Finite Group Databasebeta

← Group #72277324

Character table — Group #72277324

Order 2400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size112222222221010121212122020242424242424242424242424242424242424303040404040404040404060606060120120120120150150200200
order12455101020202020445510103655551010101020202020202020202020241215153030606060601010202020202020221212
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111-1-1111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311-11111-1-1-1-11-111111111111111-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-11111-1-11-11-1
χ411-11111-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-111-1-111-11-11
χ5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5200222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222−1+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+52−1−52−1−52−1+52−1+5222−1−52−1−52−1−52−1−52−1+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+52−1−52−1+52−1−521−521−521+521+5200222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-21−521−521−521−521+521+521+521+52-22-2−1+52−1−52−1+52−1−521−521−521+521+521−521+52−1+52−1−5200000000
χ822-2−1−52−1+52−1−52−1+521+521+521−521−5200222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-21+521+521+521+521−521−521−521−52-22-2−1−52−1+52−1−52−1+521+521+521−521−521+521−52−1−52−1+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
χ1333-33333-3-3-3-33-31−521+521−521+52001−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521-100000000011-1-11−521+52−1+52−1−52-1100
χ1433-33333-3-3-3-33-31+521−521+521−52001+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521-100000000011-1-11+521−52−1−52−1+52-1100
χ1533-33333-3-3-3-3-331−521+521−521+52001−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521-100000000011-1-1−1+52−1−521−521+521-100
χ1633-33333-3-3-3-3-331+521−521+521−52001+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521-100000000011-1-1−1−52−1+521+521−521-100
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
χ1944-44444-4-4-4-44-4-1-1-1-111-1-1-1-1-1-1-1-1111111111100-11111-1-1-1-10000-1-111001-1
χ2044-44444-4-4-4-4-44-1-1-1-111-1-1-1-1-1-1-1-1111111111100-11111-1-1-1-1000011-1-100-11
χ214-4044-4-4000000−1+5−1−51−51+5-22−1+5−1−5−1+5−1−51−51+51−51+50000000000000-2-2220000000000000000
χ224-4044-4-4000000−1−5−1+51+51−5-22−1−5−1+5−1−5−1+51+51−51+51−50000000000000-2-2220000000000000000
χ234-40−1+5−1−51−51+5−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ700−1+5−1−51−51+5-223−52-1-13+52−3+5211−3−5200ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ11+ζ19ζ11−ζ190001−521+52−1+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000
χ244-40−1+5−1−51−51+5−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ700−1−5−1+51+51−5-22-13−523+52-11−3+52−3−52100−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ190001−521+52−1+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000
χ254-40−1+5−1−51−51+52ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ700−1+5−1−51−51+5-223−52-1-13+52−3+5211−3−5200−ζ3+ζ7ζ3−ζ7−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ190001−521+52−1+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000
χ264-40−1+5−1−51−51+52ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ700−1−5−1+51+51−5-22-13−523+52-11−3+52−3−52100ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ190001−521+52−1+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000
χ274-40−1−5−1+51+51−52ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ1900−1+5−1−51−51+5-22-13+523−52-11−3−52−3+52100−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ190001+521−52−1−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000
χ284-40−1−5−1+51+51−52ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ1900−1−5−1+51+51−5-223+52-1-13−52−3−5211−3+5200ζ11−ζ19−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ3+ζ70001+521−52−1−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000
χ294-40−1−5−1+51+51−5−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ1900−1+5−1−51−51+5-22-13+523−52-11−3−52−3+52100ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ190001+521−52−1−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000
χ304-40−1−5−1+51+51−5−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ1900−1−5−1+51+51−5-223+52-1-13−52−3−5211−3+5200−ζ11+ζ19ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7ζ3−ζ70001+521−52−1−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000
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
χ3355-55555-5-5-5-55-50000-1-1000000000000000000-111-1-1-1-11111-1-11100001-1-11
χ3455-55555-5-5-5-5-550000-1-1000000000000000000-111-1-1-1-11111-1-1110000-111-1
χ35666−3+352−3−352−3+352−3−352−3+352−3+352−3−352−3−352001−51+51−51+500−3+5211−3−52−3+5211−3−521−51+5−3+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+52−3−5211−3+52−3−5211+51−511−3+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+5211−3−52−3+5211−51+511−3−52−3−52−3+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+52−3−5211−3+521+51−5−3−52−3−521111−3+52−3+52-2-20000000001+521−521+521−5200000000
χ3966-6−3+352−3−352−3+352−3−3523−3523−3523+3523+352001−51+51−51+500−3+5211−3−52−3+5211−3−52−1+5−1−53−523−52-1-1-1-13+523+522-2000000000−1+52−1−521−521+5200000000
χ4066-6−3+352−3−352−3+352−3−3523−3523−3523+3523+352001+51−51+51−5001−3+52−3−5211−3+52−3−521−1−5−1+5-1-13−523−523+523+52-1-12-2000000000−1+52−1−521−521+5200000000
χ4166-6−3−352−3+352−3−352−3+3523+3523+3523−3523−352001−51+51−51+5001−3−52−3+5211−3−52−3+521−1+5−1−5-1-13+523+523−523−52-1-12-2000000000−1−52−1+521+521−5200000000
χ4266-6−3−352−3+352−3−352−3+3523+3523+3523−3523−352001+51−51+51−500−3−5211−3+52−3−5211−3+52−1−5−1+53+523+52-1-1-1-13−523−522-2000000000−1−52−1+521+521−5200000000
χ43888−2+25−2−25−2+25−2−25−2+25−2+25−2−25−2−2500-2-2-2-2221−521−521+521+521−521−521+521+52-2-21−521−521−521−521+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+521−521−521+521+521−521−52-2-21+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+25−2−25−2+25−2−252−252−252+252+2500-2-2-2-2221−521−521+521+521−521−521+521+5222−1+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+25−2−25−2+252+252+252−252−2500-2-2-2-2221+521+521−521−521+521+521−521−5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2−1−52−1+52−1−52−1+521+521+521−521−52000000000000
χ478-8088-8-8000000-2-2222-2-2-2-2-22222000000000000022-2-20000000000000000
χ488-80−2+25−2−252−252+25−4ζ11+4ζ194ζ11−4ζ194ζ3−4ζ7−4ζ3+4ζ700-2-2222-21−521−521+521+52−1+52−1+52−1−52−1−5200ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7000−1+52−1−521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000
χ498-80−2+25−2−252−252+254ζ11−4ζ19−4ζ11+4ζ19−4ζ3+4ζ74ζ3−4ζ700-2-2222-21−521−521+521+52−1+52−1+52−1−52−1−5200−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7000−1+52−1−521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000
χ508-80−2−25−2+252+252−254ζ3−4ζ7−4ζ3+4ζ74ζ11−4ζ19−4ζ11+4ζ1900-2-2222-21+521+521−521−52−1−52−1−52−1+52−1+5200−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19000−1−52−1+521+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000
χ518-80−2−25−2+252+252−25−4ζ3+4ζ74ζ3−4ζ7−4ζ11+4ζ194ζ11−4ζ1900-2-2222-21+521+521−521−52−1−52−1−52−1+52−1+5200ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19000−1−52−1+521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000
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+552−5−552−5+552−5−5525−5525−5525+5525+552000000-2-2000000000000000000-2221−521+521−521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−5200000000
χ551010-10−5−552−5+552−5−552−5+5525+5525+5525−5525−552000000-2-2000000000000000000-2221+521−521+521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+5200000000
χ5612-1201212-12-1200000022-2-2002222-2-2-2-2000000000000000000000000000000000
χ5712-120−3+35−3−353−353+35−6ζ11+6ζ196ζ11−6ζ196ζ3−6ζ7−6ζ3+6ζ70022-2-200−1+52−1+52−1−52−1−521−521−521+521+5200−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ700000000000000000000000
χ5812-120−3+35−3−353−353+356ζ11−6ζ19−6ζ11+6ζ19−6ζ3+6ζ76ζ3−6ζ70022-2-200−1+52−1+52−1−52−1−521−521−521+521+5200ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ700000000000000000000000
χ5912-120−3−35−3+353+353−356ζ3−6ζ7−6ζ3+6ζ76ζ11−6ζ19−6ζ11+6ζ190022-2-200−1−52−1−52−1+52−1+521+521+521−521−5200ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ1900000000000000000000000
χ6012-120−3−35−3+353+353−35−6ζ3+6ζ76ζ3−6ζ7−6ζ11+6ζ196ζ11−6ζ190022-2-200−1−52−1−52−1+52−1+521+521+521−521−5200−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ1900000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1).