Finite Group Databasebeta

← Group #90996

Character table — Group #90996

Order 480.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size112222222222222224444444444444444444444121212121212121212122020202020206060
order12222355666101010101010661010101015153030303030303030303030303030241010101020202020441212121244
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ5111-1-11111-1-11111111-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1i−iii−i−ii−i
χ6111-1-11111-1-11111111-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1−ii−i−iii−ii
χ7111-1-11111-1-11111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111i−iii−i−i−ii
χ8111-1-11111-1-11111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111−ii−i−iiii−i
χ9222222−1−52−1+52222−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000
χ10222222−1−52−1+52222−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−521+521+521−521−5200000000
χ11222222−1+52−1−52222−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000
χ12222222−1+52−1−52222−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+5200000000
χ1322222-122-1-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000022-1-1-1-100
χ1422222-122-1-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-2111100
χ15222-2-22−1−52−1+522-2-2−1−52−1−52−1+52−1+52−1−52−1+522-21+521+521−521−52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−522-2−1−52−1−52−1+52−1+521+521+521−521−5200000000
χ16222-2-22−1−52−1+522-2-2−1−52−1−52−1+52−1+52−1−52−1+522-21+521+521−521−52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-221+521+521−521−52−1−52−1−52−1+52−1+5200000000
χ17222-2-22−1+52−1−522-2-2−1+52−1+52−1−52−1−52−1+52−1−522-21−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+522-2−1+52−1+52−1−52−1−521−521−521+521+5200000000
χ18222-2-22−1+52−1−522-2-2−1+52−1+52−1−52−1−52−1+52−1−522-21−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-221−521−521+521+52−1+52−1+52−1−52−1−5200000000
χ19222-2-2-122-111222222-11-2-2-2-2-1-1-1-1-1-1-1-11111111100000000002i−2i−i−iii00
χ20222-2-2-122-111222222-11-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000−2i2iii−i−i00
χ2122-22-2222222-2-2-2-222-2-22-22-2222-2-22-2-222-2-222-2-2000000000000000000
χ2222-22-22−1−52−1+522221+521+521−521−52−1−52−1+52-2-2−1−521+52−1+521−52−1−52−1+52−1−521+521+52−1+521−521−52−1−52−1−521+521+52−1+52−1+521−521−5200−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ5800000000
χ2322-22-22−1−52−1+522221+521+521−521−52−1−52−1+52-2-2−1−521+52−1+521−52−1−52−1+52−1−521+521+52−1+521−521−52−1−52−1−521+521+52−1+52−1+521−521−5200ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ5800000000
χ2422-22-22−1+52−1−522221−521−521+521+52−1+52−1−52-2-2−1+521−52−1−521+52−1+52−1−52−1+521−521−52−1−521+521+52−1+52−1+521−521−52−1−52−1−521+521+5200ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ4600000000
χ2522-22-22−1+52−1−522221−521−521+521+52−1+52−1−52-2-2−1+521−52−1−521+52−1+52−1−52−1+521−521−52−1−521+521+52−1+52−1+521−521−52−1−52−1−521+521+5200−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ4600000000
χ2622-22-2-122-1-1-1-2-2-2-222112-22-2-1-1-111-111-1-111-1-111000000000000−i3i3−i3i300
χ2722-22-2-122-1-1-1-2-2-2-222112-22-2-1-1-111-111-1-111-1-111000000000000i3−i3i3−i300
χ2822-2-222222-2-2-2-2-2-222-22-22-22222-2-22-2-2-2-222-2-222000000000000000000
χ2922-2-222−1−52−1+522-2-21+521+521−521−52−1−52−1+52-221+52−1−521−52−1+52−1−52−1+52−1−521+521+52−1+521−521−521+521+52−1−52−1−521−521−52−1+52−1+5200−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ5800000000
χ3022-2-222−1−52−1+522-2-21+521+521−521−52−1−52−1+52-221+52−1−521−52−1+52−1−52−1+52−1−521+521+52−1+521−521−521+521+52−1−52−1−521−521−52−1+52−1+5200ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ5800000000
χ3122-2-222−1+52−1−522-2-21−521−521+521+52−1+52−1−52-221−52−1+521+52−1−52−1+52−1−52−1+521−521−52−1−521+521+521−521−52−1+52−1+521+521+52−1−52−1−5200ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ4600000000
χ3222-2-222−1+52−1−522-2-21−521−521+521+52−1+52−1−52-221−52−1+521+52−1−52−1+52−1−52−1+521−521−52−1−521+521+521−521−52−1+52−1+521+521+52−1−52−1−5200−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ4600000000
χ3322-2-22-122-111-2-2-2-2221-1-22-22-1-1-111-11111-1-111-1-10000000000003−3−3300
χ3422-2-22-122-111-2-2-2-2221-1-22-22-1-1-111-11111-1-111-1-1000000000000−333−300
χ3544444-2−1−5−1+5-2-2-2−1−5−1−5−1+5−1+5−1−5−1+5-2-2−1−5−1−5−1+5−1+51+521−521+521+521+521−521−521−521+521+521+521+521−521−521−521−52000000000000000000
χ3644444-2−1+5−1−5-2-2-2−1+5−1+5−1−5−1−5−1+5−1−5-2-2−1+5−1+5−1−5−1−51−521+521−521−521−521+521+521+521−521−521−521−521+521+521+521+52000000000000000000
χ37444-4-4-2−1−5−1+5-222−1−5−1−5−1+5−1+5−1−5−1+5-221+51+51−51−51+521−521+521+521+521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000000000000000000
χ38444-4-4-2−1+5−1−5-222−1+5−1+5−1−5−1−5−1+5−1−5-221−51−51+51+51−521+521−521−521−521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000000000000000
χ3944-44-4-2−1−5−1+5-2-2-21+51+51−51−5−1−5−1+522−1−51+5−1+51−51+521−521+52−1−52−1−521−52−1+52−1+521+521+52−1−52−1−521−521−52−1+52−1+52000000000000000000
χ4044-44-4-2−1+5−1−5-2-2-21−51−51+51+5−1+5−1−522−1+51−5−1−51+51−521+521−52−1+52−1+521+52−1−52−1−521−521−52−1+52−1+521+521+52−1−52−1−52000000000000000000
χ4144-4-44-2−1−5−1+5-2221+51+51−51−5−1−5−1+52-21+5−1−51−5−1+51+521−521+52−1−52−1−521−52−1+52−1+52−1−52−1−521+521+52−1+52−1+521−521−52000000000000000000
χ4244-4-44-2−1+5−1−5-2221−51−51+51+5−1+5−1−52-21−5−1+51+5−1−51−521+521−52−1+52−1+521+52−1−52−1−52−1+52−1+521−521−52−1−52−1−521+521+52000000000000000000
χ434-4000444-4000000-4-400000044-400-40000000000000000000000000000
χ444-40004−1−5−1+5-400−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ581+51−5000000−1−5−1+51+5−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ461−52ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ5800000000000000000000000000
χ454-40004−1−5−1+5-4002ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ581+51−5000000−1−5−1+51+52ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ461−5−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ5800000000000000000000000000
χ464-40004−1+5−1−5-4002ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ461−51+5000000−1+5−1−51−52ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ581+52ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ4600000000000000000000000000
χ474-40004−1+5−1−5-400−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ461−51+5000000−1+5−1−51−5−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ581+5−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ4600000000000000000000000000
χ484-4000-2442−2i32i30000-4-4000000-2-2200200−2i32i300−2i32i300000000000000000000
χ494-4000-24422i3−2i30000-4-4000000-2-22002002i3−2i3002i3−2i300000000000000000000
χ504-4000-2−1−5−1+52−2i32i3−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ581+51−50000001+521−52−1−52ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−1+52−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ46ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58000000000000000000
χ514-4000-2−1−5−1+52−2i32i32ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ581+51−50000001+521−52−1−52−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46−1+52ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ46ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58000000000000000000
χ524-4000-2−1−5−1+522i3−2i3−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ581+51−50000001+521−52−1−52ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−1+52−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ46−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58000000000000000000
χ534-4000-2−1−5−1+522i3−2i32ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ581+51−50000001+521−52−1−52−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46−1+52ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ46−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58000000000000000000
χ544-4000-2−1+5−1−52−2i32i32ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ461−51+50000001−521+52−1+52−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−1−52−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ46000000000000000000
χ554-4000-2−1+5−1−52−2i32i3−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ461−51+50000001−521+52−1+52ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58−1−52ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46ζ2−ζ22+ζ38−ζ58−ζ2+ζ22−ζ38+ζ58ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58ζ14+ζ26−ζ34−ζ46−ζ14−ζ26+ζ34+ζ46ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ46000000000000000000
χ564-4000-2−1+5−1−522i3−2i32ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ461−51+50000001−521+52−1+52−ζ2−ζ22+ζ38+ζ58ζ2+ζ22−ζ38−ζ58−1−52−ζ14+ζ26−ζ34+ζ46ζ14−ζ26+ζ34−ζ46−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ46000000000000000000
χ574-4000-2−1+5−1−522i3−2i3−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ461−51+50000001−521+52−1+52ζ2+ζ22−ζ38−ζ58−ζ2−ζ22+ζ38+ζ58−1−52ζ14−ζ26+ζ34−ζ46−ζ14+ζ26−ζ34+ζ46−ζ2+ζ22−ζ38+ζ58ζ2−ζ22+ζ38−ζ58−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58−ζ14−ζ26+ζ34+ζ46ζ14+ζ26−ζ34−ζ46−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ46000000000000000000

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