Finite Group Databasebeta

← Group #13024680

Character table — Group #13024680

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222444444444448888888888888161616161616161616162020202020204040404040404040404040404080808080
order12222244224510101010101010410101010202020202020202024101010102020202022444444444888888884444
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
χ9111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-111-1-111-111-1-111-1-111-1-11-11-1
χ10111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-111-1-111-111-1-1-1-111-1-111-11-11
χ11111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-111-1-11-1-111ii−i−i−i−iiii−i−ii
χ12111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-111-1-11-1-111−i−iiiii−i−i−iii−i
χ13111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-111-1-1-11111-1-111-1-1-11-11
χ14111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-111-1-1-111-1-111-1-1111-11-1
χ15111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-111-1-1111-1-1ii−i−i−i−iii−iii−i
χ16111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-111-1-1111-1-1−i−iiiii−i−ii−i−ii
χ1722222222-2-2222222222-2-2-2-2-2-2-2-2-22222000000000022-2-2-2-220000000000000000
χ1822222222-2-2222222222-2-2-2-2-2-2-2-2-222220000000000-2-22222-20000000000000000
χ19222222-2-222-222222222-22222-2-2-2-2-2-2-2-200000000002222-2-2-20000000000000000
χ20222222-2-222-222222222-22222-2-2-2-2-2-2-2-20000000000-2-2-2-22220000000000000000
χ212-22-2-22002-20222-2-2-22-2022-2-20000000000000000002-22-20000000i2−i2i2−i2i2−i2i2−i20000
χ222-22-2-22002-20222-2-2-22-2022-2-20000000000000000002-22-20000000−i2i2−i2i2−i2i2−i2i20000
χ232-22-2-22002-20222-2-2-22-2022-2-2000000000000000000-22-2200000002−22−2−22−220000
χ242-22-2-22002-20222-2-2-22-2022-2-2000000000000000000-22-220000000−22−222−22−20000
χ252-22-2-2200-220222-2-2-22-20-2-2220000000000000000002-2-220000000i2−i2−i2i2i2−i2−i2i20000
χ262-22-2-2200-220222-2-2-22-20-2-2220000000000000000002-2-220000000−i2i2i2−i2−i2i2i2−i20000
χ272-22-2-2200-220222-2-2-22-20-2-222000000000000000000-222-200000002−2−22−222−20000
χ282-22-2-2200-220222-2-2-22-20-2-222000000000000000000-222-20000000−222−22−2−220000
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
χ3144444444-4-44-1-1-1-1-1-1-1-1-411111111-1-1-1-10055−5−555−5−500000000000000000000000
χ3244444444-4-44-1-1-1-1-1-1-1-1-411111111-1-1-1-100−5−555−5−55500000000000000000000000
χ33444444-4-444-4-1-1-1-1-1-1-1-1-4-1-1-1-1111111110055−5−5−5−55500000000000000000000000
χ34444444-4-444-4-1-1-1-1-1-1-1-1-4-1-1-1-11111111100−5−55555−5−500000000000000000000000
χ35444444-4-4-4-4-4-1-1-1-1-1-1-1-141111-1-1-1-111114-4-1-1-1-1111100000000000000000000000
χ36444444-4-4-4-4-4-1-1-1-1-1-1-1-141111-1-1-1-11111-441111-1-1-1-100000000000000000000000
χ374444-4-44400-44-4-44-4-44400000000044-4-4000000000000000000000000000000000
χ384444-4-44400-4-111-111-1-105−55−555−5−5-1-11100−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000000
χ394444-4-44400-4-111-111-1-105−55−555−5−5-1-11100ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000
χ404444-4-44400-4-111-111-1-10−55−55−5−555-1-11100−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000000
χ414444-4-44400-4-111-111-1-10−55−55−5−555-1-11100ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000000
χ424444-4-4-4-40044-4-44-4-444000000000-4-444000000000000000000000000000000000
χ434444-4-4-4-4004-111-111-1-105−55−5−5−55511-1-100−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000000
χ444444-4-4-4-4004-111-111-1-105−55−5−5−55511-1-100ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000000
χ454444-4-4-4-4004-111-111-1-10−55−5555−5−511-1-100−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000
χ464444-4-4-4-4004-111-111-1-10−55−5555−5−511-1-100ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000000
χ4744-4-4004i−4i000400400-4-40000000004i−4i00000000000000000002-22i−2i000000000000
χ4844-4-4004i−4i000400400-4-40000000004i−4i0000000000000000000-22−2i2i000000000000
χ4944-4-400−4i4i000400400-4-4000000000−4i4i00000000000000000002-2−2i2i000000000000
χ5044-4-400−4i4i000400400-4-4000000000−4i4i0000000000000000000-222i−2i000000000000
χ514-44-44-4000004-4-4-4444-40000000000000000000000000004i−4i00000000000000000
χ524-44-44-4000004-4-4-4444-4000000000000000000000000000−4i4i00000000000000000
χ5388-8-8008i−8i000-225−25-225−2522000000000−2i2i2i5−2i5000000000000000000000000000000000
χ5488-8-8008i−8i000-2−2525-2−252522000000000−2i2i−2i52i5000000000000000000000000000000000
χ5588-8-800−8i8i000-225−25-225−25220000000002i−2i−2i52i5000000000000000000000000000000000
χ5688-8-800−8i8i000-2−2525-2−2525220000000002i−2i2i5−2i5000000000000000000000000000000000
χ578-88-88-800000-2222-2-2-22025−25−252500000000000000000000000000000000000000000
χ588-88-88-800000-2222-2-2-220−252525−2500000000000000000000000000000000000000000
χ598-88-8-88008-80-2-2-2222-220-2-22200000000000000000000000000000000000000000
χ608-88-8-8800-880-2-2-2222-22022-2-200000000000000000000000000000000000000000
χ618-8-880000000800-800-880000000000000000000000000000000000000000000000
χ628-8-880000000-225−252−25252-200000−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ360000000000000000000000000000000000000
χ638-8-880000000-225−252−25252-2000002ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ360000000000000000000000000000000000000
χ648-8-880000000-2−2525225−252-200000−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ360000000000000000000000000000000000000
χ658-8-880000000-2−2525225−252-2000002ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ360000000000000000000000000000000000000

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