Finite Group Databasebeta

← Group #11752437

Character table — Group #11752437

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222244444444444444444444558888888888888888881010101010101020202020202020206060606060606060
order122344666225666610101012121515303030303030221010101020203030303030303030606060602446666226666121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111-1-11-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11111-1-111-1-1
χ6111111111-1-11-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-111-1-111-1-111
χ7111111111-1-11-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii
χ8111111111-1-11-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−i
χ91111-1-11111-1111-1-1111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111-111-1-1-1-1i−ii−ii−ii−i
χ101111-1-11111-1111-1-1111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111-111-1-1-1-1−ii−ii−ii−ii
χ111111-1-11111-1111-1-1111-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111111-11-1-11-11
χ121111-1-11111-1111-1-1111-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-11111-11-111-11-1
χ131111-1-1111-111-1-111111-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-11111-11-1-111-1-1i−i−iii−i−ii
χ141111-1-1111-111-1-111111-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-11111-11-1-111-1-1−iii−i−iii−i
χ151111-1-1111-111-1-111111-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-11-111-1-1111-1-11-111-1
χ161111-1-1111-111-1-111111-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-11-111-1-111-111-11-1-11
χ17222-122-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-100000000
χ18222-122-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111-2-211111100000000
χ19222-122-1-1-1-2-221111222-1-1-1-1-1-1-1-1-1-122-2-2-2-22211111111-1-1-1-1222-1-1-1-1-2-21111-1-100000000
χ20222-122-1-1-1-2-221111222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-22211111111-1-1-1-1-2-2-2111122-1-1-1-11100000000
χ21222-1-2-2-1-1-12-22-1-11122211-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1111111112-2-2-1-1-1-12-2-1-1111100000000
χ22222-1-2-2-1-1-12-22-1-11122211-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-111111111-2221111-2211-1-1-1-100000000
χ23222-1-2-2-1-1-1-22211-1-122211-1-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-111112-2-2-1-1-1-1-2211-1-11100000000
χ24222-1-2-2-1-1-1-22211-1-122211-1-1-1-1-1-1-1-1-2-2-2-222-2-21111-1-1-1-11111-22211112-2-1-111-1-100000000
χ2522-222-2-2-220020000-2-222-222-2-2-2-2222200002-20000000022-2-2-22-222-2-20000002-200000000
χ2622-222-2-2-220020000-2-222-222-2-2-2-222-2-200002-20000000022-2-22-22-2-222000000-2200000000
χ2722-22-22-2-220020000-2-22-2222-2-2-2-222220000-2200000000-2-222-2-2222-2-2000000-2200000000
χ2822-22-22-2-220020000-2-22-2222-2-2-2-222-2-20000-2200000000-2-22222-2-2-2220000002-200000000
χ2922-2-12-211-1002−i3i3−i3i3-2-22-11-1-11111-1-12200002-2−i3−i3i3i3−i3−i3i3i3-1-111-22-2-1-11100−i3i3−i3i3-1100000000
χ3022-2-12-211-1002−i3i3−i3i3-2-22-11-1-11111-1-1-2-200002-2−i3−i3i3i3−i3−i3i3i3-1-1112-2211-1-100i3−i3i3−i31-100000000
χ3122-2-12-211-1002i3−i3i3−i3-2-22-11-1-11111-1-12200002-2i3i3−i3−i3i3i3−i3−i3-1-111-22-2-1-11100i3−i3i3−i3-1100000000
χ3222-2-12-211-1002i3−i3i3−i3-2-22-11-1-11111-1-1-2-200002-2i3i3−i3−i3i3i3−i3−i3-1-1112-2211-1-100−i3i3−i3i31-100000000
χ3322-2-1-2211-1002−i3i3i3−i3-2-221-1-1-11111-1-1220000-22−i3−i3i3i3i3i3−i3−i311-1-1-2-22-1-11100−i3i3i3−i31-100000000
χ3422-2-1-2211-1002−i3i3i3−i3-2-221-1-1-11111-1-1-2-20000-22−i3−i3i3i3i3i3−i3−i311-1-122-211-1-100i3−i3−i3i3-1100000000
χ3522-2-1-2211-1002i3−i3−i3i3-2-221-1-1-11111-1-1220000-22i3i3−i3−i3−i3−i3i3i311-1-1-2-22-1-11100i3−i3−i3i31-100000000
χ3622-2-1-2211-1002i3−i3−i3i3-2-221-1-1-11111-1-1-2-20000-22i3i3−i3−i3−i3−i3i3i311-1-122-211-1-100−i3i3i3−i3-1100000000
χ3744444444444-14444-1-1-144-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ38444444444-4-4-1-4-4-4-4-1-1-144-1-1-1-1-1-1-1-1001111-1-111111111-1-1-1-100000000000000000000000
χ394444-4-44444-4-144-4-4-1-1-1-4-4-1-1-1-1-1-1-1-100-1-11111-1-1-1-11111111100000000000000000000000
χ404444-4-4444-44-1-4-444-1-1-1-4-4-1-1-1-1-1-1-1-10011-1-1111111-1-1-1-1111100000000000000000000000
χ41444-244-2-2-244-1-2-2-2-2-1-1-1-2-21−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+i15200000000000000000000000
χ42444-244-2-2-244-1-2-2-2-2-1-1-1-2-21+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−i15200000000000000000000000
χ43444-244-2-2-2-4-4-12222-1-1-1-2-21−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+i15200000000000000000000000
χ44444-244-2-2-2-4-4-12222-1-1-1-2-21+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−i15200000000000000000000000
χ45444-2-4-4-2-2-24-4-1-2-222-1-1-1221−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−i15200000000000000000000000
χ46444-2-4-4-2-2-24-4-1-2-222-1-1-1221+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+i15200000000000000000000000
χ47444-2-4-4-2-2-2-44-122-2-2-1-1-1221−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−i15200000000000000000000000
χ48444-2-4-4-2-2-2-44-122-2-2-1-1-1221+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+i15200000000000000000000000
χ4944-444-4-4-4400-1000011-14-4-1-11111-1-100−55−55-11−555−5−555−5-1-11100000000000000000000000
χ5044-444-4-4-4400-1000011-14-4-1-11111-1-1005−55−5-115−5−555−5−55-1-11100000000000000000000000
χ5144-44-44-4-4400-1000011-1-44-1-11111-1-100−555−51-1−555−55−5−5511-1-100000000000000000000000
χ5244-44-44-4-4400-1000011-1-44-1-11111-1-1005−5−551-15−5−55−555−511-1-100000000000000000000000
χ5344-4-24-422-200-1−2i32i3−2i32i311-1-221−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i152005−55−5-11ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ461−i1521+i152−1+i152−1−i15200000000000000000000000
χ5444-4-24-422-200-1−2i32i3−2i32i311-1-221+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i15200−55−55-11ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ581+i1521−i152−1−i152−1+i15200000000000000000000000
χ5544-4-24-422-200-12i3−2i32i3−2i311-1-221−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i15200−55−55-11−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ461−i1521+i152−1+i152−1−i15200000000000000000000000
χ5644-4-24-422-200-12i3−2i32i3−2i311-1-221+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i152005−55−5-11−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ581+i1521−i152−1−i152−1+i15200000000000000000000000
χ5744-4-2-4422-200-1−2i32i32i3−2i311-12-21−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i152005−5−551-1ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−1+i152−1−i1521−i1521+i15200000000000000000000000
χ5844-4-2-4422-200-1−2i32i32i3−2i311-12-21+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i15200−555−51-1ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−1−i152−1+i1521+i1521−i15200000000000000000000000
χ5944-4-2-4422-200-12i3−2i3−2i32i311-12-21−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i15200−555−51-1−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−1+i152−1−i1521−i1521+i15200000000000000000000000
χ6044-4-2-4422-200-12i3−2i3−2i32i311-12-21+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i152005−5−551-1−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−1−i152−1+i1521+i1521−i15200000000000000000000000
χ614-4040000-4004000000-400440000-4-44-40000000000000000000004-4000000000000000000
χ624-4040000-4004000000-400440000-4-4-44000000000000000000000-44000000000000000000
χ634-40-200−2i32i32004000000-400-2-2−2i32i3−2i32i3224-4000000000000000000000-22−2i32i30000000000000000
χ644-40-200−2i32i32004000000-400-2-2−2i32i3−2i32i322-440000000000000000000002-22i3−2i30000000000000000
χ654-40-2002i3−2i32004000000-400-2-22i3−2i32i3−2i3224-4000000000000000000000-222i3−2i30000000000000000
χ664-40-2002i3−2i32004000000-400-2-22i3−2i32i3−2i322-440000000000000000000002-2−2i32i30000000000000000
χ678-8080000-800-20000−2525200-2-2−252525−25220000000000000000000000000000000000000000000
χ688-8080000-800-2000025−25200-2-225−25−2525220000000000000000000000000000000000000000000
χ698-80-400−4i34i3400-20000−25252001+i151−i152ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ58−1−i15−1+i150000000000000000000000000000000000000000000
χ708-80-400−4i34i3400-2000025−252001−i151+i152ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ582ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ46−1+i15−1−i150000000000000000000000000000000000000000000
χ718-80-4004i3−4i3400-20000−25252001−i151+i15−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−1+i15−1−i150000000000000000000000000000000000000000000
χ728-80-4004i3−4i3400-2000025−252001+i151−i15−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−1−i15−1+i150000000000000000000000000000000000000000000

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