Finite Group Databasebeta

← Group #10624045

Character table — Group #10624045

Order 720.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size112222222244444444446666666666888899101212121212121212121218181818202020203030606090
order123355661010361515151530303030241010101020202020151530304426123030303060606060202020206666246124
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-111111111111111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-11111-1-1-1-11111-1-111-11111-1-1-1-1-1-1-1-11111-11-11-1
χ4111111111111111111111-11111-1-1-1-11111-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11
χ511111111111111111111-11-1-1-1-111111111-1-11-11-1-1-1-11111-1-1-1-111111-11-1-1
χ611111111111111111111-11-1-1-1-111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-11-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1
χ92222−1+52−1−5222−1+52−1−5222−1+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+52−1−52−1−52−1+52−1−52−1+52−1−5222022−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000
χ102222−1+52−1−5222−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−52-2-202-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000
χ112222−1+52−1−5222−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-20-221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000
χ122222−1+52−1−5222−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-21−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52220-2-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000
χ132222−1−52−1+5222−1−52−1+5222−1−52−1+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+52−1−52−1+52−1−52−1+5222022−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000
χ142222−1−52−1+5222−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1+52-2-202-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000
χ152222−1−52−1+5222−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-221+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-20-221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000
χ162222−1−52−1+5222−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-21+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52220-2-21+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000
χ17222-122-1222-1-1-1-12222-1-10200002222-1-1-1-10020-10000-1-1-1-100002-1-1-120-100
χ18222-122-1222-1-1-1-12222-1-10200002222-1-1-1-100-20-10000-1-1-1-10000-2111-20100
χ19222-122-1222-1-1-1-12222-1-10-20000-2-2-2-2-1-1-1-1002010000111100002-1-1-1-20100
χ20222-122-1222-1-1-1-12222-1-10-20000-2-2-2-2-1-1-1-100-201000011110000-211120-100
χ2122-12222-122-1-122-1-1-1-1222022220000-1-1-1-1002-10-1-1-1-100000000-12-1-1020-10
χ2222-12222-122-1-122-1-1-1-1222022220000-1-1-1-100-2-10-1-1-1-1000000001-2110-2010
χ2322-12222-122-1-122-1-1-1-122-20-2-2-2-20000-1-1-1-100210111100000000-12-1-10-2010
χ2422-12222-122-1-122-1-1-1-122-20-2-2-2-20000-1-1-1-100-2101111000000001-211020-10
χ252-22222-2-2-2-22-22222-2-2-2-2000000000022-2-22i−2i000000000002i−2i2i−2i000000000
χ262-22222-2-2-2-22-22222-2-2-2-2000000000022-2-2−2i2i00000000000−2i2i−2i2i000000000
χ272-222−1+52−1−52-2-21−521+522-2−1+52−1−52−1+52−1−521−521+521−521+5200ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−1+52−1−521−521+522i−2i000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7000000000
χ282-222−1+52−1−52-2-21−521+522-2−1+52−1−52−1+52−1−521−521+521−521+5200ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−1+52−1−521−521+52−2i2i000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7000000000
χ292-222−1+52−1−52-2-21−521+522-2−1+52−1−52−1+52−1−521−521+521−521+5200−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−1+52−1−521−521+52−2i2i000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7000000000
χ302-222−1+52−1−52-2-21−521+522-2−1+52−1−52−1+52−1−521−521+521−521+5200−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−1+52−1−521−521+522i−2i000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7000000000
χ312-222−1−52−1+52-2-21+521−522-2−1−52−1+52−1−52−1+521+521−521+521−5200−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−1−52−1+521+521−52−2i2i000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19000000000
χ322-222−1−52−1+52-2-21+521−522-2−1−52−1+52−1−52−1+521+521−521+521−5200−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−1−52−1+521+521−522i−2i000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19000000000
χ332-222−1−52−1+52-2-21+521−522-2−1−52−1+52−1−52−1+521+521−521+521−5200ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−1−52−1+521+521−522i−2i000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19000000000
χ342-222−1−52−1+52-2-21+521−522-2−1−52−1+52−1−52−1+521+521−521+521−5200ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−1−52−1+521+521−52−2i2i000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19000000000
χ35444-2−1+5−1−5-24−1+5−1−5-2-21−521+52−1+5−1−5−1+5−1−51−521+52040000−1+5−1+5−1−5−1−51−521+521−521+520000-200001−521−521+521+520000000000000
χ36444-2−1+5−1−5-24−1+5−1−5-2-21−521+52−1+5−1−5−1+5−1−51−521+520-400001−51−51+51+51−521+521−521+52000020000−1+52−1+52−1−52−1−520000000000000
χ37444-2−1−5−1+5-24−1−5−1+5-2-21+521−52−1−5−1+5−1−5−1+51+521−52040000−1−5−1−5−1+5−1+51+521−521+521−520000-200001+521+521−521−520000000000000
χ38444-2−1−5−1+5-24−1−5−1+5-2-21+521−52−1−5−1+5−1−5−1+51+521−520-400001+51+51−51−51+521−521+521−52000020000−1−52−1−52−1+52−1+520000000000000
χ3944-24−1+5−1−54-2−1+5−1−5-2-2−1+5−1−51−521+521−521+52−1+5−1−540−1+5−1+5−1−5−1−500001−521+521−521+52000-201−521−521+521+5200000000000000000
χ4044-24−1+5−1−54-2−1+5−1−5-2-2−1+5−1−51−521+521−521+52−1+5−1−5-401−51−51+51+500001−521+521−521+5200020−1+52−1+52−1−52−1−5200000000000000000
χ4144-24−1−5−1+54-2−1−5−1+5-2-2−1−5−1+51+521−521+521−52−1−5−1+540−1−5−1−5−1+5−1+500001+521−521+521−52000-201+521+521−521−5200000000000000000
χ4244-24−1−5−1+54-2−1−5−1+5-2-2−1−5−1+51+521−521+521−52−1−5−1+5-401+51+51−51−500001+521−521+521−5200020−1−52−1−52−1+52−1+5200000000000000000
χ4344-2-244-2-24411-2-2-2-2-2-2-2-20000000000111100400000000000000-2-21100000
χ4444-2-244-2-24411-2-2-2-2-2-2-2-20000000000111100-40000000000000022-1-100000
χ454-44-2442-4-4-4-22-2-244-4-4220000000000-2-22200000000000000000000000000
χ464-44-2−1+5−1−52-41−51+5-221−521+52−1+5−1−51−51+5−1+52−1−52000000−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ71−521+52−1+52−1−52000000000ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000000000000
χ474-44-2−1+5−1−52-41−51+5-221−521+52−1+5−1−51−51+5−1+52−1−520000002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ71−521+52−1+52−1−52000000000−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000000000000
χ484-44-2−1−5−1+52-41+51−5-221+521−52−1−5−1+51+51−5−1−52−1+520000002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ191+521−52−1−52−1+52000000000−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000000000000
χ494-44-2−1−5−1+52-41+51−5-221+521−52−1−5−1+51+51−5−1−52−1+52000000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ191+521−52−1−52−1+52000000000ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000000000000
χ504-4-2444-42-4-4-2244-2-222-4-40000000000-2-22200000000000000000000000000
χ514-4-24−1+5−1−5-421−51+5-22−1+5−1−51−521+52−1+52−1−521−51+5002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800001−521+52−1+52−1−5200000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ1800000000000000000
χ524-4-24−1+5−1−5-421−51+5-22−1+5−1−51−521+52−1+52−1−521−51+500−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800001−521+52−1+52−1−5200000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800000000000000000
χ534-4-24−1−5−1+5-421+51−5-22−1−5−1+51+521−52−1−52−1+521+51−500−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400001+521−52−1−52−1+5200000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ1400000000000000000
χ544-4-24−1−5−1+5-421+51−5-22−1−5−1+51+521−52−1−52−1+521+51−5002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400001+521−52−1−52−1+5200000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ1400000000000000000
χ554-4-2-24422-4-41-1-2-2-2-22222000000000011-1-100000000000000000003-300000
χ564-4-2-24422-4-41-1-2-2-2-22222000000000011-1-10000000000000000000-3300000
χ5788-4-4−2+25−2−25-4-4−2+25−2−25221−51+51−51+51−51+51−51+50000000000−1+52−1−52−1+52−1−5200000000000000000000000000
χ5888-4-4−2−25−2+25-4-4−2−25−2+25221+51−51+51−51+51−51+51−50000000000−1−52−1+52−1−52−1+5200000000000000000000000000
χ598-8-4-4−2+25−2−25442−252+252-21−51+51−51+5−1+5−1−5−1+5−1−50000000000−1+52−1−521−521+5200000000000000000000000000
χ608-8-4-4−2−25−2+25442+252−252-21+51−51+51−5−1−5−1+5−1−5−1+50000000000−1−52−1+521+521−5200000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.