Finite Group Databasebeta

← Group #13085469

Character table — Group #13085469

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size112222222444444444444444448888888888881010101012121212121212121212121212121220202020202020606060606060606060180180
order122336666356666101010151530303030303015151530303030303030303044121226610101010303030303030303012121212121212266882424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1111111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1i−iii−i−ii−i
χ611111111111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1−ii−i−iii−ii
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111i−iii−i−i−ii
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111−ii−i−iiii−i
χ92222-1-1-12-1-122-1-1-1222-1-1-1-1-1-1-1-12-1-1222-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-1-12-1-100000000
χ102222-1-1-12-1-122-1-1-1222-1-1-1-1-1-1-1-12-1-1222-1-1-1-1-1-12222-211-2-2-2-2111111112-1-1-1-1-1-1-21100000000
χ112222-1-1-12-1-122-1-1-1222-1-1-1-1-1-1-1-12-1-1222-1-1-1-1-1-1-2-2-2-22-1-12222-1-1-1-1-1-1-1-1-2111111-21100000000
χ122222-1-1-12-1-122-1-1-1222-1-1-1-1-1-1-1-12-1-1222-1-1-1-1-1-1-2-2-2-2-211-2-2-2-211111111-21111112-1-100000000
χ13222-1222-12-12-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1000000000000000-122-1-1-1-100022-1-1-1-100
χ14222-1222-12-12-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1000000000000000-122-1-1-1-1000-2-2111100
χ15222-1222-12-12-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2110000000000000001-2-211110002i−2i−i−iii00
χ16222-1222-12-12-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2110000000000000001-2-21111000−2i2iii−i−i00
χ1722-222-2-22222-2-2-222-2-22222-2-2-2-22222-2-222-2-2-2-22-222000000000000000-22-222-2-200000000000
χ1822-222-2-22222-2-2-222-2-22222-2-2-2-22222-2-222-2-2-2-2-22-2-20000000000000002-22-2-22200000000000
χ1922-22-1112-1-12-211-12-2-2-1-1-1-111112-1-12-2-2-1-111112-2220−i3i30000−i3−i3−i3−i3i3i3i3i3-2-11-1-1110−i3i300000000
χ2022-22-1112-1-12-211-12-2-2-1-1-1-111112-1-12-2-2-1-111112-2220i3−i30000i3i3i3i3−i3−i3−i3−i3-2-11-1-1110i3−i300000000
χ2122-22-1112-1-12-211-12-2-2-1-1-1-111112-1-12-2-2-1-11111-22-2-20−i3i30000−i3−i3−i3−i3i3i3i3i321-111-1-10i3−i300000000
χ2222-22-1112-1-12-211-12-2-2-1-1-1-111112-1-12-2-2-1-11111-22-2-20i3−i30000i3i3i3i3−i3−i3−i3−i321-111-1-10−i3i300000000
χ2322-2-12-2-2-12-12111-12-2-22222-2-2-2-2-1-1-1-111-1-111112-2-1-100000000000000012-2-1-11100000−i3i3−i3i300
χ2422-2-12-2-2-12-12111-12-2-22222-2-2-2-2-1-1-1-111-1-111112-2-1-100000000000000012-2-1-11100000i3−i3i3−i300
χ2522-2-12-2-2-12-12111-12-2-22222-2-2-2-2-1-1-1-111-1-11111-2211000000000000000-1-2211-1-1000003−3−3300
χ2622-2-12-2-2-12-12111-12-2-22222-2-2-2-2-1-1-1-111-1-11111-2211000000000000000-1-2211-1-100000−333−300
χ274444444444-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000444-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ284444444444-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4-4-4111111111111000000000000000000
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χ304444-2-2-24-2-2-14-2-2-2-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152-11−i1521+i152-1-1-11−i1521+i1521−i1521−i1521+i1521+i1520000-4221111−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152000000000000000000
χ314444-2-2-24-2-2-14-2-2-2-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-11+i1521−i152-1-1-11+i1521−i1521+i1521+i1521−i1521−i15200004-2-2-1-1-1-11+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i152000000000000000000
χ324444-2-2-24-2-2-14-2-2-2-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-11+i1521−i152-1-1-11+i1521−i1521+i1521+i1521−i1521−i1520000-4221111−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152000000000000000000
χ33444-2-2-2-2-2-214-2111444-2-2-2-2-2-2-2-2-211-2-2-211111144-2-2000000000000000-2-2-2111100000000000
χ34444-2-2-2-2-2-214-2111444-2-2-2-2-2-2-2-2-211-2-2-2111111-4-422000000000000000222-1-1-1-100000000000
χ3544-444-4-4444-1-4-4-44-111-1-1-1-11111-1-1-1-111-1-111110000000−5−555−5−55555−5−5000000000000000000
χ3644-444-4-4444-1-4-4-44-111-1-1-1-11111-1-1-1-111-1-11111000000055−5−555−5−5−5−555000000000000000000
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χ4044-44-2224-2-2-1-422-2-1111+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152-11+i1521−i152-1111+i1521−i152−1−i152−1−i152−1+i152−1+i152000002i3−2i355−5−5−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58000000000000000000
χ4144-4-2-222-2-2142-1-114-4-4-2-2-2-22222-211-22211-1-1-1-14-4-2-20000000000000002-2211-1-100000000000
χ4244-4-2-222-2-2142-1-114-4-4-2-2-2-22222-211-22211-1-1-1-1-4422000000000000000-22-2-1-11100000000000
χ434-404400-4-444000-4-40044-4-40000444-400-4-400000000000000000000000000000000000000000
χ444-404400-4-44-1000-41−55-1-111−55−55-1-1-11−5511−55−550000000ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58000000000000000000
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χ464-404400-4-44-1000-415−5-1-1115−55−5-1-1-115−5115−55−50000000ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58000000000000000000
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χ484-404-2−2i32i3-42-240−2i32i32-400-2-222−2i32i32i3−2i34-2-2-40022−2i32i32i3−2i30000000000000000000000000000000000000
χ494-404-2−2i32i3-42-2-10−2i32i321−551+i1521−i152−1−i152−1+i152ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58-11+i1521−i1521−55−1−i152−1+i152ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ580000000ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ34+ζ38−ζ46ζ2−ζ34−ζ38+ζ46−ζ14−ζ22+ζ26+ζ58ζ14+ζ22−ζ26−ζ58−ζ2−ζ34+ζ38+ζ46ζ2+ζ34−ζ38−ζ46ζ14−ζ22−ζ26+ζ58−ζ14+ζ22+ζ26−ζ58000000000000000000
χ504-404-2−2i32i3-42-2-10−2i32i321−551+i1521−i152−1−i152−1+i152ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58-11+i1521−i1521−55−1−i152−1+i152ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ580000000−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ34−ζ38+ζ46−ζ2+ζ34+ζ38−ζ46ζ14+ζ22−ζ26−ζ58−ζ14−ζ22+ζ26+ζ58ζ2+ζ34−ζ38−ζ46−ζ2−ζ34+ζ38+ζ46−ζ14+ζ22+ζ26−ζ58ζ14−ζ22−ζ26+ζ58000000000000000000
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χ534-404-22i3−2i3-42-2402i3−2i32-400-2-2222i3−2i3−2i32i34-2-2-400222i3−2i3−2i32i30000000000000000000000000000000000000
χ544-404-22i3−2i3-42-2-102i3−2i321−551−i1521+i152−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46-11−i1521+i1521−55−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ460000000ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ14−ζ22−ζ26+ζ58−ζ14+ζ22+ζ26−ζ58−ζ2−ζ34+ζ38+ζ46ζ2+ζ34−ζ38−ζ46−ζ14−ζ22+ζ26+ζ58ζ14+ζ22−ζ26−ζ58−ζ2+ζ34+ζ38−ζ46ζ2−ζ34−ζ38+ζ46000000000000000000
χ554-404-22i3−2i3-42-2-102i3−2i321−551−i1521+i152−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46-11−i1521+i1521−55−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ460000000−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ14+ζ22+ζ26−ζ58ζ14−ζ22−ζ26+ζ58ζ2+ζ34−ζ38−ζ46−ζ2−ζ34+ζ38+ζ46ζ14+ζ22−ζ26−ζ58−ζ14−ζ22+ζ26+ζ58ζ2−ζ34−ζ38+ζ46−ζ2+ζ34+ζ38−ζ46000000000000000000
χ564-404-22i3−2i3-42-2-102i3−2i3215−51+i1521−i152−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58-11+i1521−i15215−5−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ580000000ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ34+ζ38+ζ46ζ2+ζ34−ζ38−ζ46−ζ14+ζ22+ζ26−ζ58ζ14−ζ22−ζ26+ζ58ζ2−ζ34−ζ38+ζ46−ζ2+ζ34+ζ38−ζ46−ζ14−ζ22+ζ26+ζ58ζ14+ζ22−ζ26−ζ58000000000000000000
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χ624-40-2-22i3−2i322140−i3i3-1-400-2-2222i3−2i3−2i32i3-211200-1-1−i3i3i3−i30023−23000000000000000000−33−3i3i00000000000
χ634-40-2-22i3−2i322140−i3i3-1-400-2-2222i3−2i3−2i32i3-211200-1-1−i3i3i3−i300−23230000000000000000003−33i−3i00000000000
χ64888-4888-48-4-2-4-4-4-4-2-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000000000000000
χ65888-4-4-4-4-4-42-2-4222-2-2-21−i151+i151−i151+i151−i151−i151+i151+i151−1+i152−1−i152111−1+i152−1−i152−1+i152−1+i152−1−i152−1−i1520000000000000000000000000000000000000
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χ6788-8-48-8-8-48-4-2444-4-222-2-2-2-222221111-1-111-1-1-1-10000000000000000000000000000000000000
χ6888-8-4-444-4-42-24-2-22-2221−i151+i151−i151+i15−1+i15−1+i15−1−i15−1−i151−1+i152−1−i1521-1-1−1+i152−1−i1521−i1521−i1521+i1521+i1520000000000000000000000000000000000000
χ6988-8-4-444-4-42-24-2-22-2221+i151−i151+i151−i15−1−i15−1−i15−1+i15−1+i151−1−i152−1+i1521-1-1−1−i152−1+i1521+i1521+i1521−i1521−i1520000000000000000000000000000000000000
χ708-80-48004-8-4-200042−2525-2-222−2525−2525111-15−5-1-15−55−50000000000000000000000000000000000000
χ718-80-48004-8-4-20004225−25-2-22225−2525−25111-1−55-1-1−55−550000000000000000000000000000000000000
χ728-80-4-4−4i34i3442-202i3−2i3-22−25251+i151−i15−1−i15−1+i152ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ46−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ581−1−i152−1+i152-15−51+i1521−i152−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ580000000000000000000000000000000000000
χ738-80-4-4−4i34i3442-202i3−2i3-2225−251−i151+i15−1+i15−1−i152ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ461−1+i152−1−i152-1−551−i1521+i152−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ460000000000000000000000000000000000000
χ748-80-4-44i3−4i3442-20−2i32i3-22−25251−i151+i15−1+i15−1−i15−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ582ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ461−1+i152−1−i152-15−51−i1521+i152ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ460000000000000000000000000000000000000
χ758-80-4-44i3−4i3442-20−2i32i3-2225−251+i151−i15−1−i15−1+i15−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ581−1−i152−1+i152-1−551+i1521−i152ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ580000000000000000000000000000000000000

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