Finite Group Databasebeta

← Group #13104196

Character table — Group #13104196

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122444444444444444488888888888888882020202020202020252525254040404040404040404040404040404050505050505050505050
order12224455551010101010101010101010105101010202020202020202020202020222244442222101010101010101020202020202020204488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ51111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ61111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111
χ81111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1
χ91-1-111-11111-1-1-1-1-1-11111-1-11-1-111111-1-1-1-111-1-11-11-1i−ii−i11-1-111-1-111-1-1ii−i−iii−i−i1-1ii−i−iii−i−i
χ101-1-111-11111-1-1-1-1-1-11111-1-11-1-111111-1-1-1-111-1-11-11-1−ii−ii11-1-111-1-111-1-1−i−iii−i−iii1-1−i−iii−i−iii
χ111-1-111-11111-1-1-1-1-1-11111-1-11-1-111111-1-1-1-111-1-1-11-11i−ii−i11-1-1-1-111-1-111ii−i−iii−i−i1-1−i−iii−i−iii
χ121-1-111-11111-1-1-1-1-1-11111-1-11-1-111111-1-1-1-111-1-1-11-11−ii−ii11-1-1-1-111-1-111−i−iii−i−iii1-1ii−i−iii−i−i
χ131-1-11-111111-1-1-1-1-1-11111-1-11-1-11-1-1-1-11111-1-1111-1-11i−i−ii-1-11111-1-1-1-111ii−i−i−i−iii1-1ii−i−i−i−iii
χ141-1-11-111111-1-1-1-1-1-11111-1-11-1-11-1-1-1-11111-1-1111-1-11−iii−i-1-11111-1-1-1-111−i−iiiii−i−i1-1−i−iiiii−i−i
χ151-1-11-111111-1-1-1-1-1-11111-1-11-1-11-1-1-1-11111-1-111-111-1i−i−ii-1-111-1-11111-1-1ii−i−i−i−iii1-1−i−iiiii−i−i
χ161-1-11-111111-1-1-1-1-1-11111-1-11-1-11-1-1-1-11111-1-111-111-1−iii−i-1-111-1-11111-1-1−i−iiiii−i−i1-1ii−i−i−i−iii
χ172222222222222222222222222222222222222200000000-2-2-2-20000000000000000-2-200000000
χ182222-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000-2-200000000
χ1922-2-20022222222-2-2-2-2-2-2-2-222-2-2000000000000000000002-22-2000000000000000000i2−i2i2−i2i2−i2i2−i2
χ2022-2-20022222222-2-2-2-2-2-2-2-222-2-2000000000000000000002-22-2000000000000000000−i2i2−i2i2−i2i2−i2i2
χ2122-2-20022222222-2-2-2-2-2-2-2-222-2-200000000000000000000-22-22000000000000000000i2−i2i2−i2−i2i2−i2i2
χ2222-2-20022222222-2-2-2-2-2-2-2-222-2-200000000000000000000-22-22000000000000000000−i2i2−i2i2i2−i2i2−i2
χ232-22-2002222-2-2-2-222-2-2-2-2222-22-2000000000000000000002-2-220000000000000000002−2−222−2−22
χ242-22-2002222-2-2-2-222-2-2-2-2222-22-2000000000000000000002-2-22000000000000000000−222−2−222−2
χ252-22-2002222-2-2-2-222-2-2-2-2222-22-200000000000000000000-222-20000000000000000002−2−22−222−2
χ262-22-2002222-2-2-2-222-2-2-2-2222-22-200000000000000000000-222-2000000000000000000−222−22−2−22
χ272-2-222-22222-2-2-2-2-2-22222-2-22-2-222222-2-2-2-222-2-200000000-2-2220000000000000000-2200000000
χ282-2-22-222222-2-2-2-2-2-22222-2-22-2-22-2-2-2-22222-2-2220000000022-2-20000000000000000-2200000000
χ29444444−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-1−1+53−523+52−1−5−1+53−523+52−1−5-1-1-1-1222200000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000000000000
χ30444444−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-1−1+53−523+52−1−5−1+53−523+52−1−5-1-1-1-1-2-2-2-2000000001−521+521−521+521−521+521−521+52000000000000000000
χ314444443−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-13−52−1−5−1+53+523−52−1−5−1+53+52-1-1-1-100002222000000000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000000
χ324444443−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-13−52−1−5−1+53+523−52−1−5−1+53+52-1-1-1-10000-2-2-2-20000000000001−521+521−521+521−521+521−521+520000000000
χ334444443+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-13+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-100002222000000000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000000
χ344444443+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-13+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-10000-2-2-2-20000000000001+521−521+521−521+521−521+521−520000000000
χ35444444−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-1−1−53+523−52−1+5−1−53+523−52−1+5-1-1-1-1222200000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000000000000
χ36444444−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-1−1−53+523−52−1+5−1−53+523−52−1+5-1-1-1-1-2-2-2-2000000001+521−521+521−521+521−521+521−52000000000000000000
χ374444-4-4−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-11−5−3+52−3−521+51−5−3+52−3−521+5111122-2-200000000−1+52−1−52−1+52−1−521−521+521−521+52000000000000000000
χ384444-4-4−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-11−5−3+52−3−521+51−5−3+52−3−521+51111-2-222000000001−521+521−521+52−1+52−1−52−1+52−1−52000000000000000000
χ394444-4-43−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-1−3+521+51−5−3−52−3+521+51−5−3−521111000022-2-2000000000000−1+52−1−52−1+52−1−521−521+521−521+520000000000
χ404444-4-43−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-1−3+521+51−5−3−52−3+521+51−5−3−5211110000-2-2220000000000001−521+521−521+52−1+52−1−52−1+52−1−520000000000
χ414444-4-43+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-1−3−521−51+5−3+52−3−521−51+5−3+521111000022-2-2000000000000−1−52−1+52−1−52−1+521+521−521+521−520000000000
χ424444-4-43+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-1−3−521−51+5−3+52−3−521−51+5−3+5211110000-2-2220000000000001+521−521+521−52−1−52−1+52−1−52−1+520000000000
χ434444-4-4−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-11+5−3−52−3+521−51+5−3−52−3+521−5111122-2-200000000−1−52−1+52−1−52−1+521+521−521+521−52000000000000000000
χ444444-4-4−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-11+5−3−52−3+521−51+5−3−52−3+521−51111-2-222000000001+521−521+521−52−1−52−1+52−1−52−1+52000000000000000000
χ454-4-444-4−1+5−1−53−523+521−51+5−3+52−3−52−3+52−3−52−1+5−1−53−523+521−51+5-111-1−1+53−523+52−1−51−5−3+52−3−521+5-1-1112-22-200000000−1+52−1−521−521+52−1+52−1−521−521+52000000000000000000
χ464-4-444-4−1+5−1−53−523+521−51+5−3+52−3−52−3+52−3−52−1+5−1−53−523+521−51+5-111-1−1+53−523+52−1−51−5−3+52−3−521+5-1-111-22-22000000001−521+52−1+52−1−521−521+52−1+52−1−52000000000000000000
χ474-4-444-43−523+52−1−5−1+5−3+52−3−521+51−51+51−53−523+52−1−5−1+5−3+52−3−52-111-13−52−1−5−1+53+52−3+521+51−5−3−52-1-11100002i−2i2i−2i000000000000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ484-4-444-43−523+52−1−5−1+5−3+52−3−521+51−51+51−53−523+52−1−5−1+5−3+52−3−52-111-13−52−1−5−1+53+52−3+521+51−5−3−52-1-1110000−2i2i−2i2i000000000000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ494-4-444-43+523−52−1+5−1−5−3−52−3+521−51+51−51+53+523−52−1+5−1−5−3−52−3+52-111-13+52−1+5−1−53−52−3−521−51+5−3+52-1-11100002i−2i2i−2i000000000000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
χ504-4-444-43+523−52−1+5−1−5−3−52−3+521−51+51−51+53+523−52−1+5−1−5−3−52−3+52-111-13+52−1+5−1−53−52−3−521−51+5−3+52-1-1110000−2i2i−2i2i000000000000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
χ514-4-444-4−1−5−1+53+523−521+51−5−3−52−3+52−3−52−3+52−1−5−1+53+523−521+51−5-111-1−1−53+523−52−1+51+5−3−52−3+521−5-1-1112-22-200000000−1−52−1+521+521−52−1−52−1+521+521−52000000000000000000
χ524-4-444-4−1−5−1+53+523−521+51−5−3−52−3+52−3−52−3+52−1−5−1+53+523−521+51−5-111-1−1−53+523−52−1+51+5−3−52−3+521−5-1-111-22-22000000001+521−52−1−52−1+521+521−52−1−52−1+52000000000000000000
χ534-4-44-44−1+5−1−53−523+521−51+5−3+52−3−52−3+52−3−52−1+5−1−53−523+521−51+5-111-11−5−3+52−3−521+5−1+53−523+52−1−511-1-12-2-2200000000−1+52−1−521−521+521−521+52−1+52−1−52000000000000000000
χ544-4-44-44−1+5−1−53−523+521−51+5−3+52−3−52−3+52−3−52−1+5−1−53−523+521−51+5-111-11−5−3+52−3−521+5−1+53−523+52−1−511-1-1-222-2000000001−521+52−1+52−1−52−1+52−1−521−521+52000000000000000000
χ554-4-44-443−523+52−1−5−1+5−3+52−3−521+51−51+51−53−523+52−1−5−1+5−3+52−3−52-111-1−3+521+51−5−3−523−52−1−5−1+53+5211-1-100002i−2i−2i2i000000000000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ564-4-44-443−523+52−1−5−1+5−3+52−3−521+51−51+51−53−523+52−1−5−1+5−3+52−3−52-111-1−3+521+51−5−3−523−52−1−5−1+53+5211-1-10000−2i2i2i−2i000000000000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ574-4-44-443+523−52−1+5−1−5−3−52−3+521−51+51−51+53+523−52−1+5−1−5−3−52−3+52-111-1−3−521−51+5−3+523+52−1+5−1−53−5211-1-100002i−2i−2i2i000000000000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
χ584-4-44-443+523−52−1+5−1−5−3−52−3+521−51+51−51+53+523−52−1+5−1−5−3−52−3+52-111-1−3−521−51+5−3+523+52−1+5−1−53−5211-1-10000−2i2i2i−2i000000000000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
χ594-4-44-44−1−5−1+53+523−521+51−5−3−52−3+52−3−52−3+52−1−5−1+53+523−521+51−5-111-11+5−3−52−3+521−5−1−53+523−52−1+511-1-12-2-2200000000−1−52−1+521+521−521+521−52−1−52−1+52000000000000000000
χ604-4-44-44−1−5−1+53+523−521+51−5−3−52−3+52−3−52−3+52−1−5−1+53+523−521+51−5-111-11+5−3−52−3+521−5−1−53+523−52−1+511-1-1-222-2000000001+521−52−1−52−1+52−1−52−1+521+521−52000000000000000000
χ61888888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23333-2-2-2-2-2-2-2-2333300000000000000000000000000000000000000
χ628888-8-8-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2333322222222-3-3-3-300000000000000000000000000000000000000
χ6388-8-800-2-2-2-2-2-2-2-22222222233-3-3000000005i−5i5i−5i00000000000000000000000000000000000000
χ6488-8-800-2-2-2-2-2-2-2-22222222233-3-300000000−5i5i−5i5i00000000000000000000000000000000000000
χ6588-8-800−2+25−2−253−53+5−2+25−2−253−53+5−3+5−3−52−252+25−3+5−3−52−252+25-2-22200000000000000000000000000000000000000000000000000
χ6688-8-8003−53+5−2−25−2+253−53+5−2−25−2+252+252−25−3+5−3−52+252−25−3+5−3−5-2-22200000000000000000000000000000000000000000000000000
χ6788-8-8003+53−5−2+25−2−253+53−5−2+25−2−252−252+25−3−5−3+52−252+25−3−5−3+5-2-22200000000000000000000000000000000000000000000000000
χ6888-8-800−2−25−2+253+53−5−2−25−2+253+53−5−3−5−3+52+252−25−3−5−3+52+252−25-2-22200000000000000000000000000000000000000000000000000
χ698-88-800-2-2-2-22222-2-22222-2-23-33-3000000005i−5i−5i5i00000000000000000000000000000000000000
χ708-88-800-2-2-2-22222-2-22222-2-23-33-300000000−5i5i5i−5i00000000000000000000000000000000000000
χ718-88-800−2+25−2−253−53+52−252+25−3+5−3−53−53+52−252+25−3+5−3−5−2+25−2−25-22-2200000000000000000000000000000000000000000000000000
χ728-88-8003−53+5−2−25−2+25−3+5−3−52+252−25−2−25−2+25−3+5−3−52+252−253−53+5-22-2200000000000000000000000000000000000000000000000000
χ738-88-8003+53−5−2+25−2−25−3−5−3+52−252+25−2+25−2−25−3−5−3+52−252+253+53−5-22-2200000000000000000000000000000000000000000000000000
χ748-88-800−2−25−2+253+53−52+252−25−3−5−3+53+53−52+252−25−3−5−3+5−2−25−2+25-22-2200000000000000000000000000000000000000000000000000
χ758-8-888-8-2-2-2-2222222-2-2-2-2223-3-33-2-2-2-2222233-3-300000000000000000000000000000000000000
χ768-8-88-88-2-2-2-2222222-2-2-2-2223-3-332222-2-2-2-2-3-33300000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.