Finite Group Databasebeta

← Group #10624046

Character table — Group #10624046

Order 720.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1122222222444444444466888810121212121212121212121212121218202020203030363645456060
order123355661010361515151530303030221515303026610101010303030303030303046666442020441212
χ1111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1111111111111111-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111-1111111-111-1-11111-1-1-1-1-111111-1-1-1-1-11-1
χ4111111111111111111111-11111-11-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-11
χ511111111111111111111-1111111-11-1-111-1-1-1-11111-11111-11-1-1-1-1-11
χ611111111111111111111-111111-1-11-1-111-1-1-1-11111-1-1-1-1-11-1-1-1111-1
χ711111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-111
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+52022−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522000000−1−52−1+520000
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+5202-2−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−52-20000001+521−520000
χ112222−1−52−1+5222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-22−1−52−1+52−1−52−1+520-221+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52-20000001+521−520000
χ122222−1−52−1+5222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+520-2-21+521−521+521−521+521+521−521−521+521+521−521−522000000−1−52−1+520000
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+52−1−52022−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522000000−1+52−1−520000
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+52−1−5202-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52-20000001−521+520000
χ152222−1+52−1−5222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-22−1+52−1−52−1+52−1−520-221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52-20000001−521+520000
χ162222−1+52−1−5222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−520-2-21−521+521−521+521−521−521+521+521−521−521+521+522000000−1+52−1−520000
χ17222-1222-122-1-12-12-12-12-102-1-1-1-120-100220000-1-1-1-102-1-1-10200000-1
χ18222-1222-122-1-12-12-12-12-102-1-1-1-1-20-100220000-1-1-1-10-21110-2000001
χ19222-1222-122-1-12-12-12-12-10-2-1-1-1-120100-2-20000111102-1-1-10-2000001
χ20222-1222-122-1-12-12-12-12-10-2-1-1-1-1-20100-2-2000011110-21110200000-1
χ2122-1222-1222-1-1-12-12-12-1220-1-1-1-12-102200-1-1-1-100000-12-1-1200000-10
χ2222-1222-1222-1-1-12-12-12-1220-1-1-1-1-2-102200-1-1-1-1000001-211-20000010
χ2322-1222-1222-1-1-12-12-12-12-20-1-1-1-1210-2-200111100000-12-1-1-20000010
χ2422-1222-1222-1-1-12-12-12-12-20-1-1-1-1-210-2-2001111000001-211200000-10
χ252-22222-2-2-2-22-22222-2-2-2-20022-2-20000000000000000000000002i−2i00
χ262-22222-2-2-2-22-22222-2-2-2-20022-2-2000000000000000000000000−2i2i00
χ27444-2−1−5−1+54-2−1−5−1+5-2-2−1−51+52−1+51−52−1−51+52−1+51−52041+521−521+521−5200-200−1−5−1+500001+521+521−521−520000000000000
χ28444-2−1−5−1+54-2−1−5−1+5-2-2−1−51+52−1+51−52−1−51+52−1+51−520-41+521−521+521−52002001+51−50000−1−52−1−52−1+52−1+520000000000000
χ29444-2−1+5−1−54-2−1+5−1−5-2-2−1+51−52−1−51+52−1+51−52−1−51+52041−521+521−521+5200-200−1+5−1−500001−521−521+521+520000000000000
χ30444-2−1+5−1−54-2−1+5−1−5-2-2−1+51−52−1−51+52−1+51−52−1−51+520-41−521+521−521+52002001−51+50000−1+52−1+52−1−52−1−520000000000000
χ3144-24−1−5−1+5-24−1−5−1+5-2-21+52−1−51−52−1+51+52−1−51−52−1+5401+521−521+521−520-20−1−5−1+5001+521+521−521−5200000000000000000
χ3244-24−1−5−1+5-24−1−5−1+5-2-21+52−1−51−52−1+51+52−1−51−52−1+5-401+521−521+521−520201+51−500−1−52−1−52−1+52−1+5200000000000000000
χ3344-24−1+5−1−5-24−1+5−1−5-2-21−52−1+51+52−1−51−52−1+51+52−1−5401−521+521−521+520-20−1+5−1−5001−521−521+521+5200000000000000000
χ3444-24−1+5−1−5-24−1+5−1−5-2-21−52−1+51+52−1−51−52−1+51+52−1−5-401−521+521−521+520201−51+500−1+52−1+52−1−52−1−5200000000000000000
χ3544-2-244-2-24411-2-2-2-2-2-2-2-20011114000000000000000-2-21100000000
χ3644-2-244-2-24411-2-2-2-2-2-2-2-2001111-400000000000000022-1-100000000
χ374-444−1−5−1+5-4-41+51−54-4−1−5−1−5−1+5−1+51+51+51−51−500−1−5−1+51+51−50000000000000000000000000000
χ384-444−1+5−1−5-4-41−51+54-4−1+5−1+5−1−5−1−51−51−51+51+500−1+5−1−51−51+50000000000000000000000000000
χ394-44-244-42-4-4-224-24-2-42-4200-2-2220000000000000000000000000000
χ404-44-2−1−5−1+5-421+51−5-22−1−51+52−1+51−521+5−1−521−5−1+52001+521−52−1−52−1+5200000000000ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ46−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ580000000000000
χ414-44-2−1−5−1+5-421+51−5-22−1−51+52−1+51−521+5−1−521−5−1+52001+521−52−1−52−1+5200000000000−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ46ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ580000000000000
χ424-44-2−1+5−1−5-421−51+5-22−1+51−52−1−51+521−5−1+521+5−1−52001−521+52−1+52−1−5200000000000−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ460000000000000
χ434-44-2−1+5−1−5-421−51+5-22−1+51−52−1−51+521−5−1+521+5−1−52001−521+52−1+52−1−5200000000000ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ460000000000000
χ444-4-24442-4-4-4-22-24-242-42-400-2-2220000000000000000000000000000
χ454-4-24−1−5−1+52-41+51−5-221+52−1−51−52−1+5−1−521+5−1+521−5001+521−52−1−52−1+520000000ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ46−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ5800000000000000000
χ464-4-24−1−5−1+52-41+51−5-221+52−1−51−52−1+5−1−521+5−1+521−5001+521−52−1−52−1+520000000−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ46ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ5800000000000000000
χ474-4-24−1+5−1−52-41−51+5-221−52−1+51+52−1−5−1+521−5−1−521+5001−521+52−1+52−1−520000000−ζ2+ζ22+ζ38−ζ58ζ2−ζ22−ζ38+ζ58−ζ14+ζ26+ζ34−ζ46ζ14−ζ26−ζ34+ζ4600000000000000000
χ484-4-24−1+5−1−52-41−51+5-221−52−1+51+52−1−5−1+521−5−1−521+5001−521+52−1+52−1−520000000ζ2−ζ22−ζ38+ζ58−ζ2+ζ22+ζ38−ζ58ζ14−ζ26−ζ34+ζ46−ζ14+ζ26+ζ34−ζ4600000000000000000
χ494-4-2-24422-4-41-1-2-2-2-222220011-1-10000000000000000003-300000000
χ504-4-2-24422-4-41-1-2-2-2-222220011-1-1000000000000000000-3300000000
χ5188-4-4−2−25−2+25-4-4−2−25−2+25221+51+51−51−51+51+51−51−500−1−52−1+52−1−52−1+520000000000000000000000000000
χ5288-4-4−2+25−2−25-4-4−2+25−2−25221−51−51+51+51−51−51+51+500−1+52−1−52−1+52−1−520000000000000000000000000000
χ538-8-4-4−2−25−2+25442+252−252-21+51+51−51−5−1−5−1−5−1+5−1+500−1−52−1+521+521−520000000000000000000000000000
χ548-8-4-4−2+25−2−25442−252+252-21−51−51+51+5−1+5−1+5−1−5−1−500−1+52−1−521−521+520000000000000000000000000000

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