Finite Group Databasebeta

← Group #11756985

Character table — Group #11756985

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222222244444444444444444455888888888888888888101010101010101010101020202020202030303030303030303030303030303030
order122222234466656666101010121215153030303030304410101010202030303030303030306060606022444441212121266121212128888888888888888
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
χ511111-1-11-1-1111111-1-1111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111-1-11-1-1111111-1-1111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111-1-11-1-1111111-1-1111-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii
χ811111-1-11-1-1111111-1-1111-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i
χ9111-1-1111-1-11111-1-111111-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111111-1-1-1-11111-1-111-1-111-1-111-1-1
χ10111-1-1111-1-11111-1-111111-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111111-1-1-1-111-1-111-1-111-1-111-1-111
χ11111-1-1111-1-11111-1-111111-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii
χ12111-1-1111-1-11111-1-111111-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i
χ13111-1-1-1-11111111-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ14111-1-1-1-11111111-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ15111-1-1-1-11111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ16111-1-1-1-11111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ1711-11-11-111-1-1-1111-11-1-1-111-111-1-1-1-111111-11-11-111-1-111-1-111-1-11-1-11-11-111-1-11-11-11-11-11-11-11-11-11-11-11-1
χ1811-11-11-111-1-1-1111-11-1-1-111-111-1-1-1-111111-11-11-111-1-111-1-111-1-11-1-11-11-111-1-11-11-11-1-11-11-11-11-11-11-11-11
χ1911-11-11-111-1-1-1111-11-1-1-111-111-1-1-1-111-1-11-11-11-111-1-111-1-111-1-1-111-11-11-1-111-11-11-11i−ii−ii−ii−i−ii−ii−ii−ii
χ2011-11-11-111-1-1-1111-11-1-1-111-111-1-1-1-111-1-11-11-11-111-1-111-1-111-1-1-111-11-11-1-111-11-11-11−ii−ii−ii−iii−ii−ii−ii−i
χ2111-11-1-111-11-1-1111-1-11-1-11-1111-1-1-1-111111-1-11-1111-1-1-1-111-1-111-11-11-1-1111-1-1-111-1-111-11-1-11-111-11-1-11-11
χ2211-11-1-111-11-1-1111-1-11-1-11-1111-1-1-1-111111-1-11-1111-1-1-1-111-1-111-11-11-1-1111-1-1-111-1-11-11-111-11-1-11-111-11-1
χ2311-11-1-111-11-1-1111-1-11-1-11-1111-1-1-1-111-1-11-1-11-1111-1-1-1-111-1-1111-11-111-1-1-1111-1-111-1i−ii−i−ii−ii−ii−iii−ii−i
χ2411-11-1-111-11-1-1111-1-11-1-11-1111-1-1-1-111-1-11-1-11-1111-1-1-1-111-1-1111-11-111-1-1-1111-1-111-1−ii−iii−ii−ii−ii−i−ii−ii
χ2511-1-111-11-11-1-111-111-1-1-11-1111-1-1-1-11111-111-1-11-1-11111-1-1-1-111-11-1-111-111-1-1-11-111-11-1-111-1-111-1-111-1-11
χ2611-1-111-11-11-1-111-111-1-1-11-1111-1-1-1-11111-111-1-11-1-11111-1-1-1-111-11-1-111-111-1-1-11-111-1-111-1-111-1-111-1-111-1
χ2711-1-111-11-11-1-111-111-1-1-11-1111-1-1-1-111-1-1-111-1-11-1-11111-1-1-1-1111-111-1-11-1-1111-11-1-11i−i−iii−i−ii−iii−i−iii−i
χ2811-1-111-11-11-1-111-111-1-1-11-1111-1-1-1-111-1-1-111-1-11-1-11111-1-1-1-1111-111-1-11-1-1111-11-1-11−iii−i−iii−ii−i−iii−i−ii
χ2911-1-11-1111-1-1-111-11-11-1-111-111-1-1-1-11111-11-111-1-1-111-1-11111-1-11-1-1-11-1111-1-11-1-11-111-1-11-111-11-1-11-111-1
χ3011-1-11-1111-1-1-111-11-11-1-111-111-1-1-1-11111-11-111-1-1-111-1-11111-1-11-1-1-11-1111-1-11-1-11-11-111-11-1-11-111-11-1-11
χ3111-1-11-1111-1-1-111-11-11-1-111-111-1-1-1-111-1-1-11-111-1-1-111-1-11111-1-1-1111-11-1-1-111-111-11-1i−i−ii−iii−i−iii−ii−i−ii
χ3211-1-11-1111-1-1-111-11-11-1-111-111-1-1-1-111-1-1-11-111-1-1-111-1-11111-1-1-1111-11-1-1-111-111-11-1−iii−ii−i−iii−i−ii−iii−i
χ332222222-122-1-1-12-1-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-10000000000000000
χ342222222-122-1-1-12-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-211111111110000000000000000
χ3522222-2-2-1-2-2-1-1-12-1-11122211-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2222-2-2-1-1-1-111-1-1110000000000000000
χ3622222-2-2-1-2-2-1-1-12-1-11122211-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-11111111122-2-2-2221111-1-111-1-10000000000000000
χ37222-2-222-1-2-2-1-1-1211-1-122211-1-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-11111-2-22-2-222-1-1-1-11111-1-10000000000000000
χ38222-2-222-1-2-2-1-1-1211-1-122211-1-1-1-1-1-1-1-1-2-2-2-222-2-21111-1-1-1-1111122-222-2-21111-1-1-1-1110000000000000000
χ39222-2-2-2-2-122-1-1-121111222-1-1-1-1-1-1-1-1-1-122-2-2-2-22211111111-1-1-1-1222-2-2-2-2-1-1-1-1-1-111110000000000000000
χ40222-2-2-2-2-122-1-1-121111222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-22211111111-1-1-1-1-2-2-22222111111-1-1-1-10000000000000000
χ4122-22-22-2-12-211-12-11-11-2-22-11-1-11111-1-1222-22-22-2-1-111-1-111-1-1112-2-22-22-2-1-111-11-11-110000000000000000
χ4222-22-22-2-12-211-12-11-11-2-22-11-1-11111-1-1-2-22-22-22-2-1-111-1-111-1-111-222-22-2211-1-11-11-11-10000000000000000
χ4322-22-2-22-1-2211-12-111-1-2-221-1-1-11111-1-1222-2-22-22-1-11111-1-111-1-1-22-22-2-22-1-1111-1-111-10000000000000000
χ4422-22-2-22-1-2211-12-111-1-2-221-1-1-11111-1-1-2-22-2-22-22-1-11111-1-111-1-12-22-222-211-1-1-111-1-110000000000000000
χ4522-2-222-2-1-2211-121-1-11-2-221-1-1-11111-1-122-222-2-2211-1-1-1-11111-1-1-22-2-222-2-1-1111-11-1-110000000000000000
χ4622-2-222-2-1-2211-121-1-11-2-221-1-1-11111-1-1-2-2-222-2-2211-1-1-1-11111-1-12-222-2-2211-1-1-11-111-10000000000000000
χ4722-2-22-22-12-211-121-11-1-2-22-11-1-11111-1-122-22-222-211-1-111-1-1-1-1112-2-2-22-22-1-111-111-11-10000000000000000
χ4822-2-22-22-12-211-121-11-1-2-22-11-1-11111-1-1-2-2-22-222-211-1-111-1-1-1-111-2222-22-211-1-11-1-11-110000000000000000
χ494444444444444-14444-1-1-144-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000
χ504444444-244-2-2-2-1-2-2-2-2-1-1-1-2-21−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
χ514444444-244-2-2-2-1-2-2-2-2-1-1-1-2-21+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
χ5244444-4-44-4-4444-144-4-4-1-1-1-4-4-1-1-1-1-1-1-1-100-1-11111-1-1-1-111111111000000000000000000000000000000000
χ5344444-4-4-2-4-4-2-2-2-1-2-222-1-1-1221−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
χ5444444-4-4-2-4-4-2-2-2-1-2-222-1-1-1221+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
χ55444-4-4444-4-4444-1-4-444-1-1-1-4-4-1-1-1-1-1-1-1-10011-1-1111111-1-1-1-11111000000000000000000000000000000000
χ56444-4-444-2-4-4-2-2-2-122-2-2-1-1-1221−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
χ57444-4-444-2-4-4-2-2-2-122-2-2-1-1-1221+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
χ58444-4-4-4-4444444-1-4-4-4-4-1-1-144-1-1-1-1-1-1-1-1001111-1-111111111-1-1-1-1000000000000000000000000000000000
χ59444-4-4-4-4-244-2-2-2-12222-1-1-1-2-21−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
χ60444-4-4-4-4-244-2-2-2-12222-1-1-1-2-21+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
χ6144-44-44-444-4-4-44-14-44-411-14-4-1-11111-1-100-11-11-11-1-111-1-111-1-111000000000000000000000000000000000
χ6244-44-44-4-24-422-2-1-22-2211-1-221−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
χ6344-44-44-4-24-422-2-1-22-2211-1-221+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
χ6444-44-4-444-44-4-44-14-4-4411-1-44-1-11111-1-100-111-11-1-1-11111-1-111-1-1000000000000000000000000000000000
χ6544-44-4-44-2-4422-2-1-222-211-12-21−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
χ6644-44-4-44-2-4422-2-1-222-211-12-21+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
χ6744-4-444-44-44-4-44-1-444-411-1-44-1-11111-1-1001-1-111-111-1-1-1-11111-1-1000000000000000000000000000000000
χ6844-4-444-4-2-4422-2-12-2-2211-12-21−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
χ6944-4-444-4-2-4422-2-12-2-2211-12-21+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
χ7044-4-44-4444-4-4-44-1-44-4411-14-4-1-11111-1-1001-11-1-1111-1-111-1-1-1-111000000000000000000000000000000000
χ7144-4-44-44-24-422-2-12-22-211-1-221−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
χ7244-4-44-44-24-422-2-12-22-211-1-221+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
χ734-40000040000-44000000-400440000-4-44i−4i00000000000000000000000004i−4i000000000000000000000000
χ744-40000040000-44000000-400440000-4-4−4i4i0000000000000000000000000−4i4i000000000000000000000000
χ754-400000-200−2i32i324000000-400-2-2−2i32i3−2i32i3224i−4i0000000000000000000000000−2i2i23−230000000000000000000000
χ764-400000-200−2i32i324000000-400-2-2−2i32i3−2i32i322−4i4i00000000000000000000000002i−2i−23230000000000000000000000
χ774-400000-2002i3−2i324000000-400-2-22i3−2i32i3−2i3224i−4i0000000000000000000000000−2i2i−23230000000000000000000000
χ784-400000-2002i3−2i324000000-400-2-22i3−2i32i3−2i322−4i4i00000000000000000000000002i−2i23−230000000000000000000000
χ798-80000080000-8-20000−2525200-2-2−252525−252200000000000000000000000000000000000000000000000000000
χ808-80000080000-8-2000025−25200-2-225−25−25252200000000000000000000000000000000000000000000000000000
χ818-800000-400−4i34i34-20000−25252001+i151−i152ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ58−1−i15−1+i1500000000000000000000000000000000000000000000000000000
χ828-800000-400−4i34i34-2000025−252001−i151+i152ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ582ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ46−1+i15−1−i1500000000000000000000000000000000000000000000000000000
χ838-800000-4004i3−4i34-20000−25252001−i151+i15−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−1+i15−1−i1500000000000000000000000000000000000000000000000000000
χ848-800000-4004i3−4i34-2000025−252001+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.