Finite Group Databasebeta

← Group #13024580

Character table — Group #13024580

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222444444444448888888888888161616161616161616162020202020204040404040404040404040404080808080
order12222244444510101010101010420202020202020202020202044202020202020202044444422244888888888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ9111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-1-1-1111-1-1ii−i−iii−i−ii−ii−i
χ10111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-1-1-1111-1-1−i−iii−i−iii−ii−ii
χ11111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-11111-1-1-11111-1-1-1-1111-1-11
χ12111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-11111-1-1-111-1-11111-1-1-111-1
χ13111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11-1-111ii−i−iii−i−i−ii−ii
χ14111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11-1-111−i−iii−i−iiii−ii−i
χ15111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11111-111-1-111-1-1-1-111-111-1
χ16111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11111-111-1-1-1-11111-1-11-1-11
χ17222222222-2-222222222-2-2-2-2-22222-2-2-2-200000000002222-2-2-20000000000000000
χ18222222222-2-222222222-2-2-2-2-22222-2-2-2-20000000000-2-2-2-22220000000000000000
χ19222222-2-2-22222222222-2-2-2-2-2-2-2-2-22222000000000022-2-222-20000000000000000
χ20222222-2-2-22222222222-2-2-2-2-2-2-2-2-222220000000000-2-222-2-220000000000000000
χ2122-2-22-20002i−2i2222-2-2-2-20000000002i2i−2i−2i00000000002i−2i002-200000i2−i22−22−2i2−i20000
χ2222-2-22-20002i−2i2222-2-2-2-20000000002i2i−2i−2i00000000002i−2i002-200000−i2i2−22−22−i2i20000
χ2322-2-22-20002i−2i2222-2-2-2-20000000002i2i−2i−2i0000000000−2i2i00-22000002−2−i2i2i2−i2−220000
χ2422-2-22-20002i−2i2222-2-2-2-20000000002i2i−2i−2i0000000000−2i2i00-2200000−22i2−i2−i2i22−20000
χ2522-2-22-2000−2i2i2222-2-2-2-2000000000−2i−2i2i2i00000000002i−2i00-22000002−2i2−i2−i2i2−220000
χ2622-2-22-2000−2i2i2222-2-2-2-2000000000−2i−2i2i2i00000000002i−2i00-2200000−22−i2i2i2−i22−20000
χ2722-2-22-2000−2i2i2222-2-2-2-2000000000−2i−2i2i2i0000000000−2i2i002-200000i2−i2−22−22i2−i20000
χ2822-2-22-2000−2i2i2222-2-2-2-2000000000−2i−2i2i2i0000000000−2i2i002-200000−i2i22−22−2−i2i20000
χ2944444444444-1-1-1-1-1-1-1-14-1-1-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-100000000000000000000000
χ3044444444444-1-1-1-1-1-1-1-14-1-1-1-1-1-1-1-1-1-1-1-1-4-41111111100000000000000000000000
χ31444444444-4-4-1-1-1-1-1-1-1-1-41111-1-1-1-111110055−5−555−5−500000000000000000000000
χ32444444444-4-4-1-1-1-1-1-1-1-1-41111-1-1-1-1111100−5−555−5−55500000000000000000000000
χ33444444-4-4-444-1-1-1-1-1-1-1-1-411111111-1-1-1-10055−5−5−5−55500000000000000000000000
χ34444444-4-4-444-1-1-1-1-1-1-1-1-411111111-1-1-1-100−5−55555−5−500000000000000000000000
χ35444444-4-4-4-4-4-1-1-1-1-1-1-1-14-1-1-1-1111111114-4-1-1-1-1111100000000000000000000000
χ36444444-4-4-4-4-4-1-1-1-1-1-1-1-14-1-1-1-111111111-441111-1-1-1-100000000000000000000000
χ374444-4-444-40044-4-444-4-40000044-4-40000000000000000000000000000000000000
χ384444-4-444-400-1-111-1-111055−5−5-1-1115−55−500−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000000000000000000000
χ394444-4-444-400-1-111-1-111055−5−5-1-1115−55−500ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000000000000000000000
χ404444-4-444-400-1-111-1-1110−5−555-1-111−55−5500ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000000000000000000000
χ414444-4-444-400-1-111-1-1110−5−555-1-111−55−5500−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000000000000000000000
χ424444-4-4-4-440044-4-444-4-400000-4-4440000000000000000000000000000000000000
χ434444-4-4-4-4400-1-111-1-111055−5−511-1-1−55−5500−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000000000000000000000
χ444444-4-4-4-4400-1-111-1-111055−5−511-1-1−55−5500ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000000000000000000000
χ454444-4-4-4-4400-1-111-1-1110−5−55511-1-15−55−500ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000000000000000000000
χ464444-4-4-4-4400-1-111-1-1110−5−55511-1-15−55−500−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000000000000000000000
χ4744-4-4-440000044-4-4-4-44400000000000000000000000004i−4i0000000000000000000
χ4844-4-4-440000044-4-4-4-4440000000000000000000000000−4i4i0000000000000000000
χ494-44-4004i−4i0004-4004-400000004i−4i000000000000000000000002-22i−2i000000000000
χ504-44-4004i−4i0004-4004-400000004i−4i00000000000000000000000-22−2i2i000000000000
χ514-44-400−4i4i0004-4004-40000000−4i4i000000000000000000000002-2−2i2i000000000000
χ524-44-400−4i4i0004-4004-40000000−4i4i00000000000000000000000-222i−2i000000000000
χ5388-8-88-80008i−8i-2-2-2-22222000000000−2i−2i2i2i000000000000000000000000000000000
χ5488-8-88-8000−8i8i-2-2-2-222220000000002i2i−2i−2i000000000000000000000000000000000
χ5588-8-8-8800000-2-22222-2-20000000002i5−2i5−2i52i5000000000000000000000000000000000
χ5688-8-8-8800000-2-22222-2-2000000000−2i52i52i5−2i5000000000000000000000000000000000
χ578-88-8008i−8i000-2225−25-2225−2500000−2i2i2i5−2i50000000000000000000000000000000000000
χ588-88-8008i−8i000-22−2525-22−252500000−2i2i−2i52i50000000000000000000000000000000000000
χ598-88-800−8i8i000-2225−25-2225−25000002i−2i−2i52i50000000000000000000000000000000000000
χ608-88-800−8i8i000-22−2525-22−2525000002i−2i2i5−2i50000000000000000000000000000000000000
χ618-8-8800000008-800-88000000000000000000000000000000000000000000000000
χ628-8-880000000-2225−252-2−25250−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ3800000000000000000000000000000000000000000
χ638-8-880000000-2225−252-2−252502ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ3800000000000000000000000000000000000000000
χ648-8-880000000-22−25252-225−2502ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ3800000000000000000000000000000000000000000
χ658-8-880000000-22−25252-225−250−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ3800000000000000000000000000000000000000000

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