Finite Group Databasebeta

← Group #13169407

Character table — Group #13169407

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order1222333666666666333466666666612124436661212121212121212121212124444412121212121212124412121212121212121212121212121212121212122224466666612124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-1111111-1-1-1-11-11-11-11111-1-111-1-111111-1-11-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-111111-1-111-1-1-11-11-1111-1-111-1-1111111-11-1-11-1-111-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-111-1-1-1-1111111111111-1-111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-1-1-1-1-111-1-1-1-11-11-11-1-1-111-1-111-1-1-1-1-1-1-11-1-11-1-111-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-1-1-111-1-1-11-11-11-1-1-1-111-1-111-1-1-1-11-1-11-111-1-1-1-1-1-1111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-1111111-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-111-1-11-1-111-1-1-1-1-11111-1-111-1-1-1111-1-1-11111-1-1-1-11-11
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111111-1-1-1-1-111-1-11-1-111-1-1-1-11111-1-11-11-1111-1-111-1-1-1-1-111
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-11111-1-11111-1-1-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-11111-1-1-11111-1-111-1-1-1-11
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-1-111-1-11-1-111-111-1-11111-1-1-1-1111-11-1111-1-111-1-111-11-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-111-1-111111-1-1-1-111-1-111-1111-1-1-11111-1-1111-1-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-111-1-1111
χ17222222-122-122-1-1222-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-122022000022222222-1-1-1-100-1-1-1-1-1-1-1-10000002000000-1-1-1-100000
χ18222222-122-122-1-1222-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-12-202-2000022-2-2-2-22-2-11-1100-1-111-1-111000000-2000000111100000
χ19222222-122-122-1-1222-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-220-220000-2-222-2-2-221-11-10011-1-111-1-1000000-2000000111100000
χ20222222-122-122-1-1222-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-2-20-2-20000-2-2-2-222-2-2111100111111110000002000000-1-1-1-100000
χ21222222-122-122-1-1222-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-211111111220-2-20000-2-2-2-2222211-1-1001111-1-1-1-1000000-200000011-1-100000
χ22222222-122-122-1-1222-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-2111111112-20-220000-2-222-2-22-21-1-110011-1-1-1-1110000002000000-1-11100000
χ23222222-122-122-1-1222-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-211111111-2202-2000022-2-2-2-2-22-111-100-1-11111-1-10000002000000-1-11100000
χ24222222-122-122-1-1222-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-211111111-2-20220000222222-2-2-1-11100-1-1-1-11111000000-200000011-1-100000
χ2522222-122-122-1222-1-12-12-12-1-12-12-1-12222-1-1-1-12-1-1-122-1-1-1-1-1-10220222-1-100-1-1000-102022-100-1-100-1-1-1-1-1-10200200-1-10000000-10
χ2622222-122-122-1222-1-12-12-12-1-12-12-1-12222-1-1-1-12-1-1-122-1-1-1-1-1-10-220-222-1-1001100010-20-22-100110011-1-1-1-10-200-20011000000010
χ2722222-122-122-1222-1-12-12-12-1-12-12-1-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-102-202-2-21100-1-1000-10202-2100-1-100-1-111110-200-20011000000010
χ2822222-122-122-1222-1-12-12-12-1-12-12-1-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-2-20-2-2-211001100010-20-2-210011001111110200200-1-10000000-10
χ2922222-122-122-1222-1-12-1-2-12-1-12-12-1-1-2-222-1-1-1-1-2111-2-211111102-20-222-1-10011000-10-202-21001100-1-1-1-1110-200200110000000-10
χ3022222-122-122-1222-1-12-1-2-12-1-12-12-1-1-2-222-1-1-1-1-2111-2-21111110-2-20222-1-100-1-10001020-2-2100-1-10011-1-1110200-200-1-1000000010
χ3122222-122-122-1222-1-12-1-2-12-1-12-12-1-1-2-2-2-2-1-1-1-1-2111-2-21111110220-2-2-2110011000-10-2022-1001100-1-111-1-10200-200-1-1000000010
χ3222222-122-122-1222-1-12-1-2-12-1-12-12-1-1-2-2-2-2-1-1-1-1-2111-2-21111110-2202-2-21100-1-10001020-22-100-1-1001111-1-10-200200110000000-10
χ332222-122-122-1222-12-1-122-1-12-1-12-12-12222-1-1-1-1-12-1-1-1-122-1-1-1-120220-1-122-1-10000-102020-12-1-100-1-100-1-1-1-120020-1-100000000-100
χ342222-122-122-1222-12-1-122-1-12-1-12-12-12222-1-1-1-1-12-1-1-1-122-1-1-1-1-202-20-1-12211000010-20-20-1211001100-1-1-1-1-200-201100000000100
χ352222-122-122-1222-12-1-122-1-12-1-12-12-122-2-2-1-1-1-1-12-1-1-1-122-1-1-1-120-22011-2-2-1-10000-1020201-2-1-100-1-1001111-200-201100000000100
χ362222-122-122-1222-12-1-122-1-12-1-12-12-122-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2-2011-2-211000010-20-201-211001100111120020-1-100000000-100
χ372222-122-122-1222-12-1-12-2-1-12-1-12-12-1-2-222-1-1-1-11-21111-2-2111120-2-20-1-122110000-10-20201-21100-1-100-1-111-200201100000000-100
χ382222-122-122-1222-12-1-12-2-1-12-1-12-12-1-2-222-1-1-1-11-21111-2-21111-20-220-1-122-1-100001020-201-2-1-1001100-1-111200-20-1-100000000100
χ392222-122-122-1222-12-1-12-2-1-12-1-12-12-1-2-2-2-2-1-1-1-11-21111-2-21111202-2011-2-2110000-10-2020-121100-1-10011-1-1200-20-1-100000000100
χ402222-122-122-1222-12-1-12-2-1-12-1-12-12-1-2-2-2-2-1-1-1-11-21111-2-21111-2022011-2-2-1-100001020-20-12-1-100110011-1-1-200201100000000-100
χ4122-2-2222-2-2-222-22-2-22220-2-2-22-2-222-2002i−2i2-2-22000000000000000002i−2i2i−2i00002-200000000000000002i−2i00000000000002-22i−2i000
χ4222-2-2222-2-2-222-22-2-22220-2-2-22-2-222-2002i−2i2-2-22000000000000000002i−2i2i−2i0000-2200000000000000002i−2i0000000000000-22−2i2i000
χ4322-2-2222-2-2-222-22-2-22220-2-2-22-2-222-200−2i2i2-2-2200000000000000000−2i2i−2i2i00002-20000000000000000−2i2i00000000000002-2−2i2i000
χ4422-2-2222-2-2-222-22-2-22220-2-2-22-2-222-200−2i2i2-2-2200000000000000000−2i2i−2i2i0000-220000000000000000−2i2i0000000000000-222i−2i000
χ4544444-2-24-2-24-2-2-24-2-2-214-2-21-2-21-21-2-2-20011114-2-2-2-2-211111104004000000-2-2000-20-20-200001100110000000000000000000000
χ4644444-2-24-2-24-2-2-24-2-2-214-2-21-2-21-21-2-2-20011114-2-2-2-2-21111110-400-400000022000202020000-1-100-1-10000000000000000000000
χ4744444-2-24-2-24-2-2-24-2-2-21-4-2-21-2-21-21-222001111-422222-1-1-1-1-1-10400-400000022000-2020-20000-1-100110000000000000000000000
χ4844444-2-24-2-24-2-2-24-2-2-21-4-2-21-2-21-21-222001111-422222-1-1-1-1-1-10-4004000000-2-200020-20200001100-1-10000000000000000000000
χ494444-24-2-24-2-24-2-2-24-21-24-21-2-21-21-2-2-2-2001111-24-2-211-2-21111400400000-2-20000-20-20-2000110011000000000000000000000000
χ504444-24-2-24-2-24-2-2-24-21-24-21-2-21-21-2-2-2-2001111-24-2-211-2-21111-400-40000022000020202000-1-100-1-1000000000000000000000000
χ514444-24-2-24-2-24-2-2-24-21-2-4-21-2-21-21-2-2220011112-422-1-122-1-1-1-1400-400000220000-2020-2000-1-10011000000000000000000000000
χ524444-24-2-24-2-24-2-2-24-21-2-4-21-2-21-21-2-2220011112-422-1-122-1-1-1-1-400400000-2-2000020-2020001100-1-1000000000000000000000000
χ534444-2-24-2-24-2-244-2-21-2-241-2-21-2-2-2-2144441111-2-211-2-2-2-2111100400-2-2-2-2000000000000-2-2000000001111000000000000000000
χ544444-2-24-2-24-2-244-2-21-2-241-2-21-2-2-2-2144-4-41111-2-211-2-2-2-2111100-40022220000000000002200000000-1-1-1-1000000000000000000
χ554444-2-24-2-24-2-244-2-21-2-2-41-2-21-2-2-2-21-4-444111122-1-12222-1-1-1-100-400-2-2-2-2000000000000220000000011-1-1000000000000000000
χ564444-2-24-2-24-2-244-2-21-2-2-41-2-21-2-2-2-21-4-4-4-4111122-1-12222-1-1-1-1004002222000000000000-2-200000000-1-111000000000000000000
χ5744-4-444-2-4-42442-2-4-44-2-20-422422-2-2-40000-222-200000000000000000000000004-40000000000000000000000000000000-2200000
χ5844-4-444-2-4-42442-2-4-44-2-20-422422-2-2-40000-222-20000000000000000000000000-4400000000000000000000000000000002-200000
χ5944-4-44-24-42-44-2-44-42-24-202-42-2-424-22004i−4i-222-2000000000000000004i−4i−2i2i0000000000000000000000−2i2i00000000000000000000
χ6044-4-44-24-42-44-2-44-42-24-202-42-2-424-2200−4i4i-222-200000000000000000−4i4i2i−2i00000000000000000000002i−2i00000000000000000000
χ6144-4-4-2442-4-4-24-442-4-2-24022-4-22-4-242004i−4i-222-200000000000000000−2i2i4i−4i0000000000000000000000−2i2i00000000000000000000
χ6244-4-4-2442-4-4-24-442-4-2-24022-4-22-4-24200−4i4i-222-2000000000000000002i−2i−4i4i00000000000000000000002i−2i00000000000000000000
χ6344-4-4-2-2422-4-2-2-44221-2-20-122122-2-2-1004i−4i1-1-11003-3000033-3-300000−2i2i−2i2i0000000000000000000000i−i3i−3i000000000000000000
χ6444-4-4-2-2422-4-2-2-44221-2-20-122122-2-2-1004i−4i1-1-1100-330000-3-33300000−2i2i−2i2i0000000000000000000000i−i−3i3i000000000000000000
χ6544-4-4-2-2422-4-2-2-44221-2-20-122122-2-2-100−4i4i1-1-11003-3000033-3-3000002i−2i2i−2i0000000000000000000000−ii−3i3i000000000000000000
χ6644-4-4-2-2422-4-2-2-44221-2-20-122122-2-2-100−4i4i1-1-1100-330000-3-333000002i−2i2i−2i0000000000000000000000−ii3i−3i000000000000000000
χ674-44-4444-4-4-4-4-44-4444440-4-4-4-444-4-44000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-4-42-4-4-22444-2-20-422-4-2-222423−2300-2-222000023−2323−2323−2323−2300000000000000000000000000000000000000000000000000000
χ694-44-444-2-4-42-4-4-22444-2-20-422-4-2-2224−232300-2-2220000−2323−2323−2323−232300000000000000000000000000000000000000000000000000000
χ704-44-44-24-42-4-424-44-2-24-202-4224-2-42-20000-2-22200000000000000000000000−2i32i3000000000000−2i32i300000000000000000000000000
χ714-44-44-24-42-4-424-44-2-24-202-4224-2-42-20000-2-222000000000000000000000002i3−2i30000000000002i3−2i300000000000000000000000000
χ724-44-44-2-2-422-42-224-2-2-21022-12-212-1-223−230011-1-1000023−23−33−33−3300000000000−2i32i3000000000000i3−i3003i−3i0000000000000000000000
χ734-44-44-2-2-422-42-224-2-2-21022-12-212-1-223−230011-1-1000023−23−33−33−33000000000002i3−2i3000000000000−i3i300−3i3i0000000000000000000000
χ744-44-44-2-2-422-42-224-2-2-21022-12-212-1-2−23230011-1-10000−23233−33−33−300000000000−2i32i3000000000000i3−i300−3i3i0000000000000000000000
χ754-44-44-2-2-422-42-224-2-2-21022-12-212-1-2−23230011-1-10000−23233−33−33−3000000000002i3−2i3000000000000−i3i3003i−3i0000000000000000000000
χ764-44-4-2442-4-42-44-4-24-2-24022-42-242-4-20000-2-222000000000000000000000−2i32i3000000000000−2i32i30000000000000000000000000000
χ774-44-4-2442-4-42-44-4-24-2-24022-42-242-4-20000-2-2220000000000000000000002i3−2i30000000000002i3−2i30000000000000000000000000000
χ784-44-4-24-22-422-4-22-24-21-202-1221-2-12-223−230011-1-10000−3323−23−33−33000000000−2i32i3000000000000i3−i3003i−3i000000000000000000000000
χ794-44-4-24-22-422-4-22-24-21-202-1221-2-12-223−230011-1-10000−3323−23−33−330000000002i3−2i3000000000000−i3i300−3i3i000000000000000000000000
χ804-44-4-24-22-422-4-22-24-21-202-1221-2-12-2−23230011-1-100003−3−23233−33−3000000000−2i32i3000000000000i3−i300−3i3i000000000000000000000000
χ814-44-4-24-22-422-4-22-24-21-202-1221-2-12-2−23230011-1-100003−3−23233−33−30000000002i3−2i3000000000000−i3i3003i−3i000000000000000000000000
χ824-4-44444444-4-4-4-4-4-44440444-4-4-4-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-244-2-4-422-4-44-2-204-2-2-42222-40000-22-2200000000000000000000000000000000000000000000000000000000−2i32i30000000
χ844-4-4444-244-2-4-422-4-44-2-204-2-2-42222-40000-22-22000000000000000000000000000000000000000000000000000000002i3−2i30000000
χ854-4-444-244-24-42-4-4-42-24-20-24-22-42-4220000-22-22000000000000000000000000000000000000000000000000000000−2i32i3000000000
χ864-4-444-244-24-42-4-4-42-24-20-24-22-42-4220000-22-220000000000000000000000000000000000000000000000000000002i3−2i3000000000
χ874-4-44-244-2442-4-4-42-4-2-240-2-2422-42-420000-22-220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ884-4-44-244-2442-4-4-42-4-2-240-2-2422-42-420000-22-2200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9188-8-88-4-4-8448-44-4-84-4-42044-2-44-2-42400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-44-84-484-44-8-42-404-24-4-242-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4444-4-44-4442220-2-2-22-2-222-20000-111-1006-60000-3-33300000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4444-4-44-4442220-2-2-22-2-222-20000-111-100-66000033-3-300000000000000000000000000000000000000000000000000000
χ958-88-8-4-4844-8448-8-4-42-4-40-244-2-4-4442000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-444444-44-4-42220-2-2-2-222-2-2243−4300-1-1110000−2323−23233−33−300000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-444444-44-4-42220-2-2-2-222-2-22−434300-1-111000023−2323−23−33−3300000000000000000000000000000000000000000000000000000
χ988-8-888-4-48-4-4-8444-84-4-420-4-4244-24-2400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-48-44-8444-8-42-40-42-44-24-24400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-4-4844-8-8442-4-402-4-4-24444-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-4-4-44444442220222-2-2-2-2-2-20000-11-110000000033−33−333300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-4-4-44444442220222-2-2-2-2-2-20000-11-1100000000−333333−3300000000000000000000000000000000000000000000000000000

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