-4-2200-2000000002-220000000000000−2323000000000000000000−23230000000000000000000000
χ724-44-4-244-2-44-442-4-420-2-24−2i32i3-2-2-422224-400-200−2i32i3−2i32i3002-22−2i32i3−2i32i300000000000000000000000000000000000000000000000000000
χ734-44-4-244-2-44-442-4-420-2-242i3−2i3-2-2-422224-400-2002i3−2i32i3−2i3002-222i3−2i32i3−2i300000000000000000000000000000000000000000000000000000
χ744-44-4-24-2-2-442-22-4220-21-2−2i32i3-21222-1-1-2200100−2i32i3i3−i300-11-1i3−i3i3−i30000000000023−230000000000000000003i−3i−33000000000000000000
χ754-44-4-24-2-2-442-22-4220-21-2−2i32i3-21222-1-1-2200100−2i32i3i3−i300-11-1i3−i3i3−i300000000000−2323000000000000000000−3i3i3−3000000000000000000
χ764-44-4-24-2-2-442-22-4220-21-22i3−2i3-21222-1-1-22001002i3−2i3−i3i300-11-1−i3i3−i3i30000000000023−23000000000000000000−3i3i−33000000000000000000
χ774-44-4-24-2-2-442-22-4220-21-22i3−2i3-21222-1-1-22001002i3−2i3−i3i300-11-1−i3i3−i3i300000000000−23230000000000000000003i−3i3−3000000000000000000
χ784-44-4-2-24-22-2-4422-4201-2-2−2i32i31-22-1-122-2200100i3−i3−2i32i300-11-1i3−i3i3−i300000000023−2300000000000000003i−3i−330000000000000000000000
χ794-44-4-2-24-22-2-4422-4201-2-2−2i32i31-22-1-122-2200100i3−i3−2i32i300-11-1i3−i3i3−i3000000000−23230000000000000000−3i3i3−30000000000000000000000
χ804-44-4-2-24-22-2-4422-4201-2-22i3−2i31-22-1-122-2200100−i3i32i3−2i300-11-1−i3i3−i3i300000000023−230000000000000000−3i3i−330000000000000000000000
χ814-44-4-2-24-22-2-4422-4201-2-22i3−2i31-22-1-122-2200100−i3i32i3−2i300-11-1−i3i3−i3i3000000000−232300000000000000003i−3i3−30000000000000000000000
χ824-4-44444-4-4-4-4-4444-4044400-4-4-4-44-44-4400400000000-4-44000000000000000000000000000000000000000000000000000000000
χ834-4-4444-2-4-4-42244-2-404-2-200-422-442-22-200-20000000022-20000000000000000000000000000000000000000000000−2i32i3000000000
χ844-4-4444-2-4-4-42244-2-404-2-200-422-442-22-200-20000000022-200000000000000000000000000000000000000000000002i3−2i3000000000
χ854-4-444-24-422-4-44-24-40-24-2002-422-2-442-200-20000000022-200000000000000000000000000000000000000000000−2i32i300000000000
χ864-4-444-24-422-4-44-24-40-24-2002-422-2-442-200-20000000022-2000000000000000000000000000000000000000000002i3−2i300000000000
χ874-4-44-2442-4-4-4-4-24420-2-240022-42-22-2-4400-20000000022-20000000000000000000000000000000000000000000000000023−2300000
χ884-4-44-2442-4-4-4-4-24420-2-240022-42-22-2-4400-20000000022-200000000000000000000000000000000000000000000000000−232300000
χ898888-4-4-4-4-4-4-4-4-4-4-4-48222-4-422222222200-1-4-4222222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-82224422222222200-144-2-2-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000
χ9188-8-8-48-448-8-444-84-40-42-4004-2-4-442-244002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-484-448-844-8-402-4-400-24-42-2-4444002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-44-44444-4022200-2-222-22-2-2-200-10000006-6-111-3-33300000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-44-44444-4022200-2-222-22-2-2-200-1000000-66-11133-3-300000000000000000000000000000000000000000000000000000
χ958-88-88-4-484-44-4-844-80-4-4200-4-4-244442-200200000000-22-2000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4-44-44-444440222−4i34i322-2-2-2-2-22-200-1002i3−2i32i3−2i3001-11−i3i3−i3i300000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-44-44-4444402224i3−4i322-2-2-2-2-22-200-100−2i32i3−2i32i3001-11i3−i3i3−i300000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-844448-4-4-80-4-420044-24-44-4-2200200000000-2-22000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-44-8-844-48-440-42-4004-244-4-224-400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48444-8-8-4-48402-4-400-244-224-44-400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444444-4-4-44022200-2-2-2-22-22-2200-10000000011-1−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444444-4-4-44022200-2-2-2-22-22-2200-10000000011-13i3−3i3−3i33i300000000000000000000000000000000000000000000000000000

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