Finite Group Databasebeta

← Group #13024678

Character table — Group #13024678

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222444444444448888888888888161616161616161616162020202020204040404040404040404040404080808080
order12222244444510101010101010420202020202020202020202044202020202020202022224422444888888884444
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
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11-1-111111111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111iiii−i−i−i−i−i−iii
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111−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
χ13111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111ii−i−iii−i−i−ii−ii
χ14111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111−i−iii−i−iiii−ii−i
χ15111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1111111-1-1-111-1-1-1-111-111-1
χ16111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1111111-1-1-1-1-11111-1-11-1-11
χ17222222222-2-222222222-2-2-2-2-22222-2-2-2-2000000000022-2-22200-200000000000000
χ18222222222-2-222222222-2-2-2-2-22222-2-2-2-20000000000-2-222-2-200200000000000000
χ19222222-2-2-22222222222-2-2-2-2-2-2-2-2-2222200000000002222-2-200-200000000000000
χ20222222-2-2-22222222222-2-2-2-2-2-2-2-2-222220000000000-2-2-2-22200200000000000000
χ212-22-2-220002-22-2-22-2-22200000000022-2-200000000002-22-20000000i2−i2i2−i2i2−i2i2−i20000
χ222-22-2-220002-22-2-22-2-22200000000022-2-200000000002-22-20000000−i2i2−i2i2−i2i2−i2i20000
χ232-22-2-220002-22-2-22-2-22200000000022-2-20000000000-22-2200000002−22−2−22−220000
χ242-22-2-220002-22-2-22-2-22200000000022-2-20000000000-22-220000000−22−222−22−20000
χ252-22-2-22000-222-2-22-2-222000000000-2-22200000000002-2-2200000002−2−222−2−220000
χ262-22-2-22000-222-2-22-2-222000000000-2-22200000000002-2-220000000−222−2−222−20000
χ272-22-2-22000-222-2-22-2-222000000000-2-2220000000000-222-20000000i2−i2−i2i2−i2i2i2−i20000
χ282-22-2-22000-222-2-22-2-222000000000-2-2220000000000-222-20000000−i2i2i2−i2i2−i2−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
χ374444-4-444-4004-4-4444-4-40000044-4-40000000000000000000000000000000000000
χ384444-4-444-400-111-1-1-111055−5−5-1-1115−55−500−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
χ394444-4-444-400-111-1-1-111055−5−5-1-1115−55−500ζ6−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
χ404444-4-444-400-111-1-1-1110−5−555-1-111−55−5500ζ6−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
χ414444-4-444-400-111-1-1-1110−5−555-1-111−55−5500−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
χ424444-4-4-4-44004-4-4444-4-400000-4-4440000000000000000000000000000000000000
χ434444-4-4-4-4400-111-1-1-111055−5−511-1-1−55−5500−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
χ444444-4-4-4-4400-111-1-1-111055−5−511-1-1−55−5500ζ6−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
χ454444-4-4-4-4400-111-1-1-1110−5−55511-1-15−55−500ζ6−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
χ464444-4-4-4-4400-111-1-1-1110−5−55511-1-15−55−500−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
χ4744-4-4004i−4i000400-44-400000004i−4i00000000000000000000002-202i−2i000000000000
χ4844-4-4004i−4i000400-44-400000004i−4i0000000000000000000000-220−2i2i000000000000
χ4944-4-400−4i4i000400-44-40000000−4i4i00000000000000000000002-20−2i2i000000000000
χ5044-4-400−4i4i000400-44-40000000−4i4i0000000000000000000000-2202i−2i000000000000
χ514-44-44-4000004444-4-4-4-40000000000000000000000000004i−4i00000000000000000
χ524-44-44-4000004444-4-4-4-4000000000000000000000000000−4i4i00000000000000000
χ5388-8-8008i−8i000-225−252-2225−2500000−2i2i2i5−2i50000000000000000000000000000000000000
χ5488-8-8008i−8i000-2−25252-22−252500000−2i2i−2i52i50000000000000000000000000000000000000
χ5588-8-800−8i8i000-225−252-2225−25000002i−2i−2i52i50000000000000000000000000000000000000
χ5688-8-800−8i8i000-2−25252-22−2525000002i−2i2i5−2i50000000000000000000000000000000000000
χ578-88-88-800000-2-2-2-2222200000000025−25−2525000000000000000000000000000000000
χ588-88-88-800000-2-2-2-22222000000000−252525−25000000000000000000000000000000000
χ598-88-8-880008-8-222-222-2-2000000000-2-222000000000000000000000000000000000
χ608-88-8-88000-88-222-222-2-200000000022-2-2000000000000000000000000000000000
χ618-8-880000000800-8-88000000000000000000000000000000000000000000000000
χ628-8-880000000-225−2522-2−25250−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ3800000000000000000000000000000000000000000
χ638-8-880000000-225−2522-2−252502ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ3800000000000000000000000000000000000000000
χ648-8-880000000-2−252522-225−2502ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ3800000000000000000000000000000000000000000
χ658-8-880000000-2−252522-225−250−2ζ6+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.