Finite Group Databasebeta

← Group #72277320

Character table — Group #72277320

Order 2400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size112222222221010121212122020242424242424242424242424242424242424303040404040404040404060606060120120120120150150200200
order122551010101010102455101036555510101010101010101010101010104461515303030303030202020201010202024612
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111-1-1111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311-111-1-1-1-1111-11111111111-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-111-1-1-111-1
χ411-111-1-1-1-111-111111111111-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-1-1-1111-1-11
χ5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5200222222−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5200000000
χ6222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5200222222−1−52−1−52−1+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+52222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5200000000
χ722-2−1+52−1−521−521−521+521+52−1+52−1−5200222222−1+52−1+52−1−52−1−52-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+522-2-2−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−521−521+5200000000
χ822-2−1−52−1+521+521+521−521−52−1−52−1+5200222222−1−52−1−52−1+52−1+52-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−522-2-2−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+521+521−5200000000
χ933333333333331−521+521−521+52001−521+521−521+521−521+521−521+521−521+521−521−521+521+521−521−521+521+52-1-1000000000-1-1-1-11−521+521−521+52-1-100
χ1033333333333331+521−521+521−52001+521−521+521−521+521−521+521−521+521−521+521+521−521−521+521+521−521−52-1-1000000000-1-1-1-11+521−521+521−52-1-100
χ1133333333333-3-31−521+521−521+52001−521+521−521+521−521+521−521+521−521+521−521−521+521+521−521−521+521+52-1-1000000000-1-1-1-1−1+52−1−52−1+52−1−521100
χ1233333333333-3-31+521−521+521−52001+521−521+521−521+521−521+521−521+521−521+521+521−521−521+521+521−521−52-1-1000000000-1-1-1-1−1−52−1+52−1−52−1+521100
χ1333-333-3-3-3-3333-31−521+521−521+52001−521+521−521+52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-11000000000-1-1111−521+52−1+52−1−521-100
χ1433-333-3-3-3-3333-31+521−521+521−52001+521−521+521−52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-11000000000-1-1111+521−52−1−52−1+521-100
χ1533-333-3-3-3-333-331−521+521−521+52001−521+521−521+52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-11000000000-1-111−1+52−1−521−521+52-1100
χ1633-333-3-3-3-333-331+521−521+521−52001+521−521+521−52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-11000000000-1-111−1−52−1+521+521−52-1100
χ174444444444444-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1001111111110000-1-1-1-10011
χ1844444444444-4-4-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1001111111110000111100-1-1
χ1944-444-4-4-4-4444-4-1-1-1-111-1-1-1-111-1-1-1-11111111100-11111-1-1-1-10000-1-111001-1
χ2044-444-4-4-4-444-44-1-1-1-111-1-1-1-111-1-1-1-11111111100-11111-1-1-1-1000011-1-100-11
χ214-40440000-4-400−1+5−1−51−51+5-22−1+5−1−5−1+5−1−5001−51+51−51+500000000000-2-2220000000000000000
χ224-40440000-4-400−1−5−1+51+51−5-22−1−5−1+5−1−5−1+5001+51−51+51−500000000000-2-2220000000000000000
χ234-40−1+5−1−52ζ−2ζ4−2ζ+2ζ42ζ2−2ζ3−2ζ2+2ζ31−51+500−1+5−1−51−51+5-223−52-1-13+5200−3+5211−3−52ζ2−ζ3−ζ2+ζ31+2ζ+2ζ2−1−2ζ−2ζ21+2ζ+2ζ3−1−2ζ−2ζ3ζ−ζ4−ζ+ζ40001−521+52−1+52−1−52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3000000000000
χ244-40−1+5−1−52ζ−2ζ4−2ζ+2ζ42ζ2−2ζ3−2ζ2+2ζ31−51+500−1−5−1+51+51−5-22-13−523+52-1001−3+52−3−521−1−2ζ−2ζ21+2ζ+2ζ2−ζ2+ζ3ζ2−ζ3−ζ+ζ4ζ−ζ4−1−2ζ−2ζ31+2ζ+2ζ30001−521+52−1+52−1−52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3000000000000
χ254-40−1+5−1−5−2ζ+2ζ42ζ−2ζ4−2ζ2+2ζ32ζ2−2ζ31−51+500−1+5−1−51−51+5-223−52-1-13+5200−3+5211−3−52−ζ2+ζ3ζ2−ζ3−1−2ζ−2ζ21+2ζ+2ζ2−1−2ζ−2ζ31+2ζ+2ζ3−ζ+ζ4ζ−ζ40001−521+52−1+52−1−52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3000000000000
χ264-40−1+5−1−5−2ζ+2ζ42ζ−2ζ4−2ζ2+2ζ32ζ2−2ζ31−51+500−1−5−1+51+51−5-22-13−523+52-1001−3+52−3−5211+2ζ+2ζ2−1−2ζ−2ζ2ζ2−ζ3−ζ2+ζ3ζ−ζ4−ζ+ζ41+2ζ+2ζ3−1−2ζ−2ζ30001−521+52−1+52−1−52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3000000000000
χ274-40−1−5−1+52ζ2−2ζ3−2ζ2+2ζ3−2ζ+2ζ42ζ−2ζ41+51−500−1+5−1−51−51+5-22-13+523−52-1001−3−52−3+5211+2ζ+2ζ3−1−2ζ−2ζ3ζ−ζ4−ζ+ζ4−ζ2+ζ3ζ2−ζ3−1−2ζ−2ζ21+2ζ+2ζ20001+521−52−1−52−1+52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4000000000000
χ284-40−1−5−1+52ζ2−2ζ3−2ζ2+2ζ3−2ζ+2ζ42ζ−2ζ41+51−500−1−5−1+51+51−5-223+52-1-13−5200−3−5211−3+52−ζ+ζ4ζ−ζ4−1−2ζ−2ζ31+2ζ+2ζ31+2ζ+2ζ2−1−2ζ−2ζ2ζ2−ζ3−ζ2+ζ30001+521−52−1−52−1+52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4000000000000
χ294-40−1−5−1+5−2ζ2+2ζ32ζ2−2ζ32ζ−2ζ4−2ζ+2ζ41+51−500−1+5−1−51−51+5-22-13+523−52-1001−3−52−3+521−1−2ζ−2ζ31+2ζ+2ζ3−ζ+ζ4ζ−ζ4ζ2−ζ3−ζ2+ζ31+2ζ+2ζ2−1−2ζ−2ζ20001+521−52−1−52−1+52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4000000000000
χ304-40−1−5−1+5−2ζ2+2ζ32ζ2−2ζ32ζ−2ζ4−2ζ+2ζ41+51−500−1−5−1+51+51−5-223+52-1-13−5200−3−5211−3+52ζ−ζ4−ζ+ζ41+2ζ+2ζ3−1−2ζ−2ζ3−1−2ζ−2ζ21+2ζ+2ζ2−ζ2+ζ3ζ2−ζ30001+521−52−1−52−1+52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4000000000000
χ3155555555555550000-1-100000000000000000011-1-1-1-1-1-1-1-1-11111000011-1-1
χ3255555555555-5-50000-1-100000000000000000011-1-1-1-1-1-1-1-1-111110000-1-111
χ3355-555-5-5-5-5555-50000-1-10000000000000000001-11-1-1-1-1111111-1-10000-11-11
χ3455-555-5-5-5-555-550000-1-10000000000000000001-11-1-1-1-1111111-1-100001-11-1
χ35666−3+352−3−352−3+352−3+352−3−352−3−352−3+352−3−352001−51+51−51+500−3+5211−3−521−51+5−3+5211−3−52−3+52−3+521111−3−52−3−52-2-20000000001−521+521−521+5200000000
χ36666−3+352−3−352−3+352−3+352−3−352−3−352−3+352−3−352001+51−51+51−5001−3+52−3−5211+51−51−3+52−3−52111−3+52−3+52−3−52−3−5211-2-20000000001−521+521−521+5200000000
χ37666−3−352−3+352−3−352−3−352−3+352−3+352−3−352−3+352001−51+51−51+5001−3−52−3+5211−51+51−3−52−3+52111−3−52−3−52−3+52−3+5211-2-20000000001+521−521+521−5200000000
χ38666−3−352−3+352−3−352−3−352−3+352−3+352−3−352−3+352001+51−51+51−500−3−5211−3+521+51−5−3−5211−3+52−3−52−3−521111−3+52−3+52-2-20000000001+521−521+521−5200000000
χ3966-6−3+352−3−3523−3523−3523+3523+352−3+352−3−352001−51+51−51+500−3+5211−3−52−1+5−1−5−3+5211−3−523−523−52-1-1-1-13+523+52-220000000001−521+52−1+52−1−5200000000
χ4066-6−3+352−3−3523−3523−3523+3523+352−3+352−3−352001+51−51+51−5001−3+52−3−521−1−5−1+51−3+52−3−521-1-13−523−523+523+52-1-1-220000000001−521+52−1+52−1−5200000000
χ4166-6−3−352−3+3523+3523+3523−3523−352−3−352−3+352001−51+51−51+5001−3−52−3+521−1+5−1−51−3−52−3+521-1-13+523+523−523−52-1-1-220000000001+521−52−1−52−1+5200000000
χ4266-6−3−352−3+3523+3523+3523−3523−352−3−352−3+352001+51−51+51−500−3−5211−3+52−1−5−1+5−3−5211−3+523+523+52-1-1-1-13−523−52-220000000001+521−52−1−52−1+5200000000
χ43888−2+25−2−25−2+25−2+25−2−25−2−25−2+25−2−2500-2-2-2-2221−521−521+521+52-2-21−521−521+521+521−521−521−521−521+521+521+521+52002−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52000000000000
χ44888−2−25−2+25−2−25−2−25−2+25−2+25−2−25−2+2500-2-2-2-2221+521+521−521−52-2-21+521+521−521−521+521+521+521+521−521−521−521−52002−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52000000000000
χ4588-8−2+25−2−252−252−252+252+25−2+25−2−2500-2-2-2-2221−521−521+521+52221−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2−1+52−1−52−1+52−1−521−521−521+521+52000000000000
χ4688-8−2−25−2+252+252+252−252−25−2−25−2+2500-2-2-2-2221+521+521−521−52221+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2−1−52−1+52−1−52−1+521+521+521−521−52000000000000
χ478-80880000-8-800-2-2222-2-2-2-2-20022220000000000022-2-20000000000000000
χ488-80−2+25−2−254ζ−4ζ4−4ζ+4ζ44ζ2−4ζ3−4ζ2+4ζ32−252+2500-2-2222-21−521−521+521+5200−1+52−1+52−1−52−1−52−ζ+ζ4ζ−ζ4ζ−ζ4−ζ+ζ4−ζ2+ζ3ζ2−ζ3ζ2−ζ3−ζ2+ζ3000−1+52−1−521−521+52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3000000000000
χ498-80−2+25−2−25−4ζ+4ζ44ζ−4ζ4−4ζ2+4ζ34ζ2−4ζ32−252+2500-2-2222-21−521−521+521+5200−1+52−1+52−1−52−1−52ζ−ζ4−ζ+ζ4−ζ+ζ4ζ−ζ4ζ2−ζ3−ζ2+ζ3−ζ2+ζ3ζ2−ζ3000−1+52−1−521−521+52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3000000000000
χ508-80−2−25−2+254ζ2−4ζ3−4ζ2+4ζ3−4ζ+4ζ44ζ−4ζ42+252−2500-2-2222-21+521+521−521−5200−1−52−1−52−1+52−1+52−ζ2+ζ3ζ2−ζ3ζ2−ζ3−ζ2+ζ3ζ−ζ4−ζ+ζ4−ζ+ζ4ζ−ζ4000−1−52−1+521+521−52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4000000000000
χ518-80−2−25−2+25−4ζ2+4ζ34ζ2−4ζ34ζ−4ζ4−4ζ+4ζ42+252−2500-2-2222-21+521+521−521−5200−1−52−1−52−1+52−1+52ζ2−ζ3−ζ2+ζ3−ζ2+ζ3ζ2−ζ3−ζ+ζ4ζ−ζ4ζ−ζ4−ζ+ζ4000−1−52−1+521+521−52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4000000000000
χ52101010−5+552−5−552−5+552−5+552−5−552−5−552−5+552−5−552000000-2-200000000000000000022-21−521+521−521+521−521−521+521+52−1+52−1−52−1+52−1−5200000000
χ53101010−5−552−5+552−5−552−5−552−5+552−5+552−5−552−5+552000000-2-200000000000000000022-21+521−521+521−521+521+521−521−52−1−52−1+52−1−52−1+5200000000
χ541010-10−5+552−5−5525−5525−5525+5525+552−5+552−5−552000000-2-20000000000000000002-221−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+5200000000
χ551010-10−5−552−5+5525+5525+5525−5525−552−5−552−5+552000000-2-20000000000000000002-221+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−5200000000
χ5612-12012120000-12-120022-2-200222200-2-2-2-20000000000000000000000000000000
χ5712-120−3+35−3−356ζ−6ζ4−6ζ+6ζ46ζ2−6ζ3−6ζ2+6ζ33−353+350022-2-200−1+52−1+52−1−52−1−52001−521−521+521+52ζ−ζ4−ζ+ζ4−ζ+ζ4ζ−ζ4ζ2−ζ3−ζ2+ζ3−ζ2+ζ3ζ2−ζ300000000000000000000000
χ5812-120−3+35−3−35−6ζ+6ζ46ζ−6ζ4−6ζ2+6ζ36ζ2−6ζ33−353+350022-2-200−1+52−1+52−1−52−1−52001−521−521+521+52−ζ+ζ4ζ−ζ4ζ−ζ4−ζ+ζ4−ζ2+ζ3ζ2−ζ3ζ2−ζ3−ζ2+ζ300000000000000000000000
χ5912-120−3−35−3+356ζ2−6ζ3−6ζ2+6ζ3−6ζ+6ζ46ζ−6ζ43+353−350022-2-200−1−52−1−52−1+52−1+52001+521+521−521−52ζ2−ζ3−ζ2+ζ3−ζ2+ζ3ζ2−ζ3−ζ+ζ4ζ−ζ4ζ−ζ4−ζ+ζ400000000000000000000000
χ6012-120−3−35−3+35−6ζ2+6ζ36ζ2−6ζ36ζ−6ζ4−6ζ+6ζ43+353−350022-2-200−1−52−1−52−1+52−1+52001+521+521−521−52−ζ2+ζ3ζ2−ζ3ζ2−ζ3−ζ2+ζ3ζ−ζ4−ζ+ζ4−ζ+ζ4ζ−ζ400000000000000000000000

Here ζ is a primitive root of unity of order 5 (ζ5 = 1).