Finite Group Databasebeta

← Group #11756989

Character table — Group #11756989

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222222244444444444444444455888888888888888888101010101010101010101020202020202030303030303030303030303030303030
order122344444466651010101212121212121515303030303030442020202020206060606060606060606060602222224121212126666668888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ41111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ5111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111-1-1-1-1111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111-1-1-1-1111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-111-1-11111111-1-111-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111-1-111-1-111-1-111-1-111-1-111-1-1
χ101111-1-111-1-11111111-1-111-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111-1-111-1-1-1-111-1-111-1-111-1-111
χ111111-1-111-1-11111111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-111-1-11111111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-1111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-1111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1711-111-11-11-1-1-111-1-111-11-11-111-1-1-1-111111-11-11-111-1-111-1-111-1-11-11-11-1-111-1-11-11-11-11-11-11-11-11-11-11-11-1
χ1811-111-11-11-1-1-111-1-111-11-11-111-1-1-1-111111-11-11-111-1-111-1-111-1-11-11-11-1-111-1-11-11-11-1-11-11-11-11-11-11-11-11
χ1911-111-11-11-1-1-111-1-111-11-11-111-1-1-1-111-1-11-11-11-111-1-111-1-111-1-1-11-11-111-1-111-11-11-11i−ii−ii−ii−i−ii−ii−ii−ii
χ2011-111-11-11-1-1-111-1-111-11-11-111-1-1-1-111-1-11-11-11-111-1-111-1-111-1-1-11-11-111-1-111-11-11-11−ii−ii−ii−iii−ii−ii−ii−i
χ2111-111-1-11-11-1-111-1-111-1-11-1111-1-1-1-111111-1-11-1111-1-1-1-111-1-1111-1-11-11-111-1-11-1-11-111-11-1-11-111-11-1-11-11
χ2211-111-1-11-11-1-111-1-111-1-11-1111-1-1-1-111111-1-11-1111-1-1-1-111-1-1111-1-11-11-111-1-11-1-11-11-11-111-11-1-11-111-11-1
χ2311-111-1-11-11-1-111-1-111-1-11-1111-1-1-1-111-1-11-1-11-1111-1-1-1-111-1-111-111-11-11-1-111-111-11-1i−ii−i−ii−ii−ii−iii−ii−i
χ2411-111-1-11-11-1-111-1-111-1-11-1111-1-1-1-111-1-11-1-11-1111-1-1-1-111-1-111-111-11-11-1-111-111-11-1−ii−iii−ii−ii−ii−i−ii−ii
χ2511-11-111-1-11-1-111-1-11-111-1-1111-1-1-1-11111-111-1-11-1-11111-1-1-1-111-111-1-11-111-1-1-111-1-111-1-111-1-111-1-111-1-11
χ2611-11-111-1-11-1-111-1-11-111-1-1111-1-1-1-11111-111-1-11-1-11111-1-1-1-111-111-1-11-111-1-1-111-1-11-111-1-111-1-111-1-111-1
χ2711-11-111-1-11-1-111-1-11-111-1-1111-1-1-1-111-1-1-111-1-11-1-11111-1-1-1-1111-1-111-11-1-1111-1-111-1i−i−iii−i−ii−iii−i−iii−i
χ2811-11-111-1-11-1-111-1-11-111-1-1111-1-1-1-111-1-1-111-1-11-1-11111-1-1-1-1111-1-111-11-1-1111-1-111-1−iii−i−iii−ii−i−iii−i−ii
χ2911-11-11-111-1-1-111-1-11-11-111-111-1-1-1-11111-11-111-1-1-111-1-11111-1-1-11-111-1-111-1-1-11-111-11-1-11-111-11-1-11-111-1
χ3011-11-11-111-1-1-111-1-11-11-111-111-1-1-1-11111-11-111-1-1-111-1-11111-1-1-11-111-1-111-1-1-11-111-1-111-11-1-11-111-11-1-11
χ3111-11-11-111-1-1-111-1-11-11-111-111-1-1-1-111-1-1-11-111-1-1-111-1-11111-1-11-11-1-111-1-1111-11-1-11i−i−ii−iii−i−iii−ii−i−ii
χ3211-11-11-111-1-1-111-1-11-11-111-111-1-1-1-111-1-1-11-111-1-1-111-1-11111-1-11-11-1-111-1-1111-11-1-11−iii−ii−i−iii−i−ii−iii−i
χ33222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-10000000000000000
χ34222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-211111111110000000000000000
χ35222-122-2-2-2-2-1-1-12222-1-11111-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-11111111122-2-2-2-22-1-1-1-1-1-111110000000000000000
χ36222-122-2-2-2-2-1-1-12222-1-11111-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-111111111-2-22222-2111111-1-1-1-10000000000000000
χ37222-1-2-222-2-2-1-1-1222211-1-111-1-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-11111-2-222-2-22-1-1-1-111-1-1110000000000000000
χ38222-1-2-222-2-2-1-1-1222211-1-111-1-1-1-1-1-1-1-1-2-2-2-222-2-21111-1-1-1-1111122-2-222-21111-1-111-1-10000000000000000
χ39222-1-2-2-2-222-1-1-122221111-1-1-1-1-1-1-1-1-1-122-2-2-2-22211111111-1-1-1-1-2-2-2-2222-1-1-1-11111-1-10000000000000000
χ40222-1-2-2-2-222-1-1-122221111-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-22211111111-1-1-1-12222-2-2-21111-1-1-1-1110000000000000000
χ4122-2-12-22-22-211-12-2-22-11-11-11-1-11111-1-1222-22-22-2-1-111-1-111-1-1112-22-22-2-2-1-111-11-11-110000000000000000
χ4222-2-12-22-22-211-12-2-22-11-11-11-1-11111-1-1-2-22-22-22-2-1-111-1-111-1-111-22-22-22211-1-11-11-11-10000000000000000
χ4322-2-12-2-22-2211-12-2-22-111-11-1-1-11111-1-1222-2-22-22-1-11111-1-111-1-12-2-22-22-2-1-111-111-11-10000000000000000
χ4422-2-12-2-22-2211-12-2-22-111-11-1-1-11111-1-1-2-22-2-22-22-1-11111-1-111-1-1-222-22-2211-1-11-1-11-110000000000000000
χ4522-2-1-222-2-2211-12-2-221-1-111-1-1-11111-1-122-222-2-2211-1-1-1-11111-1-1-222-2-22-2-1-1111-1-111-10000000000000000
χ4622-2-1-222-2-2211-12-2-221-1-111-1-1-11111-1-1-2-2-222-2-2211-1-1-1-11111-1-12-2-222-2211-1-1-111-1-110000000000000000
χ4722-2-1-22-222-211-12-2-221-11-1-11-1-11111-1-122-22-222-211-1-111-1-1-1-111-22-222-2-2-1-1111-11-1-110000000000000000
χ4822-2-1-22-222-211-12-2-221-11-1-11-1-11111-1-1-2-2-22-222-211-1-111-1-1-1-1112-22-2-22211-1-1-11-111-10000000000000000
χ494444444444444-1-1-1-1444444-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000
χ50444444-4-4-4-4444-1-1-1-144-4-4-4-4-1-1-1-1-1-1-1-100-1-11111-1-1-1-111111111000000000000000000000000000000000
χ514444-4-444-4-4444-1-1-1-1-4-444-4-4-1-1-1-1-1-1-1-10011-1-1111111-1-1-1-11111000000000000000000000000000000000
χ524444-4-4-4-444444-1-1-1-1-4-4-4-444-1-1-1-1-1-1-1-1001111-1-111111111-1-1-1-1000000000000000000000000000000000
χ53444-2444444-2-2-2-1-1-1-1-2-2-2-2-2-21−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i15200-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152000000000000000000000000000000000
χ54444-2444444-2-2-2-1-1-1-1-2-2-2-2-2-21+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i15200-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152000000000000000000000000000000000
χ55444-244-4-4-4-4-2-2-2-1-1-1-1-2-222221−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i15200-1-111111−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000000000
χ56444-244-4-4-4-4-2-2-2-1-1-1-1-2-222221+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i15200-1-111111+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000000000
χ57444-2-4-444-4-4-2-2-2-1-1-1-122-2-2221−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1520011-1-111−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000000000
χ58444-2-4-444-4-4-2-2-2-1-1-1-122-2-2221+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1520011-1-111−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000000000
χ59444-2-4-4-4-444-2-2-2-1-1-1-12222-2-21−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i152001111-1-1−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152000000000000000000000000000000000
χ60444-2-4-4-4-444-2-2-2-1-1-1-12222-2-21+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i152001111-1-1−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152000000000000000000000000000000000
χ6144-444-44-44-4-4-44-111-14-44-44-4-1-11111-1-100-11-11-11-1-111-1-111-1-111000000000000000000000000000000000
χ6244-444-4-44-44-4-44-111-14-4-44-44-1-11111-1-100-111-11-1-1-11111-1-111-1-1000000000000000000000000000000000
χ6344-44-444-4-44-4-44-111-1-444-4-44-1-11111-1-1001-1-111-111-1-1-1-11111-1-1000000000000000000000000000000000
χ6444-44-44-444-4-4-44-111-1-44-444-4-1-11111-1-1001-11-1-1111-1-111-1-1-1-111000000000000000000000000000000000
χ6544-4-24-44-44-422-2-111-1-22-22-221−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i15200-11-11-111−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i152000000000000000000000000000000000
χ6644-4-24-44-44-422-2-111-1-22-22-221+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i15200-11-11-111+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i152000000000000000000000000000000000
χ6744-4-24-4-44-4422-2-111-1-222-22-21−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i15200-111-11-11−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152000000000000000000000000000000000
χ6844-4-24-4-44-4422-2-111-1-222-22-21+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i15200-111-11-11+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152000000000000000000000000000000000
χ6944-4-2-444-4-4422-2-111-12-2-222-21−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i152001-1-111-1−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152000000000000000000000000000000000
χ7044-4-2-444-4-4422-2-111-12-2-222-21+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i152001-1-111-1−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152000000000000000000000000000000000
χ7144-4-2-44-444-422-2-111-12-22-2-221−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i152001-11-1-11−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152000000000000000000000000000000000
χ7244-4-2-44-444-422-2-111-12-22-2-221+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i152001-11-1-11−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152000000000000000000000000000000000
χ734-40400000000-4400-4000000440000-4-44i−4i00000000000000000000000004i−4i000000000000000000000000
χ744-40400000000-4400-4000000440000-4-4−4i4i0000000000000000000000000−4i4i000000000000000000000000
χ754-40-2000000−2i32i32400-4000000-2-2−2i32i3−2i32i3224i−4i0000000000000000000000000−2i2i23−230000000000000000000000
χ764-40-2000000−2i32i32400-4000000-2-2−2i32i3−2i32i322−4i4i00000000000000000000000002i−2i−23230000000000000000000000
χ774-40-20000002i3−2i32400-4000000-2-22i3−2i32i3−2i3224i−4i0000000000000000000000000−2i2i−23230000000000000000000000
χ784-40-20000002i3−2i32400-4000000-2-22i3−2i32i3−2i322−4i4i00000000000000000000000002i−2i23−230000000000000000000000
χ798-80800000000-8-2−25252000000-2-2−252525−252200000000000000000000000000000000000000000000000000000
χ808-80800000000-8-225−252000000-2-225−25−25252200000000000000000000000000000000000000000000000000000
χ818-80-4000000−4i34i34-2−252520000001+i151−i152ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ58−1−i15−1+i1500000000000000000000000000000000000000000000000000000
χ828-80-4000000−4i34i34-225−2520000001−i151+i152ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ582ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ46−1+i15−1−i1500000000000000000000000000000000000000000000000000000
χ838-80-40000004i3−4i34-2−252520000001−i151+i15−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−1+i15−1−i1500000000000000000000000000000000000000000000000000000
χ848-80-40000004i3−4i34-225−2520000001+i151−i15−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−1−i15−1+i1500000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.